Department of Mathematics at UTSA - User contributions [en]

MAT5603

2025-09-05T14:42:54Z

Juan.gutierrez3: Added course title

''Numerical Analysis''

'''Catalog entry'''

''Prerequisite'': [[MAT1223]], [[MAT2233]] (or [[MAT2253]]), or consent of instructor.

''Contents''
Rigorous introduction to the fundamental methods of numerical analysis, emphasizing both theoretical foundations and practical applications. Areas of study include the solution of nonlinear equations, interpolation and curve fitting, numerical differentiation and integration, Fourier transforms, and optimization.

= Scaffolded Numerical Analysis Curriculum (15 Weeks) =

== Phase 1: Foundation - Numbers and Errors (Weeks 1-3) ==

=== Topics ===
* Computer arithmetic and floating-point representation
* Error types and propagation
* Condition numbers and stability
* Root-finding for single variables

=== Student Learning Outcomes (SLOs) ===
* Explain IEEE 754 floating-point representation and identify representation limitations
* Calculate and distinguish between absolute, relative, forward, and backward errors
* Compute condition numbers and assess problem sensitivity to input perturbations
* Implement and analyze convergence of bisection, fixed-point iteration, and Newton's method
* Select appropriate root-finding methods based on problem characteristics and convergence requirements

=== Scaffolding ===
* Establishes error analysis framework used throughout entire course
* Introduces iteration and convergence concepts that extend to matrix methods
* Newton's method foundation for later multivariable extensions

=== Weekly Content ===

==== Week 1: Computer Arithmetic ====
* IEEE 754 standard, machine epsilon, rounding errors
* '''Sauer''': Chapter 0
* '''Burden & Faires''': Chapter 1.2
* '''Quarteroni et al.''': Chapter 2

==== Week 2: Error Analysis ====
* Absolute vs relative error, forward vs backward error analysis
* Condition numbers of problems and algorithms
* '''Sauer''': Chapter 0
* '''Kincaid & Cheney''': Chapter 2

==== Week 3: Single Variable Root-Finding ====
* Bisection method, fixed-point iteration, Newton's method, secant method
* Convergence analysis and rates
* '''Sauer''': Chapter 1
* '''Burden & Faires''': Chapter 2
* '''Quarteroni et al.''': Chapter 6

----

== Phase 2: Linear Foundations (Weeks 4-7) ==

=== Topics ===
* Direct methods for linear systems
* Matrix decompositions (LU, Cholesky)
* Iterative methods for linear systems
* Convergence theory for iterative methods

=== Student Learning Outcomes (SLOs) ===
* Perform Gaussian elimination with pivoting and explain stability considerations
* Implement LU decomposition and apply to multiple right-hand sides efficiently
* Estimate condition numbers and predict solution sensitivity
* Implement Jacobi, Gauss-Seidel, and SOR methods
* Analyze convergence of iterative methods using spectral radius
* Choose between direct and iterative approaches based on problem characteristics

=== Scaffolding ===
* Extends error analysis to linear algebra settings
* Matrix iteration concepts build on scalar fixed-point theory from Phase 1
* Linear system solving becomes essential tool for subsequent interpolation and optimization phases
* Condition number analysis connects to Phase 1 concepts

=== Weekly Content ===

==== Week 4: Gaussian Elimination and LU Decomposition ====
* Gaussian elimination, partial pivoting, LU factorization
* '''Sauer''': Chapter 2.1-2.3
* '''Burden & Faires''': Chapter 6.1-6.2
* '''Quarteroni et al.''': Chapter 3

==== Week 5: Matrix Conditioning and Special Systems ====
* Condition numbers for matrices, Cholesky decomposition
* '''Sauer''': Chapter 2.4
* '''Burden & Faires''': Chapter 6.6
* '''Kincaid & Cheney''': Chapter 4

==== Week 6: Iterative Methods - Basic ====
* Jacobi and Gauss-Seidel methods, matrix splitting
* '''Sauer''': Chapter 2.5
* '''Burden & Faires''': Chapter 7.1-7.2
* '''Quarteroni et al.''': Chapter 4

==== Week 7: Iterative Methods - Convergence Theory ====
* Spectral radius, SOR method, convergence analysis
* '''Sauer''': Chapter 2.5
* '''Burden & Faires''': Chapter 7.3
* '''Quarteroni et al.''': Chapter 4

----

== Phase 3: Interpolation and Approximation (Weeks 8-11) ==

=== Topics ===
* Polynomial interpolation (Lagrange, Newton forms)
* Interpolation error analysis
* Spline interpolation
* Chebyshev interpolation and optimal node placement

=== Student Learning Outcomes (SLOs) ===
* Construct interpolating polynomials using Lagrange and Newton divided difference forms
* Derive and apply interpolation error bounds
* Explain Runge phenomenon and strategies to avoid it
* Implement natural and clamped cubic splines by solving tridiagonal systems
* Apply Chebyshev nodes to minimize interpolation error
* Select appropriate interpolation methods based on data characteristics and accuracy requirements

=== Scaffolding ===
* Uses linear system solving from Phase 2 for spline coefficient determination
* Error analysis from Phase 1 extends to approximation errors
* Establishes approximation theory foundation for later least squares and optimization
* Condition number concepts apply to interpolation matrix analysis

=== Weekly Content ===

==== Week 8: Polynomial Interpolation ====
* Lagrange interpolation, Newton divided differences
* '''Sauer''': Chapter 3.1-3.2
* '''Burden & Faires''': Chapter 3.1-3.2
* '''Quarteroni et al.''': Chapter 8

==== Week 9: Interpolation Error Analysis ====
* Error bounds, Runge phenomenon, Chebyshev nodes
* '''Sauer''': Chapter 3.3
* '''Burden & Faires''': Chapter 3.3
* '''Quarteroni et al.''': Chapter 8

==== Week 10: Spline Interpolation - Construction ====
* Piecewise linear interpolation, cubic splines
* '''Sauer''': Chapter 3.4
* '''Burden & Faires''': Chapter 3.5
* '''Quarteroni et al.''': Chapter 8

==== Week 11: Spline Interpolation - Applications ====
* Natural, clamped, and periodic boundary conditions
* Implementation and applications
* '''Sauer''': Chapter 3.4
* '''Burden & Faires''': Chapter 3.5
* '''Kincaid & Cheney''': Chapter 6

----

== Phase 4: Calculus Operations and Data Fitting (Weeks 12-15) ==

=== Topics ===
* Numerical differentiation and Richardson extrapolation
* Numerical integration (Newton-Cotes, composite rules)
* Least squares approximation
* Introduction to nonlinear systems

=== Student Learning Outcomes (SLOs) ===
* Derive finite difference formulas and analyze their error behavior
* Apply Richardson extrapolation to improve derivative approximations
* Implement trapezoid, Simpson's, and composite integration rules
* Derive error bounds for numerical integration methods
* Solve linear least squares problems using normal equations and QR decomposition
* Extend Newton's method to nonlinear systems of equations
* Connect optimization concepts to earlier root-finding methods

=== Scaffolding ===
* Numerical differentiation uses interpolation polynomials from Phase 3
* Integration connects to interpolation through Newton-Cotes derivation
* Error analysis from Phase 1 applied to differentiation and integration
* Least squares requires linear system solving from Phase 2
* Multivariable Newton's method extends single-variable version from Phase 1
* Sets foundation for optimization methods in advanced courses

=== Weekly Content ===

==== Week 12: Numerical Differentiation ====
* Finite differences, Richardson extrapolation, error analysis
* '''Sauer''': Chapter 5.1
* '''Burden & Faires''': Chapter 4.1
* '''Quarteroni et al.''': Chapter 10

==== Week 13: Numerical Integration ====
* Trapezoid rule, Simpson's rule, composite formulas
* '''Sauer''': Chapter 5.2-5.3
* '''Burden & Faires''': Chapter 4.2-4.3
* '''Quarteroni et al.''': Chapter 10

==== Week 14: Least Squares and Data Fitting ====
* Linear least squares, normal equations, QR approach
* '''Sauer''': Chapter 4.1-4.2
* '''Burden & Faires''': Chapter 8.1
* '''Quarteroni et al.''': Chapter 9

==== Week 15: Nonlinear Systems ====
* Newton's method for systems, Jacobian matrices
* '''Sauer''': Chapter 4.3
* '''Burden & Faires''': Chapter 10.2
* '''Quarteroni et al.''': Chapter 6

== Final Assessment ==
'''Final Exam Period''': Comprehensive assessment covering error analysis, linear systems, interpolation, and calculus operations with emphasis on method selection and scaffolded problem-solving.

== Key Scaffolding Connections ==
* '''Error Analysis''' (Phase 1) threads through everything
* '''Linear Systems''' (Phases 2) are used in interpolation, least squares, and nonlinear systems
* '''Newton's Method''' evolves: single variable → systems
* '''Iteration Theory''' develops: fixed-point → linear systems
* '''Approximation''' builds: interpolation → integration → differential equations
* '''Optimization Connection''': Least squares introduces objective function minimization

MAT5603

2025-08-26T22:31:06Z

Juan.gutierrez3: First version of potential topics for this course

'''Catalog entry'''

''Prerequisite'': [[MAT1223]], [[MAT2233]] (or [[MAT2253]]), or consent of instructor.

''Contents''
Rigorous introduction to the fundamental methods of numerical analysis, emphasizing both theoretical foundations and practical applications. Areas of study include the solution of nonlinear equations, interpolation and curve fitting, numerical differentiation and integration, Fourier transforms, and optimization.

= Scaffolded Numerical Analysis Curriculum (15 Weeks) =

== Phase 1: Foundation - Numbers and Errors (Weeks 1-3) ==

=== Topics ===
* Computer arithmetic and floating-point representation
* Error types and propagation
* Condition numbers and stability
* Root-finding for single variables

=== Student Learning Outcomes (SLOs) ===
* Explain IEEE 754 floating-point representation and identify representation limitations
* Calculate and distinguish between absolute, relative, forward, and backward errors
* Compute condition numbers and assess problem sensitivity to input perturbations
* Implement and analyze convergence of bisection, fixed-point iteration, and Newton's method
* Select appropriate root-finding methods based on problem characteristics and convergence requirements

=== Scaffolding ===
* Establishes error analysis framework used throughout entire course
* Introduces iteration and convergence concepts that extend to matrix methods
* Newton's method foundation for later multivariable extensions

=== Weekly Content ===

==== Week 1: Computer Arithmetic ====
* IEEE 754 standard, machine epsilon, rounding errors
* '''Sauer''': Chapter 0
* '''Burden & Faires''': Chapter 1.2
* '''Quarteroni et al.''': Chapter 2

==== Week 2: Error Analysis ====
* Absolute vs relative error, forward vs backward error analysis
* Condition numbers of problems and algorithms
* '''Sauer''': Chapter 0
* '''Kincaid & Cheney''': Chapter 2

==== Week 3: Single Variable Root-Finding ====
* Bisection method, fixed-point iteration, Newton's method, secant method
* Convergence analysis and rates
* '''Sauer''': Chapter 1
* '''Burden & Faires''': Chapter 2
* '''Quarteroni et al.''': Chapter 6

----

== Phase 2: Linear Foundations (Weeks 4-7) ==

=== Topics ===
* Direct methods for linear systems
* Matrix decompositions (LU, Cholesky)
* Iterative methods for linear systems
* Convergence theory for iterative methods

=== Student Learning Outcomes (SLOs) ===
* Perform Gaussian elimination with pivoting and explain stability considerations
* Implement LU decomposition and apply to multiple right-hand sides efficiently
* Estimate condition numbers and predict solution sensitivity
* Implement Jacobi, Gauss-Seidel, and SOR methods
* Analyze convergence of iterative methods using spectral radius
* Choose between direct and iterative approaches based on problem characteristics

=== Scaffolding ===
* Extends error analysis to linear algebra settings
* Matrix iteration concepts build on scalar fixed-point theory from Phase 1
* Linear system solving becomes essential tool for subsequent interpolation and optimization phases
* Condition number analysis connects to Phase 1 concepts

=== Weekly Content ===

==== Week 4: Gaussian Elimination and LU Decomposition ====
* Gaussian elimination, partial pivoting, LU factorization
* '''Sauer''': Chapter 2.1-2.3
* '''Burden & Faires''': Chapter 6.1-6.2
* '''Quarteroni et al.''': Chapter 3

==== Week 5: Matrix Conditioning and Special Systems ====
* Condition numbers for matrices, Cholesky decomposition
* '''Sauer''': Chapter 2.4
* '''Burden & Faires''': Chapter 6.6
* '''Kincaid & Cheney''': Chapter 4

==== Week 6: Iterative Methods - Basic ====
* Jacobi and Gauss-Seidel methods, matrix splitting
* '''Sauer''': Chapter 2.5
* '''Burden & Faires''': Chapter 7.1-7.2
* '''Quarteroni et al.''': Chapter 4

==== Week 7: Iterative Methods - Convergence Theory ====
* Spectral radius, SOR method, convergence analysis
* '''Sauer''': Chapter 2.5
* '''Burden & Faires''': Chapter 7.3
* '''Quarteroni et al.''': Chapter 4

----

== Phase 3: Interpolation and Approximation (Weeks 8-11) ==

=== Topics ===
* Polynomial interpolation (Lagrange, Newton forms)
* Interpolation error analysis
* Spline interpolation
* Chebyshev interpolation and optimal node placement

=== Student Learning Outcomes (SLOs) ===
* Construct interpolating polynomials using Lagrange and Newton divided difference forms
* Derive and apply interpolation error bounds
* Explain Runge phenomenon and strategies to avoid it
* Implement natural and clamped cubic splines by solving tridiagonal systems
* Apply Chebyshev nodes to minimize interpolation error
* Select appropriate interpolation methods based on data characteristics and accuracy requirements

=== Scaffolding ===
* Uses linear system solving from Phase 2 for spline coefficient determination
* Error analysis from Phase 1 extends to approximation errors
* Establishes approximation theory foundation for later least squares and optimization
* Condition number concepts apply to interpolation matrix analysis

=== Weekly Content ===

==== Week 8: Polynomial Interpolation ====
* Lagrange interpolation, Newton divided differences
* '''Sauer''': Chapter 3.1-3.2
* '''Burden & Faires''': Chapter 3.1-3.2
* '''Quarteroni et al.''': Chapter 8

==== Week 9: Interpolation Error Analysis ====
* Error bounds, Runge phenomenon, Chebyshev nodes
* '''Sauer''': Chapter 3.3
* '''Burden & Faires''': Chapter 3.3
* '''Quarteroni et al.''': Chapter 8

==== Week 10: Spline Interpolation - Construction ====
* Piecewise linear interpolation, cubic splines
* '''Sauer''': Chapter 3.4
* '''Burden & Faires''': Chapter 3.5
* '''Quarteroni et al.''': Chapter 8

==== Week 11: Spline Interpolation - Applications ====
* Natural, clamped, and periodic boundary conditions
* Implementation and applications
* '''Sauer''': Chapter 3.4
* '''Burden & Faires''': Chapter 3.5
* '''Kincaid & Cheney''': Chapter 6

----

== Phase 4: Calculus Operations and Data Fitting (Weeks 12-15) ==

=== Topics ===
* Numerical differentiation and Richardson extrapolation
* Numerical integration (Newton-Cotes, composite rules)
* Least squares approximation
* Introduction to nonlinear systems

=== Student Learning Outcomes (SLOs) ===
* Derive finite difference formulas and analyze their error behavior
* Apply Richardson extrapolation to improve derivative approximations
* Implement trapezoid, Simpson's, and composite integration rules
* Derive error bounds for numerical integration methods
* Solve linear least squares problems using normal equations and QR decomposition
* Extend Newton's method to nonlinear systems of equations
* Connect optimization concepts to earlier root-finding methods

=== Scaffolding ===
* Numerical differentiation uses interpolation polynomials from Phase 3
* Integration connects to interpolation through Newton-Cotes derivation
* Error analysis from Phase 1 applied to differentiation and integration
* Least squares requires linear system solving from Phase 2
* Multivariable Newton's method extends single-variable version from Phase 1
* Sets foundation for optimization methods in advanced courses

=== Weekly Content ===

==== Week 12: Numerical Differentiation ====
* Finite differences, Richardson extrapolation, error analysis
* '''Sauer''': Chapter 5.1
* '''Burden & Faires''': Chapter 4.1
* '''Quarteroni et al.''': Chapter 10

==== Week 13: Numerical Integration ====
* Trapezoid rule, Simpson's rule, composite formulas
* '''Sauer''': Chapter 5.2-5.3
* '''Burden & Faires''': Chapter 4.2-4.3
* '''Quarteroni et al.''': Chapter 10

==== Week 14: Least Squares and Data Fitting ====
* Linear least squares, normal equations, QR approach
* '''Sauer''': Chapter 4.1-4.2
* '''Burden & Faires''': Chapter 8.1
* '''Quarteroni et al.''': Chapter 9

==== Week 15: Nonlinear Systems ====
* Newton's method for systems, Jacobian matrices
* '''Sauer''': Chapter 4.3
* '''Burden & Faires''': Chapter 10.2
* '''Quarteroni et al.''': Chapter 6

== Final Assessment ==
'''Final Exam Period''': Comprehensive assessment covering error analysis, linear systems, interpolation, and calculus operations with emphasis on method selection and scaffolded problem-solving.

== Key Scaffolding Connections ==
* '''Error Analysis''' (Phase 1) threads through everything
* '''Linear Systems''' (Phases 2) are used in interpolation, least squares, and nonlinear systems
* '''Newton's Method''' evolves: single variable → systems
* '''Iteration Theory''' develops: fixed-point → linear systems
* '''Approximation''' builds: interpolation → integration → differential equations
* '''Optimization Connection''': Least squares introduces objective function minimization

MAT2253

2025-01-29T04:02:32Z

Juan.gutierrez3: /* Applied Linear Algebra */ Added textbooks

==Applied Linear Algebra==

Prerequisite: [[MAT1214]]/[[MAT1213]] Calculus I

This comprehensive course in linear algebra provides an in-depth exploration of core concepts and their applications to optimization, data analysis, and neural networks. Students will gain a strong foundation in the fundamental notions of linear systems of equations, vectors, and matrices, as well as advanced topics such as eigenvalues, eigenvectors, and canonical solutions to linear systems of differential equations. The course also explores he critical techniques of calculus operations in vectors and matrices, optimization, and Taylor series in one and multiple variables. By the end of the course, students will have a thorough understanding of the mathematical framework underlying principal component analysis, gradient descent, and the implementation of simple neural networks.

The primary textbook is "Mathematics for Machine Learning" by Deisenroth, Faisal, and Ong, 2020, Cambridge University Press. The book is available for free for personal use at https://mml-book.github.io/book/mml-book.pdf

The secondary textbook is "Pattern Recognition and Machine Learning" by Bishop, 2006, Springer Information Science and Statistics. The book is available for free for personal use at https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf

{| class="wikitable"
! Session !! Section !! Topic !! Prerequisites !! SLOs
|-
| 1 || 2.1 || Systems of Linear Equations || ||
|-
| 2 || 2.2 || Matrices || ||
|-
| 3 || 2.3 || Solving systems of linear equations || ||
|-
| 4 || 3.1, 3.2, 3.3 || Norms, Inner Products, Lengths & Distances || ||
|-
| 5 || 3.4 || Angles & orthogonality || ||
|-
| 6 || 2.4, 2.5 || Vector spaces & Linear Independendence || ||
|-
| 7 || Mini-test || || ||
|-
| 8 || 2.6 || Basis & Rank || ||
|-
| 9 || 2.7 || Linear Mappings || ||
|-
| 10 || 4.1 || Determinant and Traces || ||
|-
| 11 || 4.2 || Eigenvalues & Eigenvectors || ||
|-
| 12 || 4.3, 4.4 || Matrix Factorization || ||
|-
| 13 || 3.5 || Orthonormal Basis || ||
|-
| 14 || 3.7 || Inner Product of Functions || ||
|-
| 15 || 3.9 || Rotations || ||
|-
| 16 || Mini-test || || ||
|-
| 17 || 5.1 || Vector Calculus || ||
|-
| 18 || 5.1 || Taylor Series || ||
|-
| 19 || 5.1 || Differentiation Rules Review || ||
|-
| 20 || 5.2 || Partial Derivatives || ||
|-
| 21 || 5.2 || Gradients - Examples, visualizations, computaiton || ||
|-
| 22 || 5.2 || Rules for Partial Differentiation & Chain Rule || ||
|-
| 23 || Mini-test || || ||
|-
| 24 || 5.3 || Gradients of Vector-Valued Functions || ||
|-
| 25 || 5.3 || Gradients of Vector-Valued Functions || ||
|-
| 26 || 5.4, Dhrymes 78 || Gradients of Matrices || ||
|-
| 27 || 5.5, Dhrymes 78 || Useful Identities for Computing Gradients || ||
|-
| 28 || 5.7 || Higher-Order Derivatives || ||
|-
| 29 || Notes || Minimization via Newton's Method & Backpropagation || ||
|-
| 30 || Min-test || || ||
|-
| 31 || 5.8 || Linearization & Multivariate Taylor Series || ||
|-
| 32 || Notes || Linear optimization: Simplex method || ||
|-
| 33 || 7.1 || Optimization Using Gradient Descent || ||
|-
| 34 || 7.2 || Constrained Optimization and Lagrange Multipliers || ||
|-
| 35 || 7.3 || Convex Optimization || ||
|-
| 36 || Mini-Test || || ||
|-
| 37 || Bishop, Duda et al. || Feed-forward Artificial Neural Networks || ||
|-
| 38 || Bishop, Duda et al. || Backpropagation in ANNs || ||
|-
| 39 || Bishop, Duda et al. || Activation Functions: Linear & Nonlinear || ||
|-
| 40 || Bishop, Duda et al. || Step-by-step simple ANN || ||
|-
| 41 || Bishop, Duda et al. || Measures of performance || ||
|-
| 42 || Bishop, Duda et al. || More complex architectures of ANNs || ||
|-
| 43 || Mini-test || || ||
|-
| 44 || Final project || || ||
|-
| 45 || Review || || ||
|}

MAT2253

2025-01-28T18:59:10Z

Juan.gutierrez3: /* List of Topics */ Edited by Vu Hoang, Stephen Peña, Juan B. Gutiérrez

==Applied Linear Algebra==

Prerequisite: [[MAT1214]]/[[MAT1213]] Calculus I

This comprehensive course in linear algebra provides an in-depth exploration of core concepts and their applications to optimization, data analysis, and neural networks. Students will gain a strong foundation in the fundamental notions of linear systems of equations, vectors, and matrices, as well as advanced topics such as eigenvalues, eigenvectors, and canonical solutions to linear systems of differential equations. The course also delves into the critical techniques of calculus operations in vectors and matrices, optimization, and Taylor series in one and multiple variables. By the end of the course, students will have a thorough understanding of the mathematical framework underlying principal component analysis, gradient descent, and the implementation of simple neural networks.

{| class="wikitable"
! Session !! Section !! Topic !! Prerequisites !! SLOs
|-
| 1 || 2.1 || Systems of Linear Equations || ||
|-
| 2 || 2.2 || Matrices || ||
|-
| 3 || 2.3 || Solving systems of linear equations || ||
|-
| 4 || 3.1, 3.2, 3.3 || Norms, Inner Products, Lengths & Distances || ||
|-
| 5 || 3.4 || Angles & orthogonality || ||
|-
| 6 || 2.4, 2.5 || Vector spaces & Linear Independendence || ||
|-
| 7 || Mini-test || || ||
|-
| 8 || 2.6 || Basis & Rank || ||
|-
| 9 || 2.7 || Linear Mappings || ||
|-
| 10 || 4.1 || Determinant and Traces || ||
|-
| 11 || 4.2 || Eigenvalues & Eigenvectors || ||
|-
| 12 || 4.3, 4.4 || Matrix Factorization || ||
|-
| 13 || 3.5 || Orthonormal Basis || ||
|-
| 14 || 3.7 || Inner Product of Functions || ||
|-
| 15 || 3.9 || Rotations || ||
|-
| 16 || Mini-test || || ||
|-
| 17 || 5.1 || Vector Calculus || ||
|-
| 18 || 5.1 || Taylor Series || ||
|-
| 19 || 5.1 || Differentiation Rules Review || ||
|-
| 20 || 5.2 || Partial Derivatives || ||
|-
| 21 || 5.2 || Gradients - Examples, visualizations, computaiton || ||
|-
| 22 || 5.2 || Rules for Partial Differentiation & Chain Rule || ||
|-
| 23 || Mini-test || || ||
|-
| 24 || 5.3 || Gradients of Vector-Valued Functions || ||
|-
| 25 || 5.3 || Gradients of Vector-Valued Functions || ||
|-
| 26 || 5.4, Dhrymes 78 || Gradients of Matrices || ||
|-
| 27 || 5.5, Dhrymes 78 || Useful Identities for Computing Gradients || ||
|-
| 28 || 5.7 || Higher-Order Derivatives || ||
|-
| 29 || Notes || Minimization via Newton's Method & Backpropagation || ||
|-
| 30 || Min-test || || ||
|-
| 31 || 5.8 || Linearization & Multivariate Taylor Series || ||
|-
| 32 || Notes || Linear optimization: Simplex method || ||
|-
| 33 || 7.1 || Optimization Using Gradient Descent || ||
|-
| 34 || 7.2 || Constrained Optimization and Lagrange Multipliers || ||
|-
| 35 || 7.3 || Convex Optimization || ||
|-
| 36 || Mini-Test || || ||
|-
| 37 || Bishop, Duda et al. || Feed-forward Artificial Neural Networks || ||
|-
| 38 || Bishop, Duda et al. || Backpropagation in ANNs || ||
|-
| 39 || Bishop, Duda et al. || Activation Functions: Linear & Nonlinear || ||
|-
| 40 || Bishop, Duda et al. || Step-by-step simple ANN || ||
|-
| 41 || Bishop, Duda et al. || Measures of performance || ||
|-
| 42 || Bishop, Duda et al. || More complex architectures of ANNs || ||
|-
| 43 || Mini-test || || ||
|-
| 44 || Final project || || ||
|-
| 45 || Review || || ||
|}

MAT1213

2025-01-21T15:45:12Z

Juan.gutierrez3:

The textbook for this course is
[https://openstax.org/details/calculus-volume-1 Calculus (Volume 1) by Gilbert Strang, Edwin Herman, et al.]

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history].

==Topics List - Table==

{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

2.2

||

[[The Limit of a Function]]

||

* [[Functions|Evaluation of a function]] including the [[Absolute Value Functions| Absolute Value]] , [[Rational Functions|Rational]] , and [[Piecewise Functions|Piecewise]] functions
* [[Functions|Domain and Range of a Function]]

||

*Describe the limit of a function using correct notation.
*Use a table of values to estimate the limit of a function or to identify when the limit does not exist.
*Use a graph to estimate the limit of a function or to identify when the limit does not exist.
*Define one-sided limits and provide examples.
*Explain the relationship between one-sided and two-sided limits.
*Describe an infinite limit using correct notation.
*Define a vertical asymptote.

|-

|Week 1/2

||

2.3

||

[[The Limit Laws]]

||

*[[Factoring Polynomials]]
*[[Simplifying Radicals|Identifying conjugate radical expressions]]
*[[Rational Expression|Simplifying rational expressions]]
*[[Domain of a Function|Evaluating piecewise functions]]
*[[Trigonometric Functions|The trigonometric functions]]

||

*Recognize the basic limit laws.
*Use the limit laws to evaluate the limit of a function.
*Evaluate the limit of a function by factoring.
*Use the limit laws to evaluate the limit of a polynomial or rational function.
*Evaluate the limit of a function by factoring or by using conjugates.
*Evaluate the limit of a function by using the squeeze theorem.
*Evaluate left, right, and two sided limits of piecewise defined functions.
*Evaluate limits of the form K/0, K≠0.
*Establish and use this to evaluate other limits involving trigonometric functions.

|-

|Week 2/3

||

2.4

||

[[Continuity]]

||

* [[Functions|Domain and Range of a Function]]
* [[Interval Notation|Interval Notation]]
* [[Limits of Functions|Evaluate limits]]
* [[The Limit Laws]]
* [[Polynomial Functions|Finding roots of a function]]

||

* Continuity at a point.
* Describe three kinds of discontinuities.
* Define continuity on an interval.
* State the theorem for limits of composite functions and use the theorem to evaluate limits.
* Provide an example of the intermediate value theorem.

|-

|Week 3

||

4.6

||

[[Limits at Infinity and Asymptotes]]

||

* [[The Limit Laws]]
* [[Continuity]]

||

* Calculate the limit of a function that is unbounded.
* Identify a horizontal asymptote for the graph of a function.

|-

|Week 3/4

||

3.1

||

[[Defining the Derivative]]

||

* [[Functions|Evaluation of a function at a value]]
* [[Linear Functions and Slope|The equation of a line and its slope]]
* [[Limits of Functions|Evaluating limits]]
* [[Continuity]]

||

* Recognize the meaning of the tangent to a curve at a point.
* Calculate the slope of a secant line (average rate of change of a function over an interval).
* Calculate the slope of a tangent line.
* Find the equation of the line tangent to a curve at a point.
* Identify the derivative as the limit of a difference quotient.
* Calculate the derivative of a given function at a point.

|-

|Week 4

||

3.2

||

[[The Derivative as a Function]]

||

* [[Functions and their graphs|Graphing Functions]]
* [[Continuity|Continuity of a function at a point]]
* [[Defining the Derivative|The derivative represents the slope of the curve at a point]]
* [[Limits of Functions|When a limit fails to exist]]
* [[The Limit Laws]]

||

* Define the derivative function of a given function.
* Graph a derivative function from the graph of a given function.
* State the connection between derivatives and continuity.
* Describe three conditions for when a function does not have a derivative.
* Explain the meaning of and compute a higher-order derivative.

|-

|Week 4/5

||

3.3

||

[[Differentiation Rules]]

||

* [[Simplifying Radicals|Radical & Rational Exponents]]
* [[Simplifying Exponents|Re-write negative exponents]]
* [[The Limit Laws]]
* [[The Derivative as a Function]]

||

* State the constant, constant multiple, and power rules.
* Apply the sum and difference rules to combine derivatives.
* Use the product rule for finding the derivative of a product of functions.
* Use the quotient rule for finding the derivative of a quotient of functions.
* Extend the power rule to functions with negative exponents.
* Combine the differentiation rules to find the derivative of a polynomial or rational function.

|-

|Week 5

||

3.4

||

[[Derivatives_Rates_of_Change|Derivatives as Rates of Change]]

||

* [[Functions|Function evaluation at a value]]
* [[Solving Equations and Inequalities|Solving an algebraic equation]]
* '''[[Understanding of Velocity and Acceleration]]'''
* [[Differentiation Rules]]

||

* Determine a new value of a quantity from the old value and the amount of change.
* Calculate the average rate of change and explain how it differs from the instantaneous rate of change.
* Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.
* Predict the future population from the present value and the population growth rate.
* Use derivatives to calculate marginal cost and revenue in a business situation.

|-

|Week 5

||

3.5

||

[[Derivatives of the Trigonometric Functions]]

||

* [[Properties of the Trigonometric Functions|Trigonometric identities]]
* [[Graphs of the Sine and Cosine Functions]]
* [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* [[Differentiation Rules|Rules for finding Derivatives]]

||

* Find the derivatives of the sine and cosine function.
* Find the derivatives of the standard trigonometric functions.
* Calculate the higher-order derivatives of the sine and cosine.

|-

|Week 6

||

3.6
||

[[Chain_Rule|The Chain Rule]]

||

* [[Composition of Functions]]
* [[Trigonometric Equations|Solve Trigonometric Equations]]
* [[Differentiation Rules|Rules for finding Derivatives]]
* [[Derivatives of the Trigonometric Functions]]

||

* State the chain rule for the composition of two functions.
* Apply the chain rule together with the power rule.
* Apply the chain rule and the product/quotient rules correctly in combination when both are necessary.
* Recognize and apply the chain rule for a composition of three or more functions.
* Use interchangeably the Newton and Leibniz Notation for the Chain Rule.

|-

|Week 6

||

3.7

||

[[Derivatives of Inverse Functions]]

||

* [[One-to-one functions|Injective Functions]]
* [[Inverse Functions]] 
* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

||

* State the Inverse Function Theorem for Derivatives.
* Apply the Inverse Function Theorem to find the derivative of a function at a point given its inverse and a point on its graph.
* Derivatives of the inverse trigonometric functions.

|-

|Week 6/7

||

3.8

||

[[Implicit Differentiation]]

||

* '''[[Implicit and explicit equations]]'''
* [[Linear Equations|Linear Functions and Slope]]
* [[Functions|Function evaluation]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

||

* Assuming, for example, y is implicitly a function of x, find the derivative of y with respect to x.
* Assuming, for example, y is implicitly a function of x, and given an equation relating y to x, find the derivative of y with respect to x.
* Find the equation of a line tangent to an implicitly defined curve at a point.

|-

|Week 7

||

3.9

||

[[Derivatives of Exponential and Logarithmic Functions]]

||

* [[Logarithmic Functions|Properties of logarithms]] <
* [[The Limit of a Function]]
* [[Differentiation Rules]]
* [[The Chain Rule]]
* [[Implicit Differentiation]]

||

* Find the derivative of functions that involve exponential functions.
* Find the derivative of functions that involve logarithmic functions.
* Use logarithmic differentiation to find the derivative of functions containing combinations of powers, products, and quotients.

|-

|Week 7/8

||

4.1

||

[[Related Rates]]

||

* '''Formulas for area, volume, etc'''
* '''Similar triangles to form proportions'''
* [[Trigonometric Functions]] 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]]
* [[Differentiation Rules]]
* [[Implicit Differentiation]]

||

* Express changing quantities in terms of derivatives.
* Find relationships among the derivatives in a given problem.
* Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.

|-

|Week 8

||

4.2

||

[[Linear Approximations and Differentials]]

||

* [[Mathematical Error| Definition of Error in mathematics]]
* [[Linear Equations|Slope of a Line]]
* [[Defining the Derivative|Equation of the tangent line]]
* [[Derivatives Rates of Change|Leibnitz notation of the derivative]]

||

* Approximate the function value close to the center of the linear approximation using the linearization.
* Given an expression to be evaluated/approximated, come up with the function and its linearization
* Understand the formula for the differential; how it can be used to estimate the change in the dependent variable quantity, given the small change in the independent variable quantity.
* Use the information above to estimate potential relative (and percentage) error

|-

|Week 8/9

||

4.3

||

[[Maxima and Minima]]

||

* [[The First Derivative Test|Increasing and decreasing functions]]
* [[Solving Equations and Inequalities|Solve an algebraic equation]]
* [[Interval Notation|Interval notation]]
* [[Trigonometric Equations]]
* [[Differentiation Rules]]
* [[Derivatives of the Trigonometric Functions]]
* [[Derivatives of Exponential and Logarithmic Functions]]
* [[Continuity]]

||
*
* Know the definitions of absolute and local extrema.
* Know what a critical point is and locate it (them).
* Use the Extreme Value Theorem to find the absolute extrema of a continuous function on a closed interval.

|-

|Week 9

||

4.4

||

[[Mean Value Theorem]]

||

* [[Functions|Evaluating Functions]]
* [[Continuity]]
* [[Defining the Derivative|Slope of a Line]]

||

* Determine if the MVT applies given a function on an interval.
* Find c in the conclusion of the MVT (if algebraically feasible)
* Know the first 3 Corollaries of MVT (especially the 3rd)

|-

|Week 9

||

4.5

||

[[Derivatives and the Shape of a Graph]]

||

* [[Functions|Evaluating Functions]]
* [[Maxima and Minima|Critical Points of a Function]]
* [[Derivatives and the Shape of a Graph|Second Derivatives]]

||

* Use the First Derivative Test to find intervals on which the function is increasing and decreasing and the local extrema and their type
* Use the Concavity Test (aka the Second Derivative Test for Concavity) to find the intervals on which the function is concave up and down, and point(s) of inflection
* Understand the shape of the graph, given the signs of the first and second derivatives.

|-

|Week 10

||

4.7

||

[[Applied Optimization Problems]]

||

* '''Formulas pertaining to area and volume'''
* [[Functions|Evaluating Functions]]
* [[Trigonometric Equations]]
* [[Maxima and Minima|Critical Points of a Function]]

||

* Set up a function to be optimized and find the value(s) of the independent variable which provide the optimal solution.

|-

|Week 10

||

4.8

||

[[L’Hôpital’s Rule]]

||

* [[Rational Functions| Re-expressing Rational Functions ]]
* [[The Limit of a Function|When a Limit is Undefined]]
* [[The Derivative as a Function]]

||

* Identify indeterminate forms produced by quotients, products, subtractions, and powers, and apply L’Hôpital’s rule in each case.
* Recognize when to apply L’Hôpital’s rule.

|-

|Week 11

||

4.10

||

[[Antiderivatives]]

||

* [[Inverse Functions]]
* [[The Derivative as a Function]]
* [[Differentiation Rule]]
* [[Derivatives of the Trigonometric Functions]]

||

* Find the general antiderivative of a given function.
* Explain the terms and notation used for an indefinite integral.
* State the power rule for integrals.
* Use anti-differentiation to solve simple initial-value problems.

|-

|Week 11/12

||

5.1

||

[[Approximating Areas]]

||

* '''[[Sigma notation]]'''
* '''[[Area of a rectangle]]'''
* [[Continuity]]
* [[Toolkit Functions]]

||

* Calculate sums and powers of integers.
* Use the sum of rectangular areas to approximate the area under a curve.
* Use Riemann sums to approximate area.

|-

|Week 12

||

5.2

||

[[The Definite Integral]]

||

* [[Interval Notation|Interval notation]]
* [[Antiderivatives]]
* [[The Limit of a Function|Limits of Riemann Sums]]
* [[Continuity]]

||

* State the definition of the definite integral.
* Explain the terms integrand, limits of integration, and variable of integration.
* Explain when a function is integrable.
* Rules for the Definite Integral.
* Describe the relationship between the definite integral and net area.
* Use geometry and the properties of definite integrals to evaluate them.
* Calculate the average value of a function.

|-

|Week 12/13

||

5.3

||

[[The Fundamental Theorem of Calculus]]

||

* [[The Derivative as a Function|The Derivative of a Function]]
* [[Antiderivatives]]
* [[Mean Value Theorem]]
* [[Inverse Functions]]

||

* Describe the meaning of the Mean Value Theorem for Integrals.
* State the meaning of the Fundamental Theorem of Calculus, Part 1.
* Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
* State the meaning of the Fundamental Theorem of Calculus, Part 2.
* Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
* Explain the relationship between differentiation and integration.

|-

|Week 13

||

5.4

||

[[Integration Formulas and the Net Change Theorem]]

||

* [[Antiderivatives|Indefinite integrals]]
* [[The Fundamental Theorem of Calculus|The Fundamental Theorem (part 2)]]

||

* Apply the basic integration formulas.
* Explain the significance of the net change theorem.
* Use the net change theorem to solve applied problems.
* Apply the integrals of odd and even functions.

|-

|Week 14

||

5.5

||

[[Integration by Substitution]]

||

* [[The Definite Integral|Solving Basic Integrals]]
* [[The Derivative as a Function|The Derivative of a Function]]
* '''[[Change of Variables]]'''

||

* Use substitution to evaluate indefinite integrals.
* Use substitution to evaluate definite integrals.

|-

|Week 14/15

||

5.6

||

[[Integrals Involving Exponential and Logarithmic Functions]]

||

* [[Exponential Functions]]
* [[Logarithmic Functions]]
* [[Differentiation Rules]]
* [[Antiderivatives]]

||

* Integrate functions involving exponential functions.
* Integrate functions involving logarithmic functions.

|-

|Week 15

||

5.7

||

[[Integrals Resulting in Inverse Trigonometric Functions]]

||

* [[The inverse sine, cosine and tangent functions|Trigonometric functions and their inverses]]
* [[One-to-one functions|Injective Functions]]
* [[The Definite Integral|Rules for Integration]]

||

* Integrate functions resulting in inverse trigonometric functions.

|}

==Topics List - Narrative==

===Week 1===
====Sections====
2.2

====Topics====
[[The Limit of a Function]]

====Prerequisite Skills====
* [[Functions|Evaluation of a function]] including the [[Absolute Value Functions|Absolute Value]], [[Rational Functions|Rational]], and [[Piecewise Functions|Piecewise]] functions
* [[Functions|Domain and Range of a Function]]

====Student Learning Outcomes====
* Describe the limit of a function using correct notation.
* Use a table of values to estimate the limit of a function or to identify when the limit does not exist.
* Use a graph to estimate the limit of a function or to identify when the limit does not exist.
* Define one-sided limits and provide examples.
* Explain the relationship between one-sided and two-sided limits.
* Describe an infinite limit using correct notation.
* Define a vertical asymptote.

===Week 1/2===
====Sections====
2.3

====Topics====
[[The Limit Laws]]

====Prerequisite Skills====
* [[Factoring Polynomials]]
* [[Simplifying Radicals|Identifying conjugate radical expressions]]
* [[Rational Expression|Simplifying rational expressions]]
* [[Domain of a Function|Evaluating piecewise functions]]
* [[Trigonometric Functions|The trigonometric functions]]

====Student Learning Outcomes====
* Recognize the basic limit laws.
* Use the limit laws to evaluate the limit of a function.
* Evaluate the limit of a function by factoring.
* Use the limit laws to evaluate the limit of a polynomial or rational function.
* Evaluate the limit of a function by factoring or by using conjugates.
* Evaluate the limit of a function by using the squeeze theorem.
* Evaluate left, right, and two-sided limits of piecewise defined functions.
* Evaluate limits of the form $ K/0, K \neq 0 $.
* Establish $ \lim_{x \to 0} \frac{\sin x}{x} = 1 $ and use this to evaluate other limits involving trigonometric functions.

===Week 2/3===
====Sections====
2.4

====Topics====
[[Continuity]]

====Prerequisite Skills====
* [[Functions|Domain and Range of a Function]]
* [[Interval Notation|Interval Notation]]
* [[Limits of Functions|Evaluate limits]]
* [[The Limit Laws]]
* [[Polynomial Functions|Finding roots of a function]]

====Student Learning Outcomes====
* Continuity at a point.
* Describe three kinds of discontinuities.
* Define continuity on an interval.
* State the theorem for limits of composite functions and use the theorem to evaluate limits.
* Provide an example of the intermediate value theorem.

===Week 3===
====Sections====
4.6

====Topics====
[[Limits at Infinity and Asymptotes]]

====Prerequisite Skills====
* [[The Limit Laws]]
* [[Continuity]]

====Student Learning Outcomes====
* Calculate the limit of a function that is unbounded.
* Identify a horizontal asymptote for the graph of a function.

===Week 3/4===
====Sections====
3.1

====Topics====
[[Defining the Derivative]]

====Prerequisite Skills====
* [[Functions|Evaluation of a function at a value]]
* [[Linear Functions and Slope|The equation of a line and its slope]]
* [[Limits of Functions|Evaluating limits]]
* [[Continuity]]

====Student Learning Outcomes====
* Recognize the meaning of the tangent to a curve at a point.
* Calculate the slope of a secant line (average rate of change of a function over an interval).
* Calculate the slope of a tangent line.
* Find the equation of the line tangent to a curve at a point.
* Identify the derivative as the limit of a difference quotient.
* Calculate the derivative of a given function at a point.

===Week 4===
====Sections====
3.2

====Topics====
[[The Derivative as a Function]]

====Prerequisite Skills====
* [[Functions and their graphs|Graphing Functions]]
* [[Continuity|Continuity of a function at a point]]
* [[Defining the Derivative|The derivative represents the slope of the curve at a point]]
* [[Limits of Functions|When a limit fails to exist]]
* [[The Limit Laws]]

====Student Learning Outcomes====
* Define the derivative function of a given function.
* Graph a derivative function from the graph of a given function.
* State the connection between derivatives and continuity.
* Describe three conditions for when a function does not have a derivative.
* Explain the meaning of and compute a higher-order derivative.

===Week 4/5===
====Sections====
3.3

====Topics====
[[Differentiation Rules]]

====Prerequisite Skills====
* [[Simplifying Radicals|Radical & Rational Exponents]]
* [[Simplifying Exponents|Re-write negative exponents]]
* [[The Limit Laws]]
* [[The Derivative as a Function]]

====Student Learning Outcomes====
* State the constant, constant multiple, and power rules.
* Apply the sum and difference rules to combine derivatives.
* Use the product rule for finding the derivative of a product of functions.
* Use the quotient rule for finding the derivative of a quotient of functions.
* Extend the power rule to functions with negative exponents.
* Combine the differentiation rules to find the derivative of a polynomial or rational function.

===Week 5===
====Sections====
3.4

====Topics====
[[Derivatives_Rates_of_Change|Derivatives as Rates of Change]]

====Prerequisite Skills====
* [[Functions|Function evaluation at a value]]
* [[Solving Equations and Inequalities|Solving an algebraic equation]]
* [[Understanding of Velocity and Acceleration]]
* [[Differentiation Rules]]

====Student Learning Outcomes====
* Determine a new value of a quantity from the old value and the amount of change.
* Calculate the average rate of change and explain how it differs from the instantaneous rate of change.
* Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.
* Predict the future population from the present value and the population growth rate.
* Use derivatives to calculate marginal cost and revenue in a business situation.

===Week 5===
====Sections====
3.5

====Topics====
[[Derivatives of the Trigonometric Functions]]

====Prerequisite Skills====
* [[Properties of the Trigonometric Functions|Trigonometric identities]]
* [[Graphs of the Sine and Cosine Functions]]
* [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* [[Differentiation Rules|Rules for finding Derivatives]]

====Student Learning Outcomes====
* Find the derivatives of the sine and cosine function.
* Find the derivatives of the standard trigonometric functions.
* Calculate the higher-order derivatives of the sine and cosine.

===Week 6===
====Sections====
3.6

====Topics====
[[Chain_Rule|The Chain Rule]]

====Prerequisite Skills====
* [[Composition of Functions]]
* [[Trigonometric Equations|Solve Trigonometric Equations]]
* [[Differentiation Rules|Rules for finding Derivatives]]
* [[Derivatives of the Trigonometric Functions]]

====Student Learning Outcomes====
* State the chain rule for the composition of two functions.
* Apply the chain rule together with the power rule.
* Apply the chain rule and the product/quotient rules correctly in combination when both are necessary.
* Recognize and apply the chain rule for a composition of three or more functions.
* Use interchangeably the Newton and Leibniz Notation for the Chain Rule.

===Week 6===
====Sections====
3.7

====Topics====
[[Derivatives of Inverse Functions]]

====Prerequisite Skills====
* [[One-to-one functions|Injective Functions]]
* [[Inverse Functions]]
* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

====Student Learning Outcomes====
* State the Inverse Function Theorem for Derivatives.
* Apply the Inverse Function Theorem to find the derivative of a function at a point given its inverse and a point on its graph.
* Derivatives of the inverse trigonometric functions.

===Week 6/7===
====Sections====
3.8

====Topics====
[[Implicit Differentiation]]

====Prerequisite Skills====
* [[Implicit and explicit equations]]
* [[Linear Equations|Linear Functions and Slope]]
* [[Functions|Function evaluation]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

====Student Learning Outcomes====
* Assuming $ y $ is implicitly a function of $ x $, find the derivative of $ y $ with respect to $ x $.
* Assuming $ y $ is implicitly a function of $ x $, and given an equation relating $ y $ to $ x $, find the derivative of $ y $ with respect to $ x $.
* Find the equation of a line tangent to an implicitly defined curve at a point.

===Week 7===
====Sections====
3.9

====Topics====
[[Derivatives of Exponential and Logarithmic Functions]]

====Prerequisite Skills====
* [[Logarithmic Functions|Properties of logarithms]]
* [[The Limit of a Function]]
* [[Differentiation Rules]]
* [[The Chain Rule]]
* [[Implicit Differentiation]]

====Student Learning Outcomes====
* Find the derivative of functions that involve exponential functions.
* Find the derivative of functions that involve logarithmic functions.
* Use logarithmic differentiation to find the derivative of functions containing combinations of powers, products, and quotients.

===Week 7/8===
====Sections====
4.1

====Topics====
[[Related Rates]]

====Prerequisite Skills====
* Formulas for area, volume, etc.
* Similar triangles to form proportions
* [[Trigonometric Functions]]
* [[Properties of the Trigonometric Functions|Trigonometric Identities]]
* [[Differentiation Rules]]
* [[Implicit Differentiation]]

====Student Learning Outcomes====
* Express changing quantities in terms of derivatives.
* Find relationships among the derivatives in a given problem.
* Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.

===Week 8===
====Sections====
4.2

====Topics====
[[Linear Approximations and Differentials]]

====Prerequisite Skills====
* [[Mathematical Error|Definition of Error in mathematics]]
* [[Linear Equations|Slope of a Line]]
* [[Defining the Derivative|Equation of the tangent line]]
* [[Derivatives Rates of Change|Leibnitz notation of the derivative]]

====Student Learning Outcomes====
* Approximate the function value close to the center of the linear approximation using the linearization.
* Given an expression to be evaluated/approximated, come up with the function and its linearization.
* Understand the formula for the differential; how it can be used to estimate the change in the dependent variable quantity, given the small change in the independent variable quantity.
* Use the information above to estimate potential relative (and percentage) error.

===Week 8/9===
====Sections====
4.3

====Topics====
[[Maxima and Minima]]

====Prerequisite Skills====
* [[The First Derivative Test|Increasing and decreasing functions]]
* [[Solving Equations and Inequalities|Solve an algebraic equation]]
* [[Interval Notation|Interval notation]]
* [[Trigonometric Equations]]
* [[Differentiation Rules]]
* [[Derivatives of the Trigonometric Functions]]
* [[Derivatives of Exponential and Logarithmic Functions]]
* [[Continuity]]

====Student Learning Outcomes====
* Know the definitions of absolute and local extrema.
* Know what a critical point is and locate it (them).
* Use the Extreme Value Theorem to find the absolute extrema of a continuous function on a closed interval.

===Week 9===
====Sections====
4.4

====Topics====
[[Mean Value Theorem]]

====Prerequisite Skills====
* [[Functions|Evaluating Functions]]
* [[Continuity]]
* [[Defining the Derivative|Slope of a Line]]

====Student Learning Outcomes====
* Determine if the MVT applies given a function on an interval.
* Find $ c $ in the conclusion of the MVT (if algebraically feasible).
* Know the first 3 Corollaries of MVT (especially the 3rd).

===Week 9===
====Sections====
4.5

====Topics====
[[Derivatives and the Shape of a Graph]]

====Prerequisite Skills====
* [[Functions|Evaluating Functions]]
* [[Maxima and Minima|Critical Points of a Function]]
* [[Derivatives and the Shape of a Graph|Second Derivatives]]

====Student Learning Outcomes====
* Use the First Derivative Test to find intervals on which the function is increasing and decreasing and the local extrema and their type.
* Use the Concavity Test (aka the Second Derivative Test for Concavity) to find the intervals on which the function is concave up and down, and point(s) of inflection.
* Understand the shape of the graph, given the signs of the first and second derivatives.

===Week 10===
====Sections====
4.7

====Topics====
[[Applied Optimization Problems]]

====Prerequisite Skills====
* Formulas pertaining to area and volume
* [[Functions|Evaluating Functions]]
* [[Trigonometric Equations]]
* [[Maxima and Minima|Critical Points of a Function]]

====Student Learning Outcomes====
* Set up a function to be optimized and find the value(s) of the independent variable which provide the optimal solution.

===Week 10===
====Sections====
4.8

====Topics====
[[L’Hôpital’s Rule]]

====Prerequisite Skills====
* [[Rational Functions|Re-expressing Rational Functions]]
* [[The Limit of a Function|When a Limit is Undefined]]
* [[The Derivative as a Function]]

====Student Learning Outcomes====
* Identify indeterminate forms produced by quotients, products, subtractions, and powers, and apply L’Hôpital’s rule in each case.
* Recognize when to apply L’Hôpital’s rule.

===Week 11===
====Sections====
4.10

====Topics====
[[Antiderivatives]]

====Prerequisite Skills====
* [[Inverse Functions]]
* [[The Derivative as a Function]]
* [[Differentiation Rule]]
* [[Derivatives of the Trigonometric Functions]]

====Student Learning Outcomes====
* Find the general antiderivative of a given function.
* Explain the terms and notation used for an indefinite integral.
* State the power rule for integrals.
* Use anti-differentiation to solve simple initial-value problems.

===Week 11/12===
====Sections====
5.1

====Topics====
[[Approximating Areas]]

====Prerequisite Skills====
* [[Sigma notation]]
* [[Area of a rectangle]]
* [[Continuity]]
* [[Toolkit Functions]]

====Student Learning Outcomes====
* Calculate sums and powers of integers.
* Use the sum of rectangular areas to approximate the area under a curve.
* Use Riemann sums to approximate area.

MAT1213

2025-01-21T15:42:27Z

Juan.gutierrez3:

The textbook for this course is
[https://openstax.org/details/calculus-volume-1 Calculus (Volume 1) by Gilbert Strang, Edwin Herman, et al.]

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history].

==Topics List - Narrative==

===Week 1===
====Sections====
2.2

====Topics====
[[The Limit of a Function]]

====Prerequisite Skills====
* [[Functions|Evaluation of a function]] including the [[Absolute Value Functions|Absolute Value]], [[Rational Functions|Rational]], and [[Piecewise Functions|Piecewise]] functions
* [[Functions|Domain and Range of a Function]]

====Student Learning Outcomes====
* Describe the limit of a function using correct notation.
* Use a table of values to estimate the limit of a function or to identify when the limit does not exist.
* Use a graph to estimate the limit of a function or to identify when the limit does not exist.
* Define one-sided limits and provide examples.
* Explain the relationship between one-sided and two-sided limits.
* Describe an infinite limit using correct notation.
* Define a vertical asymptote.

===Week 1/2===
====Sections====
2.3

====Topics====
[[The Limit Laws]]

====Prerequisite Skills====
* [[Factoring Polynomials]]
* [[Simplifying Radicals|Identifying conjugate radical expressions]]
* [[Rational Expression|Simplifying rational expressions]]
* [[Domain of a Function|Evaluating piecewise functions]]
* [[Trigonometric Functions|The trigonometric functions]]

====Student Learning Outcomes====
* Recognize the basic limit laws.
* Use the limit laws to evaluate the limit of a function.
* Evaluate the limit of a function by factoring.
* Use the limit laws to evaluate the limit of a polynomial or rational function.
* Evaluate the limit of a function by factoring or by using conjugates.
* Evaluate the limit of a function by using the squeeze theorem.
* Evaluate left, right, and two-sided limits of piecewise defined functions.
* Evaluate limits of the form $ K/0, K \neq 0 $.
* Establish $ \lim_{x \to 0} \frac{\sin x}{x} = 1 $ and use this to evaluate other limits involving trigonometric functions.

===Week 2/3===
====Sections====
2.4

====Topics====
[[Continuity]]

====Prerequisite Skills====
* [[Functions|Domain and Range of a Function]]
* [[Interval Notation|Interval Notation]]
* [[Limits of Functions|Evaluate limits]]
* [[The Limit Laws]]
* [[Polynomial Functions|Finding roots of a function]]

====Student Learning Outcomes====
* Continuity at a point.
* Describe three kinds of discontinuities.
* Define continuity on an interval.
* State the theorem for limits of composite functions and use the theorem to evaluate limits.
* Provide an example of the intermediate value theorem.

===Week 3===
====Sections====
4.6

====Topics====
[[Limits at Infinity and Asymptotes]]

====Prerequisite Skills====
* [[The Limit Laws]]
* [[Continuity]]

====Student Learning Outcomes====
* Calculate the limit of a function that is unbounded.
* Identify a horizontal asymptote for the graph of a function.

===Week 3/4===
====Sections====
3.1

====Topics====
[[Defining the Derivative]]

====Prerequisite Skills====
* [[Functions|Evaluation of a function at a value]]
* [[Linear Functions and Slope|The equation of a line and its slope]]
* [[Limits of Functions|Evaluating limits]]
* [[Continuity]]

====Student Learning Outcomes====
* Recognize the meaning of the tangent to a curve at a point.
* Calculate the slope of a secant line (average rate of change of a function over an interval).
* Calculate the slope of a tangent line.
* Find the equation of the line tangent to a curve at a point.
* Identify the derivative as the limit of a difference quotient.
* Calculate the derivative of a given function at a point.

===Week 4===
====Sections====
3.2

====Topics====
[[The Derivative as a Function]]

====Prerequisite Skills====
* [[Functions and their graphs|Graphing Functions]]
* [[Continuity|Continuity of a function at a point]]
* [[Defining the Derivative|The derivative represents the slope of the curve at a point]]
* [[Limits of Functions|When a limit fails to exist]]
* [[The Limit Laws]]

====Student Learning Outcomes====
* Define the derivative function of a given function.
* Graph a derivative function from the graph of a given function.
* State the connection between derivatives and continuity.
* Describe three conditions for when a function does not have a derivative.
* Explain the meaning of and compute a higher-order derivative.

===Week 4/5===
====Sections====
3.3

====Topics====
[[Differentiation Rules]]

====Prerequisite Skills====
* [[Simplifying Radicals|Radical & Rational Exponents]]
* [[Simplifying Exponents|Re-write negative exponents]]
* [[The Limit Laws]]
* [[The Derivative as a Function]]

====Student Learning Outcomes====
* State the constant, constant multiple, and power rules.
* Apply the sum and difference rules to combine derivatives.
* Use the product rule for finding the derivative of a product of functions.
* Use the quotient rule for finding the derivative of a quotient of functions.
* Extend the power rule to functions with negative exponents.
* Combine the differentiation rules to find the derivative of a polynomial or rational function.

===Week 5===
====Sections====
3.4

====Topics====
[[Derivatives_Rates_of_Change|Derivatives as Rates of Change]]

====Prerequisite Skills====
* [[Functions|Function evaluation at a value]]
* [[Solving Equations and Inequalities|Solving an algebraic equation]]
* [[Understanding of Velocity and Acceleration]]
* [[Differentiation Rules]]

====Student Learning Outcomes====
* Determine a new value of a quantity from the old value and the amount of change.
* Calculate the average rate of change and explain how it differs from the instantaneous rate of change.
* Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.
* Predict the future population from the present value and the population growth rate.
* Use derivatives to calculate marginal cost and revenue in a business situation.

===Week 5===
====Sections====
3.5

====Topics====
[[Derivatives of the Trigonometric Functions]]

====Prerequisite Skills====
* [[Properties of the Trigonometric Functions|Trigonometric identities]]
* [[Graphs of the Sine and Cosine Functions]]
* [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* [[Differentiation Rules|Rules for finding Derivatives]]

====Student Learning Outcomes====
* Find the derivatives of the sine and cosine function.
* Find the derivatives of the standard trigonometric functions.
* Calculate the higher-order derivatives of the sine and cosine.

===Week 6===
====Sections====
3.6

====Topics====
[[Chain_Rule|The Chain Rule]]

====Prerequisite Skills====
* [[Composition of Functions]]
* [[Trigonometric Equations|Solve Trigonometric Equations]]
* [[Differentiation Rules|Rules for finding Derivatives]]
* [[Derivatives of the Trigonometric Functions]]

====Student Learning Outcomes====
* State the chain rule for the composition of two functions.
* Apply the chain rule together with the power rule.
* Apply the chain rule and the product/quotient rules correctly in combination when both are necessary.
* Recognize and apply the chain rule for a composition of three or more functions.
* Use interchangeably the Newton and Leibniz Notation for the Chain Rule.

===Week 6===
====Sections====
3.7

====Topics====
[[Derivatives of Inverse Functions]]

====Prerequisite Skills====
* [[One-to-one functions|Injective Functions]]
* [[Inverse Functions]]
* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

====Student Learning Outcomes====
* State the Inverse Function Theorem for Derivatives.
* Apply the Inverse Function Theorem to find the derivative of a function at a point given its inverse and a point on its graph.
* Derivatives of the inverse trigonometric functions.

===Week 6/7===
====Sections====
3.8

====Topics====
[[Implicit Differentiation]]

====Prerequisite Skills====
* [[Implicit and explicit equations]]
* [[Linear Equations|Linear Functions and Slope]]
* [[Functions|Function evaluation]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

====Student Learning Outcomes====
* Assuming $ y $ is implicitly a function of $ x $, find the derivative of $ y $ with respect to $ x $.
* Assuming $ y $ is implicitly a function of $ x $, and given an equation relating $ y $ to $ x $, find the derivative of $ y $ with respect to $ x $.
* Find the equation of a line tangent to an implicitly defined curve at a point.

===Week 7===
====Sections====
3.9

====Topics====
[[Derivatives of Exponential and Logarithmic Functions]]

====Prerequisite Skills====
* [[Logarithmic Functions|Properties of logarithms]]
* [[The Limit of a Function]]
* [[Differentiation Rules]]
* [[The Chain Rule]]
* [[Implicit Differentiation]]

====Student Learning Outcomes====
* Find the derivative of functions that involve exponential functions.
* Find the derivative of functions that involve logarithmic functions.
* Use logarithmic differentiation to find the derivative of functions containing combinations of powers, products, and quotients.

===Week 7/8===
====Sections====
4.1

====Topics====
[[Related Rates]]

====Prerequisite Skills====
* Formulas for area, volume, etc.
* Similar triangles to form proportions
* [[Trigonometric Functions]]
* [[Properties of the Trigonometric Functions|Trigonometric Identities]]
* [[Differentiation Rules]]
* [[Implicit Differentiation]]

====Student Learning Outcomes====
* Express changing quantities in terms of derivatives.
* Find relationships among the derivatives in a given problem.
* Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.

===Week 8===
====Sections====
4.2

====Topics====
[[Linear Approximations and Differentials]]

====Prerequisite Skills====
* [[Mathematical Error|Definition of Error in mathematics]]
* [[Linear Equations|Slope of a Line]]
* [[Defining the Derivative|Equation of the tangent line]]
* [[Derivatives Rates of Change|Leibnitz notation of the derivative]]

====Student Learning Outcomes====
* Approximate the function value close to the center of the linear approximation using the linearization.
* Given an expression to be evaluated/approximated, come up with the function and its linearization.
* Understand the formula for the differential; how it can be used to estimate the change in the dependent variable quantity, given the small change in the independent variable quantity.
* Use the information above to estimate potential relative (and percentage) error.

===Week 8/9===
====Sections====
4.3

====Topics====
[[Maxima and Minima]]

====Prerequisite Skills====
* [[The First Derivative Test|Increasing and decreasing functions]]
* [[Solving Equations and Inequalities|Solve an algebraic equation]]
* [[Interval Notation|Interval notation]]
* [[Trigonometric Equations]]
* [[Differentiation Rules]]
* [[Derivatives of the Trigonometric Functions]]
* [[Derivatives of Exponential and Logarithmic Functions]]
* [[Continuity]]

====Student Learning Outcomes====
* Know the definitions of absolute and local extrema.
* Know what a critical point is and locate it (them).
* Use the Extreme Value Theorem to find the absolute extrema of a continuous function on a closed interval.

===Week 9===
====Sections====
4.4

====Topics====
[[Mean Value Theorem]]

====Prerequisite Skills====
* [[Functions|Evaluating Functions]]
* [[Continuity]]
* [[Defining the Derivative|Slope of a Line]]

====Student Learning Outcomes====
* Determine if the MVT applies given a function on an interval.
* Find $ c $ in the conclusion of the MVT (if algebraically feasible).
* Know the first 3 Corollaries of MVT (especially the 3rd).

===Week 9===
====Sections====
4.5

====Topics====
[[Derivatives and the Shape of a Graph]]

====Prerequisite Skills====
* [[Functions|Evaluating Functions]]
* [[Maxima and Minima|Critical Points of a Function]]
* [[Derivatives and the Shape of a Graph|Second Derivatives]]

====Student Learning Outcomes====
* Use the First Derivative Test to find intervals on which the function is increasing and decreasing and the local extrema and their type.
* Use the Concavity Test (aka the Second Derivative Test for Concavity) to find the intervals on which the function is concave up and down, and point(s) of inflection.
* Understand the shape of the graph, given the signs of the first and second derivatives.

===Week 10===
====Sections====
4.7

====Topics====
[[Applied Optimization Problems]]

====Prerequisite Skills====
* Formulas pertaining to area and volume
* [[Functions|Evaluating Functions]]
* [[Trigonometric Equations]]
* [[Maxima and Minima|Critical Points of a Function]]

====Student Learning Outcomes====
* Set up a function to be optimized and find the value(s) of the independent variable which provide the optimal solution.

===Week 10===
====Sections====
4.8

====Topics====
[[L’Hôpital’s Rule]]

====Prerequisite Skills====
* [[Rational Functions|Re-expressing Rational Functions]]
* [[The Limit of a Function|When a Limit is Undefined]]
* [[The Derivative as a Function]]

====Student Learning Outcomes====
* Identify indeterminate forms produced by quotients, products, subtractions, and powers, and apply L’Hôpital’s rule in each case.
* Recognize when to apply L’Hôpital’s rule.

===Week 11===
====Sections====
4.10

====Topics====
[[Antiderivatives]]

====Prerequisite Skills====
* [[Inverse Functions]]
* [[The Derivative as a Function]]
* [[Differentiation Rule]]
* [[Derivatives of the Trigonometric Functions]]

====Student Learning Outcomes====
* Find the general antiderivative of a given function.
* Explain the terms and notation used for an indefinite integral.
* State the power rule for integrals.
* Use anti-differentiation to solve simple initial-value problems.

===Week 11/12===
====Sections====
5.1

====Topics====
[[Approximating Areas]]

====Prerequisite Skills====
* [[Sigma notation]]
* [[Area of a rectangle]]
* [[Continuity]]
* [[Toolkit Functions]]

====Student Learning Outcomes====
* Calculate sums and powers of integers.
* Use the sum of rectangular areas to approximate the area under a curve.
* Use Riemann sums to approximate area.

==Topics List - Table==

{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

2.2

||

[[The Limit of a Function]]

||

* [[Functions|Evaluation of a function]] including the [[Absolute Value Functions| Absolute Value]] , [[Rational Functions|Rational]] , and [[Piecewise Functions|Piecewise]] functions
* [[Functions|Domain and Range of a Function]]

||

*Describe the limit of a function using correct notation.
*Use a table of values to estimate the limit of a function or to identify when the limit does not exist.
*Use a graph to estimate the limit of a function or to identify when the limit does not exist.
*Define one-sided limits and provide examples.
*Explain the relationship between one-sided and two-sided limits.
*Describe an infinite limit using correct notation.
*Define a vertical asymptote.

|-

|Week 1/2

||

2.3

||

[[The Limit Laws]]

||

*[[Factoring Polynomials]]
*[[Simplifying Radicals|Identifying conjugate radical expressions]]
*[[Rational Expression|Simplifying rational expressions]]
*[[Domain of a Function|Evaluating piecewise functions]]
*[[Trigonometric Functions|The trigonometric functions]]

||

*Recognize the basic limit laws.
*Use the limit laws to evaluate the limit of a function.
*Evaluate the limit of a function by factoring.
*Use the limit laws to evaluate the limit of a polynomial or rational function.
*Evaluate the limit of a function by factoring or by using conjugates.
*Evaluate the limit of a function by using the squeeze theorem.
*Evaluate left, right, and two sided limits of piecewise defined functions.
*Evaluate limits of the form K/0, K≠0.
*Establish and use this to evaluate other limits involving trigonometric functions.

|-

|Week 2/3

||

2.4

||

[[Continuity]]

||

* [[Functions|Domain and Range of a Function]]
* [[Interval Notation|Interval Notation]]
* [[Limits of Functions|Evaluate limits]]
* [[The Limit Laws]]
* [[Polynomial Functions|Finding roots of a function]]

||

* Continuity at a point.
* Describe three kinds of discontinuities.
* Define continuity on an interval.
* State the theorem for limits of composite functions and use the theorem to evaluate limits.
* Provide an example of the intermediate value theorem.

|-

|Week 3

||

4.6

||

[[Limits at Infinity and Asymptotes]]

||

* [[The Limit Laws]]
* [[Continuity]]

||

* Calculate the limit of a function that is unbounded.
* Identify a horizontal asymptote for the graph of a function.

|-

|Week 3/4

||

3.1

||

[[Defining the Derivative]]

||

* [[Functions|Evaluation of a function at a value]]
* [[Linear Functions and Slope|The equation of a line and its slope]]
* [[Limits of Functions|Evaluating limits]]
* [[Continuity]]

||

* Recognize the meaning of the tangent to a curve at a point.
* Calculate the slope of a secant line (average rate of change of a function over an interval).
* Calculate the slope of a tangent line.
* Find the equation of the line tangent to a curve at a point.
* Identify the derivative as the limit of a difference quotient.
* Calculate the derivative of a given function at a point.

|-

|Week 4

||

3.2

||

[[The Derivative as a Function]]

||

* [[Functions and their graphs|Graphing Functions]]
* [[Continuity|Continuity of a function at a point]]
* [[Defining the Derivative|The derivative represents the slope of the curve at a point]]
* [[Limits of Functions|When a limit fails to exist]]
* [[The Limit Laws]]

||

* Define the derivative function of a given function.
* Graph a derivative function from the graph of a given function.
* State the connection between derivatives and continuity.
* Describe three conditions for when a function does not have a derivative.
* Explain the meaning of and compute a higher-order derivative.

|-

|Week 4/5

||

3.3

||

[[Differentiation Rules]]

||

* [[Simplifying Radicals|Radical & Rational Exponents]]
* [[Simplifying Exponents|Re-write negative exponents]]
* [[The Limit Laws]]
* [[The Derivative as a Function]]

||

* State the constant, constant multiple, and power rules.
* Apply the sum and difference rules to combine derivatives.
* Use the product rule for finding the derivative of a product of functions.
* Use the quotient rule for finding the derivative of a quotient of functions.
* Extend the power rule to functions with negative exponents.
* Combine the differentiation rules to find the derivative of a polynomial or rational function.

|-

|Week 5

||

3.4

||

[[Derivatives_Rates_of_Change|Derivatives as Rates of Change]]

||

* [[Functions|Function evaluation at a value]]
* [[Solving Equations and Inequalities|Solving an algebraic equation]]
* '''[[Understanding of Velocity and Acceleration]]'''
* [[Differentiation Rules]]

||

* Determine a new value of a quantity from the old value and the amount of change.
* Calculate the average rate of change and explain how it differs from the instantaneous rate of change.
* Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.
* Predict the future population from the present value and the population growth rate.
* Use derivatives to calculate marginal cost and revenue in a business situation.

|-

|Week 5

||

3.5

||

[[Derivatives of the Trigonometric Functions]]

||

* [[Properties of the Trigonometric Functions|Trigonometric identities]]
* [[Graphs of the Sine and Cosine Functions]]
* [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
* [[Differentiation Rules|Rules for finding Derivatives]]

||

* Find the derivatives of the sine and cosine function.
* Find the derivatives of the standard trigonometric functions.
* Calculate the higher-order derivatives of the sine and cosine.

|-

|Week 6

||

3.6
||

[[Chain_Rule|The Chain Rule]]

||

* [[Composition of Functions]]
* [[Trigonometric Equations|Solve Trigonometric Equations]]
* [[Differentiation Rules|Rules for finding Derivatives]]
* [[Derivatives of the Trigonometric Functions]]

||

* State the chain rule for the composition of two functions.
* Apply the chain rule together with the power rule.
* Apply the chain rule and the product/quotient rules correctly in combination when both are necessary.
* Recognize and apply the chain rule for a composition of three or more functions.
* Use interchangeably the Newton and Leibniz Notation for the Chain Rule.

|-

|Week 6

||

3.7

||

[[Derivatives of Inverse Functions]]

||

* [[One-to-one functions|Injective Functions]]
* [[Inverse Functions]] 
* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

||

* State the Inverse Function Theorem for Derivatives.
* Apply the Inverse Function Theorem to find the derivative of a function at a point given its inverse and a point on its graph.
* Derivatives of the inverse trigonometric functions.

|-

|Week 6/7

||

3.8

||

[[Implicit Differentiation]]

||

* '''[[Implicit and explicit equations]]'''
* [[Linear Equations|Linear Functions and Slope]]
* [[Functions|Function evaluation]]
* [[Differentiation Rules]]
* [[The Chain Rule]]

||

* Assuming, for example, y is implicitly a function of x, find the derivative of y with respect to x.
* Assuming, for example, y is implicitly a function of x, and given an equation relating y to x, find the derivative of y with respect to x.
* Find the equation of a line tangent to an implicitly defined curve at a point.

|-

|Week 7

||

3.9

||

[[Derivatives of Exponential and Logarithmic Functions]]

||

* [[Logarithmic Functions|Properties of logarithms]] <
* [[The Limit of a Function]]
* [[Differentiation Rules]]
* [[The Chain Rule]]
* [[Implicit Differentiation]]

||

* Find the derivative of functions that involve exponential functions.
* Find the derivative of functions that involve logarithmic functions.
* Use logarithmic differentiation to find the derivative of functions containing combinations of powers, products, and quotients.

|-

|Week 7/8

||

4.1

||

[[Related Rates]]

||

* '''Formulas for area, volume, etc'''
* '''Similar triangles to form proportions'''
* [[Trigonometric Functions]] 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]]
* [[Differentiation Rules]]
* [[Implicit Differentiation]]

||

* Express changing quantities in terms of derivatives.
* Find relationships among the derivatives in a given problem.
* Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.

|-

|Week 8

||

4.2

||

[[Linear Approximations and Differentials]]

||

* [[Mathematical Error| Definition of Error in mathematics]]
* [[Linear Equations|Slope of a Line]]
* [[Defining the Derivative|Equation of the tangent line]]
* [[Derivatives Rates of Change|Leibnitz notation of the derivative]]

||

* Approximate the function value close to the center of the linear approximation using the linearization.
* Given an expression to be evaluated/approximated, come up with the function and its linearization
* Understand the formula for the differential; how it can be used to estimate the change in the dependent variable quantity, given the small change in the independent variable quantity.
* Use the information above to estimate potential relative (and percentage) error

|-

|Week 8/9

||

4.3

||

[[Maxima and Minima]]

||

* [[The First Derivative Test|Increasing and decreasing functions]]
* [[Solving Equations and Inequalities|Solve an algebraic equation]]
* [[Interval Notation|Interval notation]]
* [[Trigonometric Equations]]
* [[Differentiation Rules]]
* [[Derivatives of the Trigonometric Functions]]
* [[Derivatives of Exponential and Logarithmic Functions]]
* [[Continuity]]

||
*
* Know the definitions of absolute and local extrema.
* Know what a critical point is and locate it (them).
* Use the Extreme Value Theorem to find the absolute extrema of a continuous function on a closed interval.

|-

|Week 9

||

4.4

||

[[Mean Value Theorem]]

||

* [[Functions|Evaluating Functions]]
* [[Continuity]]
* [[Defining the Derivative|Slope of a Line]]

||

* Determine if the MVT applies given a function on an interval.
* Find c in the conclusion of the MVT (if algebraically feasible)
* Know the first 3 Corollaries of MVT (especially the 3rd)

|-

|Week 9

||

4.5

||

[[Derivatives and the Shape of a Graph]]

||

* [[Functions|Evaluating Functions]]
* [[Maxima and Minima|Critical Points of a Function]]
* [[Derivatives and the Shape of a Graph|Second Derivatives]]

||

* Use the First Derivative Test to find intervals on which the function is increasing and decreasing and the local extrema and their type
* Use the Concavity Test (aka the Second Derivative Test for Concavity) to find the intervals on which the function is concave up and down, and point(s) of inflection
* Understand the shape of the graph, given the signs of the first and second derivatives.

|-

|Week 10

||

4.7

||

[[Applied Optimization Problems]]

||

* '''Formulas pertaining to area and volume'''
* [[Functions|Evaluating Functions]]
* [[Trigonometric Equations]]
* [[Maxima and Minima|Critical Points of a Function]]

||

* Set up a function to be optimized and find the value(s) of the independent variable which provide the optimal solution.

|-

|Week 10

||

4.8

||

[[L’Hôpital’s Rule]]

||

* [[Rational Functions| Re-expressing Rational Functions ]]
* [[The Limit of a Function|When a Limit is Undefined]]
* [[The Derivative as a Function]]

||

* Identify indeterminate forms produced by quotients, products, subtractions, and powers, and apply L’Hôpital’s rule in each case.
* Recognize when to apply L’Hôpital’s rule.

|-

|Week 11

||

4.10

||

[[Antiderivatives]]

||

* [[Inverse Functions]]
* [[The Derivative as a Function]]
* [[Differentiation Rule]]
* [[Derivatives of the Trigonometric Functions]]

||

* Find the general antiderivative of a given function.
* Explain the terms and notation used for an indefinite integral.
* State the power rule for integrals.
* Use anti-differentiation to solve simple initial-value problems.

|-

|Week 11/12

||

5.1

||

[[Approximating Areas]]

||

* '''[[Sigma notation]]'''
* '''[[Area of a rectangle]]'''
* [[Continuity]]
* [[Toolkit Functions]]

||

* Calculate sums and powers of integers.
* Use the sum of rectangular areas to approximate the area under a curve.
* Use Riemann sums to approximate area.

|-

|Week 12

||

5.2

||

[[The Definite Integral]]

||

* [[Interval Notation|Interval notation]]
* [[Antiderivatives]]
* [[The Limit of a Function|Limits of Riemann Sums]]
* [[Continuity]]

||

* State the definition of the definite integral.
* Explain the terms integrand, limits of integration, and variable of integration.
* Explain when a function is integrable.
* Rules for the Definite Integral.
* Describe the relationship between the definite integral and net area.
* Use geometry and the properties of definite integrals to evaluate them.
* Calculate the average value of a function.

|-

|Week 12/13

||

5.3

||

[[The Fundamental Theorem of Calculus]]

||

* [[The Derivative as a Function|The Derivative of a Function]]
* [[Antiderivatives]]
* [[Mean Value Theorem]]
* [[Inverse Functions]]

||

* Describe the meaning of the Mean Value Theorem for Integrals.
* State the meaning of the Fundamental Theorem of Calculus, Part 1.
* Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
* State the meaning of the Fundamental Theorem of Calculus, Part 2.
* Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
* Explain the relationship between differentiation and integration.

|-

|Week 13

||

5.4

||

[[Integration Formulas and the Net Change Theorem]]

||

* [[Antiderivatives|Indefinite integrals]]
* [[The Fundamental Theorem of Calculus|The Fundamental Theorem (part 2)]]

||

* Apply the basic integration formulas.
* Explain the significance of the net change theorem.
* Use the net change theorem to solve applied problems.
* Apply the integrals of odd and even functions.

|-

|Week 14

||

5.5

||

[[Integration by Substitution]]

||

* [[The Definite Integral|Solving Basic Integrals]]
* [[The Derivative as a Function|The Derivative of a Function]]
* '''[[Change of Variables]]'''

||

* Use substitution to evaluate indefinite integrals.
* Use substitution to evaluate definite integrals.

|-

|Week 14/15

||

5.6

||

[[Integrals Involving Exponential and Logarithmic Functions]]

||

* [[Exponential Functions]]
* [[Logarithmic Functions]]
* [[Differentiation Rules]]
* [[Antiderivatives]]

||

* Integrate functions involving exponential functions.
* Integrate functions involving logarithmic functions.

|-

|Week 15

||

5.7

||

[[Integrals Resulting in Inverse Trigonometric Functions]]

||

* [[The inverse sine, cosine and tangent functions|Trigonometric functions and their inverses]]
* [[One-to-one functions|Injective Functions]]
* [[The Definite Integral|Rules for Integration]]

||

* Integrate functions resulting in inverse trigonometric functions.

|}

Main Page

2025-01-21T15:19:14Z

Juan.gutierrez3: /* Undergraduate Studies */

<strong>UTSA Department of Mathematics</strong>

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3203]] Abstract Linear Algebra
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Abstract Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core M.Sc. Studies ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.
* Two courses in the Analysis & Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5173]] Algebra I & [[MAT5243]] General Topology I.
** [[MAT5243]] General Topology I & [[MAT5253]] General Topology II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra I & [[MAT5203]] Analysis I.
** [[MAT5173]] Algebra I & [[MAT5123]] Cryptography I.
** [[MAT5123]] Cryptography I & [[MAT5323]] Cryptography II.
* Two course in discrete mathematics among the following:
** [[MAT5423]] Discrete Mathematics I
** [[MAT5433]] Discrete Mathematics II
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I
** [[MDC5153]] Data Analytics
* [[MAT5283]] Linear Algebra

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (Pure, Applied tracks)
* [[MAT5123]] Cryptography (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (Pure, Applied tracks))
* [[MAT5213]] Analysis II (Pure track)
* [[MAT5113]] Computing for Mathematics (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[MAT5243]] General Topology
* [[MAT5253]] General Topology II
* [[MAT5323]] Cryptography II
* [[MAT5183]] Algebra II
* [[MAT5223]] Theory of Functions of a Complex Variable
* [[MAT5343]] Differential Geometry

=== M.Sc. Track in Applied & Industrial Mathematics ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MDC5153

2023-06-30T17:17:03Z

Juan.gutierrez3: /* Mathematical Foundations of Data Analytics MDC4153/MDC5153 */

== Mathematical Foundations of Data Analytics MDC4153/MDC5153 ==

'''Catalog entry'''

''Prerequisite'': [[MAT2253]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': Data Analytics refers to classic data analysis plus all other areas that support it. This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

This course uses generative AI tools to aid in data analysis. Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || None. || Understanding of government databases. Conduct basic data exploration. Identity questions answerable with data available for a specific problem.
|-
| 2 || || Scripts vs. compiled code. || Previous exposure to computer programming in any language. || Basic numeric operations in scripting vs. compiled code. Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments.
|-
| 3 || || Ethics in data analysis. || None. || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 4 - 5 || || Linear discriminants || Linear Algebra and Calculus I || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || Scripts vs. compiled code (week 2) || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || Linear discriminants (week 4-5) || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || Scripts vs. compiled code (week 2) || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || Generalized regressions (week 7) || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || Scripts vs. compiled code (week 2) || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || Clustering (week 9) || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || Scripts vs. compiled code (week 2) || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || Scripts vs. compiled code (week 2) || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || Entire course || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-06-12T16:54:09Z

Juan.gutierrez3: Changed from content to redirection to MDC5153

#REDIRECT[[MDC5153]]

MDC5153

2023-06-12T16:53:13Z

Juan.gutierrez3: Added content in this page instead of directing.

== Mathematical Foundations of Data Analytics MDC4153/MDC5153 ==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': Data Analytics refers to classic data analysis plus all other areas that support it. This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

This course uses generative AI tools to aid in data analysis. Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || None. || Understanding of government databases. Conduct basic data exploration. Identity questions answerable with data available for a specific problem.
|-
| 2 || || Scripts vs. compiled code. || Previous exposure to computer programming in any language. || Basic numeric operations in scripting vs. compiled code. Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments.
|-
| 3 || || Ethics in data analysis. || None. || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 4 - 5 || || Linear discriminants || Linear Algebra and Calculus I || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || Scripts vs. compiled code (week 2) || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || Linear discriminants (week 4-5) || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || Scripts vs. compiled code (week 2) || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || Generalized regressions (week 7) || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || Scripts vs. compiled code (week 2) || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || Clustering (week 9) || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || Scripts vs. compiled code (week 2) || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || Scripts vs. compiled code (week 2) || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || Entire course || Exposure to presentation of results in front an audience of experts.
|}

Main Page

2023-06-12T16:51:02Z

Juan.gutierrez3: /* Upper Division */ Corrected course code MDC for Mathematical Foundations of Data Analytics

<strong>UTSA Department of Mathematics</strong>

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3203]] Abstract Linear Algebra
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Abstract Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core M.Sc. Studies ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.
* Two courses in the Analysis & Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5173]] Algebra I & [[MAT5243]] General Topology I.
** [[MAT5243]] General Topology I & [[MAT5253]] General Topology II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra I & [[MAT5203]] Analysis I.
** [[MAT5173]] Algebra I & [[MAT5123]] Cryptography I.
** [[MAT5123]] Cryptography I & [[MAT5323]] Cryptography II.
* Two course in discrete mathematics among the following:
** [[MAT5423]] Discrete Mathematics I
** [[MAT5433]] Discrete Mathematics II
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I
** [[MDC5153]] Data Analytics
* [[MAT5283]] Linear Algebra

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (Pure, Applied tracks)
* [[MAT5123]] Cryptography (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (Pure, Applied tracks))
* [[MAT5213]] Analysis II (Pure track)
* [[MAT5113]] Computing for Mathematics (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[MAT5243]] General Topology
* [[MAT5253]] General Topology II
* [[MAT5323]] Cryptography II
* [[MAT5183]] Algebra II
* [[MAT5223]] Theory of Functions of a Complex Variable
* [[MAT5343]] Differential Geometry

=== M.Sc. Track in Applied & Industrial Mathematics ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MAT1073

2023-06-12T16:49:12Z

Juan.gutierrez3: Added title level 1 with course name

= College Algebra for Scientists and Engineers - MAT 1073 =

==Course Catalog==
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

==Topics List==
{| class="wikitable sortable"
! Week !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
Fundamentals
||
* [[Algebraic Properties]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills

||
Students will be able to correctly identify the algebraic properties:
* Additive & Multiplicative identity
* Additive & Multiplicative inverse
* Commutative property
* Associative property
* Distributive property

Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:
* Solving mathematical equations
* Simplifying/evaluating mathematical expressions
|-
|Week 2
||
Fundamentals
||
* [[Fractions]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Algebraic Properties]]

||
Students will be able to add, subtract fractions:
* Determine common denominators and equivalent fractions
* Work with proper and improper fractions
* Simplify to lowest terms

Students will be able to multiply, and divide fractions:
* Work with proper and improper fractions
* Simplify to lowest terms

|-
|Week 2
||
Fundamentals
||
* [[Factoring]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Algebraic Properties]]

||
Students will be able to:
* Identify factored vs non-factored forms of a polynomial
* Successfully factor binomials & trinomials and difference of squares into two binomial terms
* Factor out GCF
* Multiply and / or distribute to check their factors are correct
* Differentiate between factors and terms of a polynomial expression

|-
|Week 3
||
Module 1.1
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Algebraic Properties]]
* Understanding of the Cartesian coordinate system

||
Students will be able to:
* Solving linear equations in one variable
* Determine a linear equation
* Write and interpret a linear equation
* Graph a linear equation
|-
|Week 3
||
Module 1.2
||
* [[Systems of Equations in Two Variables]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of [[Linear Equations]] (Module 1.1)
||
Students will be able to:
* Solve systems of equations by graphing.
* Solve systems of equations by substitution.
* Solve systems of equations by elimination
* Identify inconsistent systems of equations containing two variables.
* Express the solution of a system of dependent equations containing two variables.
|-
|Week 4
||
Module 2.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
||
Students will be able to:
* Determine whether a relation represents a function.
|-
|Week 4
||
Module 2.2
||
* [[Function Notation]]
||
* Basic understanding of [[Functions]] (Module 2.1)
||
Students will be able to:
* Find the value of a [[Functions]]
* Graph the functions listed in the library of functions.
* Determine whether a function is one-to-one.
* Use the vertical line test to identify functions.
|-
|Week 4
||
Module 2.2
||
* [[Domain of a Function]]
||
* An understanding of [[Function Notation]]
||
Students will be able to:
* Find the domain of a function defined by an equation.

|-
|Week 4
||
Module 2.2
||
* [[Range of a Function]]
||
* An understanding of [[Function Notation]]
||
Students will be able to:
* Find the range of a function defined by an equation.
|-
|Week 4
||
Module 2.2
||
* [[Toolkit Functions]]
||
* Basic understanding of [[Functions]] (Module 2.1)
||
Students will be able to:
* Identify the basic toolkit functions
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 2.2)

|-
|Week 5
||
Module 3.1
||
* [[Composition of Functions]]
||
* Basic understanding of [[Functions]] (Module 2.1)
* Basic understanding of [[Function Notation]] (Module 2.2)
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
||
Students will be able to:
* Combine functions using [[Algebraic Properties]]
* Create a new function by composition of functions
* Evaluate composite functions
* Find the domain of a composite function
* Decompose a composite function into its component functions
|-
|Week 5
||
Module 3.2
||
* [[Inverse Functions]]
||
* Basic understanding of [[Functions]] (Module 2.1)
* Basic understanding of [[Function Notation]] (Module 2.2)
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
* Basic understanding of [[Composition of Functions]] (Module 3.1)
||
Students will be to able to:
* Verify inverse functions using [[Algebraic Properties]]
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
* Find or evaluate the inverse of a function
* Use the graph of a one-to-one function to graph its inverse function on the same axes

|-
|Week 6
||
Module 4.1
||
* [[Exponential Properties]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Algebraic Properties]]
||
Students will be able to:
* Use the product rule for exponents.
* Use the quotient rule for exponents.
* Use the power rule for exponents.
|-
|Week 6
||
Module 4.2
||
* [[Exponential Functions]]
||
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions (Module 2.2)
* Basic understanding of [[Exponential Properties]] (Module 4.1)
||
Students will be able to:
* Determine the difference between [[Linear Equations|Linear]] and Exponential Functions (Module 1.1)
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Evaluate exponential functions with base e.
* Evaluate exponential functions with base 10.
* Graph exponential functions.

|-
|Week 7
||
Module 5.1
||
* [[Logarithmic Properties]]
||
* Basic understanding of [[Exponential Properties]] (Module 4.1)
||
Students will be to able:
* Rewriting from exponential form to logarithmic form and vice versa
:-y=b^x\equiv\log_b(y)=x
* Use the product rule for logarithms.
* Use the quotient rule for logarithms.
* Use the power rule for logarithms.
* Expand logarithmic expressions.
* Condense logarithmic expressions.
* Use the change-of-base formula for logarithms.

|-
|Week 7
||
Module 5.2
||
* [[Logarithmic Functions]]
||
* Basic understanding of [[Inverse Functions]] (Module 3.2)
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions. (Module 2.2)
* Basic understanding of [[Exponential Properties]] (Module 4.1)

||
Students will be able to:
* Evaluate logarithms.
* Use common logarithms.
* Use natural logarithms.
* Graph logarithmic functions.

|-
|Week 8
||
Module 6.2
||
* [[Quadratic Equations]]
||
* Basic arithmetic skills
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of [[Factoring]]
||
Students will be able to:
* Determine complex number solutions
* Determine solutions of quadratic equations using factoring techniques
* Determine solutions of quadratic equations using Quadratic Formula

|-
|Week 8
||
Module 6.2
||
* [[Quadratic Functions]]
||
* Basic understanding of [[Quadratic Equations]]

||
Students will be able to:
* Basic understanding of a polynomial expression.
* Recognize characteristics of parabolas
* Understand how the graph of a parabola is related to its quadratic function
* Determine a quadratic function's minimum or maximum value
* Solve problems involving a quadratic function's minimum or maximum value

|-
|Week 9
||
Module 7.1
||
* [[Dividing Polynomials]]
||
* Basic understanding of [[Fractions]] (Fundamentals)
* Basic understanding of [[Factoring]] (Fundamentals)
* The student recalls the graphs and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
* Basic understanding of [[Quadratic Functions]] (Module 6.2)

||
Students will be able to:
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
* Use long division to divide polynomials
* Use synthetic division to divide polynomials
|-
|Week 9
||
Module 7.2
||
* [[Factoring Polynomials|Zeros of Polynomials]]
||
* Basic understanding of [[Fractions]] (Fundamentals)
* Basic understanding of [[Functions]] (Module 2.1)
* Basic understanding of [[Dividing Polynomials]] (Module 7.1)
||
Students will be able to:
* Evaluate a polynomial using the Remainder Theorem
* Use the Factor Theorem to solve a polynomial equation
* Use the Rational Zero Theorem to find rational zeros
* Find zeros of a polynomial function
* Solve real-world applications of polynomial equations

|-
|Week 10
||
Module 8.1
||
* [[Power and Polynomial Functions]]
||
* Basic understanding of [[Factoring]] (Fundamentals)
* Basic understanding of [[Quadratic Functions]] (Module 6.2)
* Basic understanding of [[Dividing Polynomials]] (Module 7.1)
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]] (Module 7.2)
||
Students will be able to:
* Find the average rate of change of a function.
* Use a graph to determine where a function is increasing, decreasing, or constant.
* Use a graph to locate local maxima and local minima.
* Use a graph to locate the absolute maximum and absolute minimum.
* Identify end behavior of power functions.

|-
|Week 10
||
Module 8.2
||
* [[Graphs of Polynomials]]
||
* Basic understanding of [[Dividing Polynomials]] (Module 7.1)
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]] (Module 7.2)
||
Students will be able to:
* Recognize characteristics of graphs of polynomial functions
* Use [[Factoring]] to find zeros of polynomial functions
* Identify zeros and their multiplicities
* Determine end behavior of polynomial functions
* Understand the relationship between degree and turning points
* Graph polynomial functions

|-
|Week 11
||
Module 9.1
||
* [[Rational Expressions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* Basic understanding of [[Fractions]] (Fundamentals)
||
Students will be able to:
* Simplify rational expressions.
* Multiply rational expressions.
* Divide rational expressions.
* Add and subtract rational expressions.

|-
|Week 11
||
Module 9.2
||
* [[Graphs of Rational Functions]]
||
* Basic understanding of [[Rational Expressions]] (Module 9.1)
||
Students will be able to:
* Identify and graph vertical asymptotes
* Identify and graph horizontal asymptotes
* Determine behavior of rational functions around vertical asymptotes
* Find the domains of rational functions
* Graph rational functions

|-
|Week 12
||
Module 10.1
||
* [[Single Transformations of Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
||
Students will be able to:
* Graph functions using vertical and horizontal shifts
* Graph functions using reflections about the x-axis and the y-axis

|-
|Week 12
||
Module 10.2
||
* [[Multiple Transformations of Functions]]
||
* Understanding of [[Single Transformations of Functions]] (Module 10.1)
||
Students will be able to:
* Determine whether a function is even, odd, or neither
* Graph functions using compressions and stretches
* Combine transformations

|}

MAT5153

2023-06-07T15:20:12Z

Juan.gutierrez3:

== Mathematical Foundations of Data Analytics MDC4153/MAT5153 ==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': Data Analytics refers to classic data analysis plus all other areas that support it. This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

This course uses generative AI tools to aid in data analysis. Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || None. || Understanding of government databases. Conduct basic data exploration. Identity questions answerable with data available for a specific problem.
|-
| 2 || || Scripts vs. compiled code. || Previous exposure to computer programming in any language. || Basic numeric operations in scripting vs. compiled code. Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments.
|-
| 3 || || Ethics in data analysis. || None. || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 4 - 5 || || Linear discriminants || Linear Algebra and Calculus I || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || Scripts vs. compiled code (week 2) || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || Linear discriminants (week 4-5) || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || Scripts vs. compiled code (week 2) || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || Generalized regressions (week 7) || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || Scripts vs. compiled code (week 2) || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || Clustering (week 9) || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || Scripts vs. compiled code (week 2) || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || Scripts vs. compiled code (week 2) || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || Entire course || Exposure to presentation of results in front an audience of experts.
|}

Main Page

2023-05-16T16:01:25Z

Juan.gutierrez3: /* Lower Division */ Updated tittle for MDC1213

<strong>UTSA Department of Mathematics</strong>

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MAT5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3203]] Abstract Linear Algebra
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Abstract Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core M.Sc. Studies ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.
* Two courses in the Analysis & Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5173]] Algebra I & [[MAT5243]] General Topology I.
** [[MAT5243]] General Topology I & [[MAT5253]] General Topology II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra I & [[MAT5203]] Analysis I.
** [[MAT5173]] Algebra I & [[MAT5123]] Cryptography I.
** [[MAT5123]] Cryptography I & [[MAT5323]] Cryptography II.
* Two course in discrete mathematics among the following:
** [[MAT5423]] Discrete Mathematics I
** [[MAT5433]] Discrete Mathematics II
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I
** [[MDC5153]] Data Analytics
* [[MAT5283]] Linear Algebra

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (Pure, Applied tracks)
* [[MAT5123]] Cryptography (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (Pure, Applied tracks))
* [[MAT5213]] Analysis II (Pure track)
* [[MAT5113]] Computing for Mathematics (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[MAT5243]] General Topology
* [[MAT5253]] General Topology II
* [[MAT5323]] Cryptography II
* [[MAT5183]] Algebra II
* [[MAT5223]] Theory of Functions of a Complex Variable
* [[MAT5343]] Differential Geometry

=== M.Sc. Track in Applied & Industrial Mathematics ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MAT5153

2023-05-16T15:58:58Z

Juan.gutierrez3: Added reference to generative AI

== Mathematical Foundations of Data Analytics MDC4153/MAT5153 ==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': Data Analytics refers to classic data analysis plus all other areas that support it. This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks. This course uses generative AI tools to aid in data analysis.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || None. || Understanding of government databases. Conduct basic data exploration. Identity questions answerable with data available for a specific problem.
|-
| 2 || || Scripts vs. compiled code. || Previous exposure to computer programming in any language. || Basic numeric operations in scripting vs. compiled code. Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments.
|-
| 3 || || Ethics in data analysis. || None. || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 4 - 5 || || Linear discriminants || Linear Algebra and Calculus I || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || Scripts vs. compiled code (week 2) || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || Linear discriminants (week 4-5) || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || Scripts vs. compiled code (week 2) || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || Generalized regressions (week 7) || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || Scripts vs. compiled code (week 2) || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || Clustering (week 9) || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || Scripts vs. compiled code (week 2) || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || Scripts vs. compiled code (week 2) || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || Entire course || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-05-16T15:18:14Z

Juan.gutierrez3: Updated title and description

== Mathematical Foundations of Data Analytics MDC4153/MAT5153 ==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': Data Analytics refers to classic data analysis plus all other areas that support it. This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || None. || Understanding of government databases. Conduct basic data exploration. Identity questions answerable with data available for a specific problem.
|-
| 2 || || Scripts vs. compiled code. || Previous exposure to computer programming in any language. || Basic numeric operations in scripting vs. compiled code. Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments.
|-
| 3 || || Ethics in data analysis. || None. || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 4 - 5 || || Linear discriminants || Linear Algebra and Calculus I || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || Scripts vs. compiled code (week 2) || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || Linear discriminants (week 4-5) || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || Scripts vs. compiled code (week 2) || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || Generalized regressions (week 7) || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || Scripts vs. compiled code (week 2) || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || Clustering (week 9) || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || Scripts vs. compiled code (week 2) || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || Scripts vs. compiled code (week 2) || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || Entire course || Exposure to presentation of results in front an audience of experts.
|}

Main Page

2023-05-16T13:54:16Z

Juan.gutierrez3: /* Upper Division */ Corrected code and title

<strong>UTSA Department of Mathematics</strong>

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MAT5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3203]] Abstract Linear Algebra
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Abstract Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core M.Sc. Studies ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.
* Two courses in the Analysis & Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5173]] Algebra I & [[MAT5243]] General Topology I.
** [[MAT5243]] General Topology I & [[MAT5253]] General Topology II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra I & [[MAT5203]] Analysis I.
** [[MAT5173]] Algebra I & [[MAT5123]] Cryptography I.
** [[MAT5123]] Cryptography I & [[MAT5323]] Cryptography II.
* Two course in discrete mathematics among the following:
** [[MAT5423]] Discrete Mathematics I
** [[MAT5433]] Discrete Mathematics II
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I
** [[MDC5153]] Data Analytics
* [[MAT5283]] Linear Algebra

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (Pure, Applied tracks)
* [[MAT5123]] Cryptography (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (Pure, Applied tracks))
* [[MAT5213]] Analysis II (Pure track)
* [[MAT5113]] Computing for Mathematics (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[MAT5243]] General Topology
* [[MAT5253]] General Topology II
* [[MAT5323]] Cryptography II
* [[MAT5183]] Algebra II
* [[MAT5223]] Theory of Functions of a Complex Variable
* [[MAT5343]] Differential Geometry

=== M.Sc. Track in Applied & Industrial Mathematics ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MDC1213

2023-04-26T21:22:54Z

Juan.gutierrez3: Changed title

== Sociocultural Foundations of Mathematics, Data Science, and Computing- MDC1213==

'''Catalog entry'''

''Prerequisite'': None.

''Content'': This introductory survey course for freshmen aims to explore the connections between mathematics, data science, and artificial intelligence, with an emphasis on their roles in shaping and understanding human culture and experience. Students will be guided through a series of 30 lessons that delve into the ways these fields intersect with ideas, values, beliefs, and other cultural aspects, fostering aesthetic and intellectual creation. Throughout the course, students will have access to the GPT-4 language model to assist with content generation and idea exploration.

This course is intended to be part of the core curriculum in the area “Language, Philosophy and Culture (040)” (3 semester credit hours). Courses in this category focus on how ideas, values, beliefs, and other aspects of culture express and affect human experience. This requirement involves the exploration of ideas that foster aesthetic and intellectual creation in order to understand the human condition across cultures.

== Lesson Overview ==

Through these lessons, students will gain a foundational understanding of the intersections between mathematics, data science, and artificial intelligence, as well as their impact on the human experience across cultures. By leveraging GPT-4 for content generation and idea exploration, students will develop the skills necessary to engage with these fields in a culturally sensitive and ethically responsible manner.

# [[Introduction to Mathematics, Data Science, and Artificial Intelligence]]
# [[The Historical Evolution of Mathematics in Cultural Context]]
# [[How Data Science Has Shaped Society and Culture]]
# [[The Role of Artificial Intelligence in Understanding Human Behavior]]
# [[The Language of Mathematics: Symbols, Expressions, and Equations]]
# [[The Art of Problem Solving: Creativity in Mathematics]]
# [[Statistics and Probability: Interpreting Data and Predicting Outcomes]]
# [[Cultural Bias in Data Collection and Interpretation]]
# [[Machine Learning and Pattern Recognition in AI]]
# [[Ethical Considerations in Data Science and AI]]
# [[Mathematics and Art: Geometry, Proportion, and Symmetry]]
# [[The Golden Ratio and Fibonacci Sequence in Nature and Culture]]
# [[Information Theory: Quantifying Cultural Transmission]]
# [[Graph Theory and Social Network Analysis]]
# [[AI in Language and Communication: NLP and GPT-4]]
# [[The Impact of AI on Employment and the Future of Work]]
# [[Game Theory: Strategic Decision Making in Cultural Context]]
# [[Fractals, Chaos Theory, and Cultural Complexity]]
# [[Music, Mathematics, and AI: A Harmonious Intersection]]
# [[AI and Literature: Text Analysis, Generation, and Critique]]
# [[Mathematical Models in Economics and Social Sciences]]
# [[Big Data and Privacy: Balancing Utility and Ethics]]
# [[AI in Healthcare: Improving Outcomes and Reducing Disparities]]
# [[Climate Change, Sustainability, and Mathematical Modeling]]
# [[The Mathematics of Democracy: Voting Systems and Fair Representation]]
# [[Bias and Fairness in AI: Challenges and Solutions]]
# [[The Role of AI in Mental Health and Emotional Well-being]]
# [[AI and the Creative Arts: Exploring New Frontiers]]
# [[The Future of AI: Possibilities, Pitfalls, and Predictions]]
# [[Final Project: Applying Mathematics, Data Science, and AI to Cultural Analysis]]

MDC1213

2023-04-26T18:56:32Z

Juan.gutierrez3:

== Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context - MDC1213==

'''Catalog entry'''

''Prerequisite'': None.

''Content'': This introductory survey course for freshmen aims to explore the connections between mathematics, data science, and artificial intelligence, with an emphasis on their roles in shaping and understanding human culture and experience. Students will be guided through a series of 30 lessons that delve into the ways these fields intersect with ideas, values, beliefs, and other cultural aspects, fostering aesthetic and intellectual creation. Throughout the course, students will have access to the GPT-4 language model to assist with content generation and idea exploration.

This course is intended to be part of the core curriculum in the area “Language, Philosophy and Culture (040)” (3 semester credit hours). Courses in this category focus on how ideas, values, beliefs, and other aspects of culture express and affect human experience. This requirement involves the exploration of ideas that foster aesthetic and intellectual creation in order to understand the human condition across cultures.

== Lesson Overview ==

Through these lessons, students will gain a foundational understanding of the intersections between mathematics, data science, and artificial intelligence, as well as their impact on the human experience across cultures. By leveraging GPT-4 for content generation and idea exploration, students will develop the skills necessary to engage with these fields in a culturally sensitive and ethically responsible manner.

# [[Introduction to Mathematics, Data Science, and Artificial Intelligence]]
# [[The Historical Evolution of Mathematics in Cultural Context]]
# [[How Data Science Has Shaped Society and Culture]]
# [[The Role of Artificial Intelligence in Understanding Human Behavior]]
# [[The Language of Mathematics: Symbols, Expressions, and Equations]]
# [[The Art of Problem Solving: Creativity in Mathematics]]
# [[Statistics and Probability: Interpreting Data and Predicting Outcomes]]
# [[Cultural Bias in Data Collection and Interpretation]]
# [[Machine Learning and Pattern Recognition in AI]]
# [[Ethical Considerations in Data Science and AI]]
# [[Mathematics and Art: Geometry, Proportion, and Symmetry]]
# [[The Golden Ratio and Fibonacci Sequence in Nature and Culture]]
# [[Information Theory: Quantifying Cultural Transmission]]
# [[Graph Theory and Social Network Analysis]]
# [[AI in Language and Communication: NLP and GPT-4]]
# [[The Impact of AI on Employment and the Future of Work]]
# [[Game Theory: Strategic Decision Making in Cultural Context]]
# [[Fractals, Chaos Theory, and Cultural Complexity]]
# [[Music, Mathematics, and AI: A Harmonious Intersection]]
# [[AI and Literature: Text Analysis, Generation, and Critique]]
# [[Mathematical Models in Economics and Social Sciences]]
# [[Big Data and Privacy: Balancing Utility and Ethics]]
# [[AI in Healthcare: Improving Outcomes and Reducing Disparities]]
# [[Climate Change, Sustainability, and Mathematical Modeling]]
# [[The Mathematics of Democracy: Voting Systems and Fair Representation]]
# [[Bias and Fairness in AI: Challenges and Solutions]]
# [[The Role of AI in Mental Health and Emotional Well-being]]
# [[AI and the Creative Arts: Exploring New Frontiers]]
# [[The Future of AI: Possibilities, Pitfalls, and Predictions]]
# [[Final Project: Applying Mathematics, Data Science, and AI to Cultural Analysis]]

MAT2313

2023-04-26T03:48:43Z

Juan.gutierrez3:

= Combinatorics and Probability - MAT2313=
''Corequisite'': [[MAT1224]].

''Content'': Basic counting principles. Permutations and combinations. Binomial and multinomial coefficients. Pigeonhole and inclusion-exclusion principles. Graphs, colorings, planarity. Eulerian and Hamiltonian graphs. Recurrence relations. Generating functions. Prerequisites: MAT1224 Calculus II and MAT 1313 Algebra and Number Systems. 3 Credit Hours

''Sample textbooks'': Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012).

==Topics List==
Course outline:

Week 1: Finite sets, strings, enumeration, the addition and product rules.

Week 2: Combinations, permutations.

Week 3: Binomial and multinomial coefficients.

Week 4: The Pigeonhole Principle. The Inclusion-Exclusion Formula, derangements, the Euler ɸ function (totient).

Week 5: Review. First midterm exam.

Week 6: Graphs and multigraphs.

Week 7: Eulerian and Hamiltonian graphs.

Week 8: Trees. Colorings. Planarity.

Week 9: Review. First midterm exam.

Week 10: Generating functions. The Binomial Theorem. Partitions.

Week 11: Recurrence relations. Linear recurrences.

Week 12: Solving recurrences by generating functions.

Week 13: Exponential generating functions. Nonlinear recurrences.

Week 15: Review.

MAT5383

2023-04-26T03:46:46Z

Juan.gutierrez3:

= Mathematical Foundations of Statistics II - MAT4383/MAT5383=

'''Catalog entry'''

''Prerequisite'': [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I.

''Content'': Mathematical Statistics II is an advanced course that delves into the mathematical foundations of point estimation, sufficiency, confidence intervals, hypothesis testing, inferences based on two samples, analysis of variance (ANOVA), and regression analysis. The course builds on the foundations established in Mathematical Statistics I and equips students with a deeper understanding of statistical methods for data analysis, inference, and prediction, essential for numerous applications in various disciplines.

==List of Topics==
{| class="wikitable"
! Session !! Section !! Topic !! Prerequisites !! SLOs
|-
| || 7 || Point Estimation || ||
|-
| 1 || 7.1 || General Concepts and Criteria || ||
|-
| 2 || 7.2 || Methods of Point Estimation || ||
|-
| 3 || 7.3 || Sufficiency || ||
|-
| 4 || 7.4 || Information and Efficiency || ||
|-
| || 8 || Statistical Intervals Based on a Single Sample || ||
|-
| 5 || 8.1 || Basic Properties of Confidence Intervals || ||
|-
| 6 || 8.2 || Large-Sample Confidence Intervals for a Population Mean and Proportion || ||
|-
| 7 || 8.3 || Intervals Based on a Normal Population Distribution || ||
|-
| 8 || 8.4 || Confidence Intervals for the Variance and Standard Deviation of a Normal Population || ||
|-
| 9 || 8.5 || Bootstrap Confidence Intervals || ||
|-
| 10 || REVIEW || || ||
|-
| 11 || TEST 1 || || ||
|-
| || 9 || Tests of Hypotheses Based on a Single Sample || ||
|-
| 12 || 9.1 || Hypotheses and Test Procedures || ||
|-
| 13 || 9.2 || Tests About a Population Mean || ||
|-
| 14 || 9.3 || Tests Concerning a Population Proportion || ||
|-
| 15 || 9.4 || P-Values || ||
|-
| 16 || 9.5 || Some Comments on Selecting a Test Procedure || ||
|-
| || 10 || Inferences Based on Two Samples || ||
|-
| 17 || 10.1 || z Tests and Confidence Intervals for a Difference Between Two Population Means || ||
|-
| 18 || 10.2 || The Two-Sample t Test and Confidence Interval || ||
|-
| 19 || 10.3 || Analysis of Paired Data || ||
|-
| 20 || 10.4 || Inferences About Two Population Proportions || ||
|-
| 21 || 10.5 || Inferences About Two Population Variances || ||
|-
| 22 || 10.6 || Comparisons Using the Bootstrap and Permutation Methods || ||
|-
| 23 || REVIEW || || ||
|-
| 24 || TEST 2 || || ||
|-
| || 11 || The Analysis of Variance || ||
|-
| 25 || 11.1 || Single-Factor ANOVA || ||
|-
| 26 || 11.2 || Multiple Comparisons in ANOVA || ||
|-
| 27 || 11.3 || More on Single-Factor ANOVA || ||
|-
| 28 || 11.4 || Two-Factor ANOVA with Kij = 1 || ||
|-
| 29 || 11.5 || Two-Factor ANOVA with Kij > 1 || ||
|-
| 30 || 12 || Regression and Correlation || ||
|-
| 31 || 12.1 || The Simple Linear and Logistic Regression Models || ||
|-
| 32 || 12.2 || Estimating Model Parameters || ||
|-
| 33 || 12.3 || Inferences About the Regression Coefficient b1 || ||
|-
| 34 || 12.4 || Inferences Concerning mY ·x* and the Prediction of Future Y Values || ||
|-
| 35 || 12.5 || Correlation || ||
|-
| 36 || 12.6 || Assessing Model Adequacy || ||
|-
| 37 || 12.7 || Multiple Regression Analysis || ||
|-
| 38 || 12.8 || Regression with Matrices || ||
|-
| 39 || REVIEW
|}

MAT5383

2023-04-26T03:46:16Z

Juan.gutierrez3: Changed name of course

= Mathematical Foundations of Statistics II - MAT4383/MAT5383=

'''Catalog entry'''

''Prerequisite'': [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I.

''Content'': Mathematical Statistics II is an advanced course that delves into point estimation, sufficiency, confidence intervals, hypothesis testing, inferences based on two samples, analysis of variance (ANOVA), and regression analysis. The course builds on the foundations established in Mathematical Statistics I and equips students with a deeper understanding of statistical methods for data analysis, inference, and prediction, essential for numerous applications in various disciplines.

==List of Topics==
{| class="wikitable"
! Session !! Section !! Topic !! Prerequisites !! SLOs
|-
| || 7 || Point Estimation || ||
|-
| 1 || 7.1 || General Concepts and Criteria || ||
|-
| 2 || 7.2 || Methods of Point Estimation || ||
|-
| 3 || 7.3 || Sufficiency || ||
|-
| 4 || 7.4 || Information and Efficiency || ||
|-
| || 8 || Statistical Intervals Based on a Single Sample || ||
|-
| 5 || 8.1 || Basic Properties of Confidence Intervals || ||
|-
| 6 || 8.2 || Large-Sample Confidence Intervals for a Population Mean and Proportion || ||
|-
| 7 || 8.3 || Intervals Based on a Normal Population Distribution || ||
|-
| 8 || 8.4 || Confidence Intervals for the Variance and Standard Deviation of a Normal Population || ||
|-
| 9 || 8.5 || Bootstrap Confidence Intervals || ||
|-
| 10 || REVIEW || || ||
|-
| 11 || TEST 1 || || ||
|-
| || 9 || Tests of Hypotheses Based on a Single Sample || ||
|-
| 12 || 9.1 || Hypotheses and Test Procedures || ||
|-
| 13 || 9.2 || Tests About a Population Mean || ||
|-
| 14 || 9.3 || Tests Concerning a Population Proportion || ||
|-
| 15 || 9.4 || P-Values || ||
|-
| 16 || 9.5 || Some Comments on Selecting a Test Procedure || ||
|-
| || 10 || Inferences Based on Two Samples || ||
|-
| 17 || 10.1 || z Tests and Confidence Intervals for a Difference Between Two Population Means || ||
|-
| 18 || 10.2 || The Two-Sample t Test and Confidence Interval || ||
|-
| 19 || 10.3 || Analysis of Paired Data || ||
|-
| 20 || 10.4 || Inferences About Two Population Proportions || ||
|-
| 21 || 10.5 || Inferences About Two Population Variances || ||
|-
| 22 || 10.6 || Comparisons Using the Bootstrap and Permutation Methods || ||
|-
| 23 || REVIEW || || ||
|-
| 24 || TEST 2 || || ||
|-
| || 11 || The Analysis of Variance || ||
|-
| 25 || 11.1 || Single-Factor ANOVA || ||
|-
| 26 || 11.2 || Multiple Comparisons in ANOVA || ||
|-
| 27 || 11.3 || More on Single-Factor ANOVA || ||
|-
| 28 || 11.4 || Two-Factor ANOVA with Kij = 1 || ||
|-
| 29 || 11.5 || Two-Factor ANOVA with Kij > 1 || ||
|-
| 30 || 12 || Regression and Correlation || ||
|-
| 31 || 12.1 || The Simple Linear and Logistic Regression Models || ||
|-
| 32 || 12.2 || Estimating Model Parameters || ||
|-
| 33 || 12.3 || Inferences About the Regression Coefficient b1 || ||
|-
| 34 || 12.4 || Inferences Concerning mY ·x* and the Prediction of Future Y Values || ||
|-
| 35 || 12.5 || Correlation || ||
|-
| 36 || 12.6 || Assessing Model Adequacy || ||
|-
| 37 || 12.7 || Multiple Regression Analysis || ||
|-
| 38 || 12.8 || Regression with Matrices || ||
|-
| 39 || REVIEW
|}

MAT5373

2023-04-26T03:44:56Z

Juan.gutierrez3: /* Mathematical Statistics I - MAT4173/5373 */

=Mathematical Foundations of Statistics I - MAT4173/5373=

'''Catalog entry'''

''Prerequisite'': [[MAT1213]]/[[MAT1214]] Calculus I.

''Content'': Mathematical Foundations of Statistics I is an introductory course that covers key concepts in statistics from a mathematical perspective, including populations and samples, descriptive statistics, probability, discrete and continuous distributions, transformations, jointly distributed random variables, covariance and correlation, order statistics, and the Central Limit Theorem. The course equips students with foundational knowledge and techniques for data analysis and statistical modeling in various fields.

== List of Topics==

{| class="wikitable"
| Session || Section || Topic || Pre-requisites
|-
| 1 || 1.1 || Populations and Samples ||
|-
| 2 || 1.2 || Pictorial and Tabular Methods in Descriptive Statistics ||
|-
| 3 || 1.3 || Measures of Location ||
|-
| 4 || 1.4 || Measures of Variability ||
|-
| 5 || 2.1 || Sample Spaces and Events ||
|-
| 6 || 2.2 || Axioms, Interpretations, and Properties of Probability ||
|-
| 7 || 2.3 || Counting Techniques ||
|-
| 8 || 2.4 || Conditional Probability ||
|-
| 9 || 2.5 || Independence ||
|-
| 10 || colspan="3" | REVIEW
|-
| 11 || colspan="3" | TEST 1
|-
| 12 || 3.1 || Random Variables ||
|-
| 13 || 3.2 || Probability Distributions for Discrete Random Variables ||
|-
| 14 || 3.3 || Expected Values of Discrete Random Variables ||
|-
| 15 || 3.4 || Moments and Moment Generating Functions ||
|-
| 16 || 3.5 || The Binomial Probability Distribution ||
|-
| 17 || 3.6 || Hypergeometric and Negative Binomial Distributions ||
|-
| 18 || 3.7 || The Poisson Probability Distribution ||
|-
| 19 || 4.1 || Probability Density Functions and Cumulative Distribution Functions ||
|-
| 20 || 4.2 || Expected Values and Moment Generating Functions ||
|-
| 21 || 4.3 || The Normal Distribution ||
|-
| 22 || 4.4 || The Gamma Distribution and Its Relatives ||
|-
| 23 || 4.5 || Other Continuous Distributions ||
|-
| 24 || 4.6 || Probability Plots ||
|-
| 25 || 4.7 || Transformations of a Random Variable ||
|-
| 26 || colspan="3" | REVIEW
|-
| 27 || colspan="3" | TEST 2
|-
| 28 || 5.1 || Jointly Distributed Random Variables ||
|-
| 29 || 5.2 || Expected Values, Covariance, and Correlation ||
|-
| 30 || 5.3 || Conditional Distributions ||
|-
| 31 || 5.4 || Transformations of Random Variables ||
|-
| 32 || 5.5 || Order Statistics ||
|-
| 33 || 6.1 || Statistics and Their Distributions ||
|-
| 34 || 6.2 || The Distribution of the Sample Mean ||
|-
| 35 || 6.3 || The Mean, Variance, and MGF for Several Variables ||
|-
| 36 || 6.4 || Distributions Based on a Normal Random Sample ||
|-
| 37 || 6.5 || Proof of the Central Limit Theorem ||
|-
| 38 || colspan="3" | REVIEW
|}

Main Page

2023-04-26T03:44:15Z

Juan.gutierrez3: /* Upper Division */ changes course name for MAT4373 & 4383

<strong>UTSA Department of Mathematics</strong>

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3203]] Abstract Linear Algebra
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Abstract Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core M.Sc. Studies ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.
* Two courses in the Analysis & Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5173]] Algebra I & [[MAT5243]] General Topology I.
** [[MAT5243]] General Topology I & [[MAT5253]] General Topology II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra I & [[MAT5203]] Analysis I.
** [[MAT5173]] Algebra I & [[MAT5123]] Cryptography I.
** [[MAT5123]] Cryptography I & [[MAT5323]] Cryptography II.
* Two course in discrete mathematics among the following:
** [[MAT5423]] Discrete Mathematics I (fall even years)
** [[MAT5433]] Discrete Mathematics II (spring even years)
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I (fall even years)
** [[MDC5153]] Data Analytics
* [[MAT5283]] Linear Algebra (fall odd years)

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[MAT5243]] General Topology
* [[MAT5253]] General Topology II
* [[MAT5323]] Cryptography II
* [[MAT5183]] Algebra II
* [[MAT5223]] Theory of Functions of a Complex Variable
* [[MAT5343]] Differential Geometry

=== M.Sc. Track in Applied & Industrial Mathematics ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MAT2313

2023-04-26T03:41:28Z

Juan.gutierrez3: Changed content from Probability to combinatorics

= Combinatorics and Probability=
3 Credit Hours

==Course Catalog==
''Corequisite'': [[MAT1224]].

''Content'': Basic counting principles. Permutations and combinations. Binomial and multinomial coefficients. Pigeonhole and inclusion-exclusion principles. Graphs, colorings, planarity. Eulerian and Hamiltonian graphs. Recurrence relations. Generating functions. Prerequisites: MAT1224 Calculus II and MAT 1313 Algebra and Number Systems.

==Description==
Introduction to the theory of probability, through the study of discrete and continuous random variables.

==Sample textbooks==
Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012).

==Topics List==
Course outline:

Week 1: Finite sets, strings, enumeration, the addition and product rules.

Week 2: Combinations, permutations.

Week 3: Binomial and multinomial coefficients.

Week 4: The Pigeonhole Principle. The Inclusion-Exclusion Formula, derangements, the Euler ɸ function (totient).

Week 5: Review. First midterm exam.

Week 6: Graphs and multigraphs.

Week 7: Eulerian and Hamiltonian graphs.

Week 8: Trees. Colorings. Planarity.

Week 9: Review. First midterm exam.

Week 10: Generating functions. The Binomial Theorem. Partitions.

Week 11: Recurrence relations. Linear recurrences.

Week 12: Solving recurrences by generating functions.

Week 13: Exponential generating functions. Nonlinear recurrences.

Week 15: Review.

MAT5153

2023-04-25T14:00:19Z

Juan.gutierrez3: /* Course Content */ Added prerequisites

==Data Analytics MDC4153/MAT5153==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || None. || Understanding of government databases. Conduct basic data exploration. Identity questions answerable with data available for a specific problem.
|-
| 2 || || Scripts vs. compiled code. || Previous exposure to computer programming in any language. || Basic numeric operations in scripting vs. compiled code. Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments.
|-
| 3 || || Ethics in data analysis. || None. || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 4 - 5 || || Linear discriminants || Linear Algebra and Calculus I || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || Scripts vs. compiled code (week 2) || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || Linear discriminants (week 4-5) || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || Scripts vs. compiled code (week 2) || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || Generalized regressions (week 7) || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || Scripts vs. compiled code (week 2) || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || Clustering (week 9) || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || Scripts vs. compiled code (week 2) || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || Scripts vs. compiled code (week 2) || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || Entire course || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-04-25T13:56:12Z

Juan.gutierrez3: /* Course Content */ Refined order lesson to ensure that a week of technical material is followed by a week of conceptual week. This increased time for completion of technical assignments,

==Data Analytics MDC4153/MAT5153==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || || Understanding of government databases. Conduct basic data exploration. Identity questions answerable with data available for a specific problem.
|-
| 2 || || Scripts vs. compiled code. || || Basic numeric operations in scripting vs. compiled code. Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments.
|-
| 3 || || Ethics in data analysis. || || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 4 - 5 || || Linear discriminants I || || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-04-25T13:42:06Z

Juan.gutierrez3: /* Course Content */

==Data Analytics MDC4153/MAT5153==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || || Understanding of government databases
|-
| 2 || || Ethics in data analysis. || || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 3 || || Scripts vs. compiled code. || || Clarity about the differences between interpreted and compiled code, and how it impacts data analysis. Setting up environments. Basic numeric operations in scripting vs. compiled code.
|-
| 4 - 5 || || Linear discriminants I || || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis. Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-04-25T13:39:56Z

Juan.gutierrez3: /* Course Content */ Refinement of order of lessons

==Data Analytics MDC4153/MAT5153==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || || Understanding of government databases
|-
| 2 || || Ethics in data analysis. || || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 3 || || Scripts vs. compiled code. Setting up environments. || || Clarity about the differences between interpreted and compiled code, and how it impacts data analysis.
|-
| 4 || || Linear discriminants || || Ability to minimize an equation involving matrices and vectors. Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis.
|-
| 5 || || Basic numeric operations in scripting vs. compiled code. || || Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 6 || || Visualization (basic and advanced). || || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || || Understanding of mathematical approaches to produce an infinite family of regressions for the purpose of data smoothing.
|-
| 8 || || Relational databases || || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-04-24T18:30:55Z

Juan.gutierrez3: /* Course Content */ Adjusted order

==Data Analytics MDC4153/MAT5153==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || || Understanding of government databases
|-
| 2 || || Ethics in data analysis. || || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 3 || || Scripts vs. compiled code. Setting up environments. || || Clarity about the differences between interpreted and compiled code, and how it impacts data analysis.
|-
| 4 || || Basic numeric operations in scripting vs. compiled code. || || Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 5 || || Linear discriminants || || Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis.
|-
| 6 || || Visualization (basic and advanced). || || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || || Understanding of mathematical approaches to produce an infinite family of regressions.
|-
| 8 || || Relational databases || || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 9 || || Clustering || || Ability to create basic clusters using multiple definitions of distance.
|-
| 10 || || Solution architecture & reproducibility. || || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 11 || || Non-linear discriminants (i.e. artificial neural networks). || || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 12 || || Management of the configuration. || || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-04-24T17:57:19Z

Juan.gutierrez3: /* Course Content */ Added Student Learning Outcomes

==Data Analytics MDC4153/MAT5153==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': This immersive Data Analytics course equips students with the essential mathematical skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will be exposed to the entire life cycle of data analysis. Throughout the course, participants will explore basic operations in scripting languages, delve into advanced visualization techniques, and investigate linear discriminants, generalized regressions, time series analysis, and non-linear discriminants, and clustering. Students will program essential algorithms, instead of using toolboxes, to explore the discrete Fourier transform, generalized regressions, clustering algorithms, and artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports.

By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || || Understanding of government databases
|-
| 2 || || Ethics in data analysis. || || Identification of biases introduced during data collection, storage, analysis, and access.
|-
| 3 || || Scripts vs. compiled code. Setting up environments. || || Clarity about the differences between interpreted and compiled code, and how it impacts data analysis.
|-
| 4 || || Basic numeric operations in scripting vs. compiled code. || || Mastery in multi-linear operations in scripting and compiled languages. Understanding of the balance between computational performance and development time.
|-
| 5 || || Linear discriminants || || Mastery of Principal Component Analysis (PCA), Fisher's linear discriminant, and multiple discriminant analysis.
|-
| 6 || || Visualization (basic and advanced). || || Understanding of different families of visualization techniques. Ability to create Circos plots.
|-
| 7 || || Generalized regressions || || Understanding of mathematical approaches to produce an infinite family of regressions,
|-
| 8 || || Clustering || || Ability to create basic clusters using multiple definitions of distance.
|-
| 9 || || Relational databases || || Ability to create, access, and use relational databases from within programming environments. Understanding of when to use relational databases
|-
| 10 || || Non-linear discriminants (i.e. artificial neural networks). || || Capability to program a fully-connected feed-forward artificial neural network from scratch. Understanding of the effect of multiple activation functions,
|-
| 11 || || Solution architecture & reproducibility. || || Capacity to design a complex data analysis solution that guarantees reproducibility, interoperability, and maintainability,
|-
| 12 || || Management of the configuration. || || Ability to program in collaborative multi-layered environments. Capacity to resolve conflicts in code, create code branches, and propagate effectively code changes across multiple environments such as development, test production, etc.
|-
| 13 || || Data analysis plans & standardized reports. || || Dexterity to break a data analysis problems into multiple interconnected components, and then produce automated reports targeting specific audiences.
|-
| 14 || || Project presentations || || Exposure to presentation of results in front an audience of experts.
|}

MAT5153

2023-04-24T17:30:53Z

Juan.gutierrez3: Refinement of content

MAT5153

2023-04-06T22:15:45Z

Juan.gutierrez3: Created page with "==Data Analytics MDC4153/MAT5153== '''Catalog entry''' ''Prerequisite'': MAT2243 Applied Linear Algebra or (MAT2233 Linear Algebra and MAT2214/MAT2213 Calcul..."

MDC5153

2023-04-06T22:15:33Z

Juan.gutierrez3: Redirected page to MAT5153

#REDIRECT[[MAT5153]]

MDC5153

2023-04-06T21:26:59Z

Juan.gutierrez3: /* Data Analytics MDC4153/MDC5153 */

MDC5153

2023-04-03T15:35:52Z

Juan.gutierrez3: /* Data Analytics MDC4153/MDC5153 */

==Data Analytics MDC4153/MDC5153==

'''Catalog entry'''

''Prerequisite'': [[MAT2243]] Applied Linear Algebra or ([[MAT2233]] Linear Algebra and [[MAT2214]]/[[MAT2213]] Calculus III).

''Content'': This immersive Data Analytics course equips students with the essential skills and knowledge required to analyze, visualize, and interpret complex datasets. Students will learn the importance of ethics in data analysis and how to set up a suitable environment for efficient processing. Throughout the course, participants will explore basic operations in Python, delve into advanced visualization techniques, and investigate linear and non-linear discriminants, such as artificial neural networks.

Furthermore, the course will provide an understanding of relational databases and their integration with programming environments, as well as guidance on creating effective data analysis plans. Emphasis will be placed on solution architecture, reproducibility, configuration management, and generating standardized reports. By the end of the course, students will have a strong foundation in data analytics, allowing them to transform raw data into valuable insights for decision-making.

== Course Content==
{| class="wikitable"
! Week !! Source !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Description of the course project. || ||
|-
| 2 || || Ethics in data analysis. || ||
|-
| 3 || || Environment setup. || ||
|-
| 4 || || Basic operations in python. || ||
|-
| 5 || || Visualization (basic and advanced). || ||
|-
| 6 || || Linear discriminants & regressions. || ||
|-
| 7 || || Relational databases. || ||
|-
| 8 || || Relational databases from python. || ||
|-
| 9 || || Non-linear discriminants (i.e. artificial neural networks). || ||
|-
| 10 || || Data analysis plans. || ||
|-
| 11 || || Solution architecture & reproducibility. || ||
|-
| 12 || || Management of the configuration. || ||
|-
| 13 || || Standardized reports. || ||
|-
| 14 || || Project presentations
|}

Main Page

2023-03-31T22:53:08Z

Juan.gutierrez3: /* Core M.Sc. Studies */

<strong>UTSA Department of Mathematics</strong>

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be eventually replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be eventually replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4373]] Mathematical Statistics I

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core M.Sc. Studies ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.
* Two courses in the Analysis & Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5173]] Algebra I & [[MAT5243]] General Topology I.
** [[MAT5243]] General Topology I & [[MAT5253]] General Topology II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra I & [[MAT5203]] Analysis I.
** [[MAT5173]] Algebra I & [[MAT5123]] Cryptography I.
** [[MAT5123]] Cryptography I & [[MAT5323]] Cryptography II.
* Two course in discrete mathematics among the following:
** [[MAT5423]] Discrete Mathematics I (fall even years)
** [[MAT5433]] Discrete Mathematics II (spring even years)
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I (fall even years)
** [[MDC5153]] Data Analytics
* [[MAT5283]] Linear Algebra (fall odd years)

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[MAT5243]] General Topology
* [[MAT5253]] General Topology II
* [[MAT5323]] Cryptography II
* [[MAT5183]] Algebra II
* [[MAT5223]] Theory of Functions of a Complex Variable
* [[MAT5343]] Differential Geometry

=== M.Sc. Track in Applied & Industrial Mathematics ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MAT2214

2023-03-31T21:51:36Z

Juan.gutierrez3:

The textbook for this course is
[https://openstax.org/details/books/calculus-volume-3 Calculus (Volume 3) by Gilbert Strang, Edwin Herman, et al.]

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-

|Week 1

||

1.1

||

[[Polar Coordinates]]

||
* [[Trigonometric Functions: Unit Circle Approach]]
* [[Inverse Trigonometric Functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-

|Week 1

||

1.2

||

[[Three-Dimensional Coordinate Systems]]

||

* [[Two-dimensional coordinate systems]]
* [[Solving Equations and Inequalities| Algebraic Expressions]]

||

* Three-dimensional coordinate systems.
* Distance Formula in Space.
* Standard Equation for a Sphere.
|-

|Weeks 1/2

||

2.1

||

[[Vectors in The Plane, Space]]

||

* [[Linear Equations|Line Segments]]
* [[Distance Formula| Distance Formula]]

||

* Vector Algebra Operations
* The Magnitude of a vector
* Unit Vectors
* The Midpoint of a Line Segment
* The Vector projection
|-

|Week 2

||

2.3

||

[[The Dot Product]]

||

* [[Trigonometric Functions|Basic Trig Functions]]
* [[Vectors]]

||
* Definition of Dot Product
* Properties of Dot Product
* Angle between vectors
* Orthogonal vectors

|-

|Week 2

||

2.4

||

[[The Cross Product]]

||

* [[Trigonometric Functions|Basic Trig Functions]]
* [[Determinants]]
* [[Vectors]]

||

* Definition of Cross Product
* Properties of the cross product
* Area of a parallelogram
* Cross product as a determinant

|-

|Week 3

||

2.5

||

[[Equations of Lines, Planes and Surfaces in Space]]

||

* [[The Dot Product]]
* [[The Cross Product]]
* [[Quadratic Functions]]
* [[Parametric Equations]]

||

* Write the vector, parametric equation of a line through a given point in a given direction, and a line through two given points.
* Find the distance from a point to a given line.
* Write the equation of a plane through a given point with a given normal, and a plane through three given points.
* Find the distance from a point to a given plane.

|-

|Week 3

||

2.6

||

[[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]]

||

* [[Quadratic Functions]]
* [[Parametric Equations]]
* '''[[Conics]]'''

||

* Find equations for cylinders that are generated by rotating lines that are parallel to a plane
* Understand basic quadratic surfaces
* Understand general quadratic surfaces

|-

|Weeks 3/4

||

3.1, 3.2

||

[[Curves in Space and Vector-Valued Functions]]

||

* [[Parametric Equations]]
* [[Vectors]]
* [[The Derivative as a Function]]
* [[The Limit of a Function]]
* [[Continuity]]
* [[The Dot Product]]
* [[The Cross Product]]

||

* Vector functions
* Limits of vector functions
* Continuity of vector functions
* Differentiation rules for vector functions
* Curves and paths in space

|-

|Week 4

||

3.3

||

[[Arc Length]]

||

* '''[[Distance Formula| The Length of a Line Segment]]'''
* [[Curves in Space and Vector-Valued Functions|Vector Functions]]
* [[Line Integrals|Integrals of Vector Functions]], [[Derivatives of Vector Functions]]

||

* The arc Length of a vector function
* Arc length parameterization

|-

|Weeks 4/5

||

3.4

||

[[Motion in Space]]

||
* [[Vectors]]
* [[Parametric Equations]]
* [[The Cross Product]]
* [[Derivatives of Vector Functions]]
||
* The Unit tangent vector
* The curvature
* The Principal Unit Normal Vector
* The Binormal Vector
* The tangential and normal components of acceleration
* The Torsion

|-

|Week 5/6

||

4.1

||

[[Functions of Several Variables]]

||

* [[Domain of a Function]]
* [[Range of a Function]]
* [[Solving Equations and Inequalities]]
* [[Graphs| Graphing a Function]]

||
* Functions of two variables
* Functions of three variables
* Domain and range of multivariable functions
* Bounded regions
* Graphs and level curves of two variable functions
* Level surfaces of three variable functions
|-

|Week 6

||

4.2

||

[[Limit and Continuity of Function of Several Variables]]

||

* [[Continuity]]
* [[The Limit Laws]]
* [[Composition of Functions]]
* [[The Dot Product]]

||

* Limits of functions of two variables
* Limits of functions of more than two variables
* Properties of limits of functions of several variables
* Two path test of non-existing of a limit
* Continuity for functions of several variables
* Continuity of composition
* Extreme values on closed and bounded domains
|-

|Week 6

||

4.3

||

[[Partial Derivatives]]

||

* [[The Derivative as a Function|The first]] and [[The Second Derivative|second derivative]] of a function
* [[Limit and Continuity of Function of Several Variables]]

||
* Partial derivatives for functions of two variables
* Partial derivatives for functions of more than two variables
* Partial derivatives and continuity
* Second order partial derivatives
* Mixed derivative theorem
|-

|Week 7

||

4.4

||

[[Directional Derivatives and Gradient Vectors]]

||
* [[Trigonometric Functions]]
* [[Vectors, Unit Vectors]]
* [[Partial Derivatives]]
* [[Gradients]]
* [[The Dot Product]]
||
* Directional derivatives for functions of two variables
* Gradients
* Properties of directional derivatives
* Tangents to level curves
* Directional derivatives for functions of three variables
|-

|Week 7

||

4.5

||
[[Tangent Plane]],
[[Differentiability]]

||
* [[Partial Derivatives]]
* [[Parametric Equations]] of Lines
* [[Equations of Lines, Planes and Surfaces in Space]]

||
* Determine the equation of a plane tangent to a given surface at a point
* Determine the parametric equation of a normal line to a given surface at a point
* The linear approximation of a function of two variables at a point
* The definition of differentiability for a function of two variables
* Differentiability implies Continuity
* Continuity of First Partial Derivatives implies Differentiability
* The definition of total differentiability for a function of two variables
* Use the total differential to approximate the change in a function of two variables
|-

|Week 7

||

4.6

||

[[The Chain Rule for Functions of more than One Variable]]

||
* [[Differentiation Rules]]
* [[The Chain Rule]]
* [[Partial Derivatives]]

||
* Chain rule for functions of one independent variable and several intermediate variables.
* Chain rule for functions of two independent variable and several intermediate variables.
* Method for implicit differentiation.
* The general chain rule for functions of several independent variables
|-
|Week 8

||

4.7

||

[[Maxima and Minima Problems]]

||
* [[Extreme values on closed and bounded domains]]
* [[Partial Derivatives]]
* [[Maxima and Minima|Maxima, Minima and Critical Points of a Function]]
* [[Limit and Continuity of Function of Several Variables]]

||
* The derivative test for local extreme values
* Extreme values on closed and bounded domains
* Critical points and saddle points for functions of two variables
* Second derivative test for local extreme values
* Absolute maxima and minima on closed and bounded regions
|-
|Week 8/9

||

4.8

||

[[Lagrange Multipliers]]

||

* [[Partial Derivatives]]
* [[Critical Points of a Function]]

||
* Lagrange Multipliers with One Constraint
* Lagrange Multipliers with Two Constraints
|-

|Week 9/10

||

5.1

||

[[Multiple Integrals|Double Integrals over Rectangular Regions]]

||

* [[Approximating Areas]]
* [[The Definite Integral|Limits of Riemann Sums]]

||
* Double Integral is the limit of Double Sums.
* Double Integrals over Rectangular Regions.
* Interated Integrals.
* Fubini's Theorem (part 1).
|-

|Week 10

||

5.2

||

[[Multiple Integrals|Double Integrals over General Regions]]

||

* [[Continuity]]
* [[Determining Volumes by Slicing]]
* [[Multiple Integrals|Double and Iterated Integrals over Rectangular regions]]

||
* Double integrals over bounded, general regions.
* Properties of double Integrals.
* Fubini's theorem (part 2)
* Changing the order of Integration.
* Calculating Volumes, Areas and Average Values
|-

|Week 11

||

5.3

||

[[Multiple Integrals|Double Integrals in Polar Coordinates]]

||

* [[Multiple Integrals|Double Integrals over General Regions]]
* [[Polar Coordinates]]

||
* Double Integrals over rectangular polar regions.
* Double Integrals over general polar regions.
* Changing Cartesian Integrals into Polar Integrals.
* Using Double Integrals in Polar Coordinates to find Volumes, Areas.
|-

|Week 11

||

5.4

||

[[Multiple Integrals|Triple Integrals in Rectangular Coordinates]]

||

* [[Multiple Integrals|Double Integrals]]
* [[Multiple Integrals|Area by Double Integration]]
* '''[[Change of Variables]]'''

||

* Triple Integrals over general bounded regions.
* Finding Volumes by evaluating Triple Integrals.
* Average value of a function in space.
* Changing Integration Order and Coordinate systems.
|-

|Week 12

||

5.5

||

[[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]]

||

* [[Multiple Integrals|Double Integrals in Polar Form]]
* [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]]

||

* Integrations in Cylindrical Coordinates.
* Equations relating rectangular and cylindrical coordinates.
* Changing Cartesian integrations into Cylindrical integrations.
* Integrations in Spherical coordinates.
* Equations relating spherical coordinates to Cartesian and cylindrical coordinates.
* Changing Cartesian integrations into Cylindrical integrations.
|-

|Week 13

||

5.6

||

[[Multiple Integrals|Applications of Multiple Integrals]]

||

* [[Multiple Integrals|Double Integral]]
* [[Multiple Integrals|Triple Integrals]]

||

* Finding Masses, Moments, Centers of Masses, Moments of Inertia in Two Dimensions.
* Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions.
|-
|Week 13/14

||

5.7

||

[[Multiple Integrals|Change of Variables in Multiple Integrals]]

||

* [[Multiple Integrals|Double Integral]]
* [[Multiple Integrals|Triple Integrals]]

||

* Determine the image of a region under a given transformation of variables.
* Compute the Jacobian of a given transformation.
* Evaluate a double integral using a change of variables.
* Evaluate a triple integral using a change of variables.
|-
|Week 14

||

6.1

||

[[Vector Fields]]

||

* [[The Dot Product]] 
* [[Directional Derivatives and Gradient Vectors]]
||
* Vector Fields in a plane.
* Vector Fields in Space.
* Potential Functions.
* Gradient Fields, Conservative Vector Fields.
* The Cross-Partial Test for Conservative Vector Fields.
* Determining Whether a Vector Field is conservative.
|-

|Week 14

||

6.2

||

[[Line Integrals]]

||

* [[Parametric Equations]]
* [[Curves in Space and Vector-Valued Functions]]
* [[Arc Length]]

||
* Line Integrals of functions a long a smooth curves in a planer or in space
* Line Integrals of of vector fields along an oriented curves in a plane or space..
* Properties of Vector Line Integrals.
* Evaluating Line Integrals.
* Applications of line integrals: Calculating Arc Length, the Mass of a wire, Work done by a force, Flux across a curve, Circulation of a force.
|-

|Week 14/15

||

6.3

||

[[Conservative Vector Fields]]

||

* [[Vector Fields and Line Integrals]]
* [[Partial Derivatives]]

||
* Describe simple and closed curves
* Define connected and simply connected regions.
* Explain how to test a vector field to determine whether it is conservative.
* Find a potential function for a conservative vector field.
* Use the Fundamental Theorem for Line Integrals to evaluate a line integral of a vector field.
|-

|Weeks 14/15

||

6.4

||

[[Green's Theorem]]

[[Stokes' Theorem]]

||

* [[Vector Fields]]
* [[Line Integrals]]
* [[Partial Derivatives]]
* [[The Dot Product]]
* [[Line Integrals|Path Independence]]
* [[Conservative Vector Fields]]

||

* Circulation form of Green's Theorem.
* Flux Form of Green’s Theorem.
* Applying Green's Theorem to find Work, Flux.

|}

MAT1223

2023-03-31T21:50:39Z

Juan.gutierrez3:

The textbook for this course is
[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]

{| class="wikitable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
| Week 1 || 1.5 || [[Integration by Substitution]] || * [[Differentiation Rules]] ||
* [[Linear Approximations and Differentials]]
|-
| Week 1 & 2 || 2.1 || [[Area between Curves]] || * [[Toolkit Functions]] || [[Graphing Elementary Functions]]
|-
| Week 2 || 2.2 || [[Determining Volumes by Slicing]] || * '''[[Areas of basic shapes]]''' ||
* '''[[Volume of a cylinder]]'''
|-
| Week 3 || 2.3 || [[Volumes of Revolution, Cylindrical Shells]] || * [[Toolkit Functions]] || [[Graphing elementary functions]]
|-
| Week 3 || 2.4 || [[Arc Length and Surface Area]] || * [[Differentiation Rules]] ||
* [[The Fundamental Theorem of Calculus]]
|-
| Week 4 || 2.5 || [[Physical Applications]] || * '''[[Areas of basic shapes]]''' ||
* '''[[Volume of a cylinder]]'''
|-
| Week 4 & 5 || 2.6 || [[Moments and Center of Mass]] || * [[Toolkit Functions]] || [[Graphing elementary functions]]
|-
| Week 5 || 3.1 || [[Integration by Parts]] || * [[Differentiation Rules]] ||
* [[Linear Approximations and Differentials]]
|-
| Week 6 || 3.2 || [[Trigonometric Integrals]] || * [[Trigonometric Functions]] ||
* [[Properties of the Trigonometric Functions]]
|-
| Week 6 & 7 || 3.3 || [[Trigonometric Substitution]] || * [[Completing the Square]] ||
* [[Trigonometric Functions]]
|-
| Week 7 || 3.4 || [[Partial Fractions]] || * [[Factoring Polynomials]] ||
* [[Completing the Square]]
|-
| Week 8 || 3.7 || [[Improper Integrals]] || * [[The Fundamental Theorem of Calculus]] ||
* [[Integration by Substitution]]
|-
| Week 9 || 5.1 || [[Sequences]] || * [[The Limit Laws]] || [[The Limit Laws and Squeeze Theorem]]
|-
| Week 10 || 5.2 || [[Infinite Series]] || * '''[[Sigma notation]]''' ||
* [[Sequences]]
|-
| Week 11 || 5.3 || [[The Divergence and Integral Tests]] || * [[The Limit Laws]] ||
* [[Limits at Infinity and Asymptotes]]
|-
| Week 11 || 5.4 || [[Comparison Tests]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]]
|-
| Week 12 || 5.5 || [[Alternating Series]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]]
|-
| Week 12 || 5.6 || [[Ratio and Root Tests]] || * '''[[Factorials]]''' ||
* [[Limits at Infinity and Asymptotes]]
|-
| Week 13 || 6.1 || [[Power Series and Functions]] || * [[Infinite Series]] || [[The Geometric Series Test]]
|-
| Week 14 || 6.2 || [[Properties of Power Series]] || * [[Differentiation Rules]] ||
* [[Antiderivatives]]
|-
| Week 15 || 6.3 || [[Taylor and Maclaurin Series]] || * [[The Derivative as a Function]] || [[Higher-Order Derivatives]]
|}

MAT2213

2023-03-31T21:43:51Z

Juan.gutierrez3: /* Topics List */

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1 || 1.2 || [[Three-Dimensional Coordinate Systems]] || ||
|-
|Weeks 1 || 2.1 || [[Vectors in The Plane, Space]] || ||
|-
|Week 1 || 2.3 || [[The Dot Product]] || ||
|-
|Week 2 || 2.4 || [[The Cross Product]] Scalar triple product || ||
|-
|Week 2 || 2.5 || [[Equations of Lines, Planes and Surfaces in Space]] || ||
|-
|Week 3 || 2.6 || [[Equations of Lines, Planes and Surfaces in Space|Equaitons of Curves. Equations of Surfaces]] || ||
|-
|Weeks 3 || 3.1, 3.2 || [[Curves in Space and Vector-Valued Functions]] Derivatives and integrals of vector functions || ||
|-
|Week 4 || 3.3 || [[Arc Length]] || ||
|-
|Weeks 4/5 || 3.4 || [[Motion in Space]] || ||
|-
|Week 5/6 || 4.1 || [[Functions of Several Variables]] || ||
|-
|Week 6 || 4.2 || [[Limit and Continuity of Function of Several Variables]] || ||
|-
|Week 6 || 4.3 || [[Partial Derivatives]] || ||
|-
|Week 7 || 4.4 || [[Directional Derivatives and Gradient Vectors]] || ||
|-
|Week 7 || 4.5 || [[Tangent Plane]], [[Differentiability]] || ||
|-
|Week 7 || 4.6 || [[The Chain Rule for Functions of more than One Variable]] || ||
|-
|Week 8 || 4.7 || [[Maxima and Minima Problems]] || ||
|-
|Week 8/9 || 4.8 || [[Lagrange Multipliers]] || ||
|-
|Week 9/10 || 5.1 || [[Multiple Integrals|Double Integrals over Rectangular Regions]] || ||
|-
|Week 10 || 5.2 || [[Multiple Integrals|Double Integrals over General Regions]] || ||
|-
|Week 11 || 5.3 || [[Multiple Integrals|Double Integrals in Polar Coordinates]] || ||
|-
|Week 11 || 5.4 || [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] || ||
|-
|Week 12 || 5.5 || [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] || ||
|-
|Week 13 || 5.6 || [[Multiple Integrals|Applications of Multiple Integrals]] || ||
|-
|Week 13/14 || 5.7 || [[Multiple Integrals|Change of Variables in Multiple Integrals]] || ||
|-
|Week 14 || 6.1 || [[Vector Fields]] || ||
|-
|Week 14 || 6.2 || [[Line Integrals]] || ||
|-
|Week 14/15 || 6.3 || [[Conservative Vector Fields]] || ||
|-
|Weeks 14/15 || 6.4 || [[Green's Theorem]] [[Stokes' Theorem]] || ||
|}

MAT2213

2023-03-31T21:36:50Z

Juan.gutierrez3: /* Topics List */

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1 || 1.1 || [[Polar Coordinates]] || ||
|-
|Week 1 || 1.2 || [[Three-Dimensional Coordinate Systems]] || ||
|-
|Weeks 1/2 || 2.1 || [[Vectors in The Plane, Space]] || ||
|-
|Week 2 || 2.3 || [[The Dot Product]] || ||
|-
|Week 2 || 2.4 || [[The Cross Product]] || ||
|-
|Week 3 || 2.5 || [[Equations of Lines, Planes and Surfaces in Space]] || ||
|-
|Week 3 || 2.6 || [[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]] || ||
|-
|Weeks 3/4 || 3.1, 3.2 || [[Curves in Space and Vector-Valued Functions]] || ||
|-
|Week 4 || 3.3 || [[Arc Length]] || ||
|-
|Weeks 4/5 || 3.4 || [[Motion in Space]] || ||
|-
|Week 5/6 || 4.1 || [[Functions of Several Variables]] || ||
|-
|Week 6 || 4.2 || [[Limit and Continuity of Function of Several Variables]] || ||
|-
|Week 6 || 4.3 || [[Partial Derivatives]] || ||
|-
|Week 7 || 4.4 || [[Directional Derivatives and Gradient Vectors]] || ||
|-
|Week 7 || 4.5 || [[Tangent Plane]], [[Differentiability]] || ||
|-
|Week 7 || 4.6 || [[The Chain Rule for Functions of more than One Variable]] || ||
|-
|Week 8 || 4.7 || [[Maxima and Minima Problems]] || ||
|-
|Week 8/9 || 4.8 || [[Lagrange Multipliers]] || ||
|-
|Week 9/10 || 5.1 || [[Multiple Integrals|Double Integrals over Rectangular Regions]] || ||
|-
|Week 10 || 5.2 || [[Multiple Integrals|Double Integrals over General Regions]] || ||
|-
|Week 11 || 5.3 || [[Multiple Integrals|Double Integrals in Polar Coordinates]] || ||
|-
|Week 11 || 5.4 || [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] || ||
|-
|Week 12 || 5.5 || [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] || ||
|-
|Week 13 || 5.6 || [[Multiple Integrals|Applications of Multiple Integrals]] || ||
|-
|Week 13/14 || 5.7 || [[Multiple Integrals|Change of Variables in Multiple Integrals]] || ||
|-
|Week 14 || 6.1 || [[Vector Fields]] || ||
|-
|Week 14 || 6.2 || [[Line Integrals]] || ||
|-
|Week 14/15 || 6.3 || [[Conservative Vector Fields]] || ||
|-
|Weeks 14/15 || 6.4 || [[Green's Theorem]] [[Stokes' Theorem]] || ||
|}

MAT2213

2023-03-31T21:17:57Z

Juan.gutierrez3: /* Topics List */ Removed HTML formatting

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-

|Week 1

||

1.1

||

[[Polar Coordinates]]

||
* [[Trigonometric Functions: Unit Circle Approach]]
* [[Inverse Trigonometric Functions]]
||
* Plot points using polar coordinates and find several polar coordinates of a single point
* Convert polar coordinates to rectangular coordinates and vice versa
* Transform equations from polar form to rectangular form and vice versa
|-

|Week 1

||

1.2

||

[[Three-Dimensional Coordinate Systems]]

||

* [[Two-dimensional coordinate systems]]
* [[Solving Equations and Inequalities| Algebraic Expressions]]

||

* Three-dimensional coordinate systems.
* Distance Formula in Space.
* Standard Equation for a Sphere.
|-

|Weeks 1/2

||

2.1

||

[[Vectors in The Plane, Space]]

||

* [[Linear Equations|Line Segments]]
* [[Distance Formula| Distance Formula]]

||

* Vector Algebra Operations
* The Magnitude of a vector
* Unit Vectors
* The Midpoint of a Line Segment
* The Vector projection
|-

|Week 2

||

2.3

||

[[The Dot Product]]

||

* [[Trigonometric Functions|Basic Trig Functions]]
* [[Vectors]]

||
* Definition of Dot Product
* Properties of Dot Product
* Angle between vectors
* Orthogonal vectors

|-

|Week 2

||

2.4

||

[[The Cross Product]]

||

* [[Trigonometric Functions|Basic Trig Functions]]
* [[Determinants]]
* [[Vectors]]

||

* Definition of Cross Product
* Properties of the cross product
* Area of a parallelogram
* Cross product as a determinant

|-

|Week 3

||

2.5

||

[[Equations of Lines, Planes and Surfaces in Space]]

||

* [[The Dot Product]]
* [[The Cross Product]]
* [[Quadratic Functions]]
* [[Parametric Equations]]

||

* Write the vector, parametric equation of a line through a given point in a given direction, and a line through two given points.
* Find the distance from a point to a given line.
* Write the equation of a plane through a given point with a given normal, and a plane through three given points.
* Find the distance from a point to a given plane.

|-

|Week 3

||

2.6

||

[[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]]

||

* [[Quadratic Functions]]
* [[Parametric Equations]]
* '''[[Conics]]'''

||

* Find equations for cylinders that are generated by rotating lines that are parallel to a plane
* Understand basic quadratic surfaces
* Understand general quadratic surfaces

|-

|Weeks 3/4

||

3.1, 3.2

||

[[Curves in Space and Vector-Valued Functions]]

||

* [[Parametric Equations]]
* [[Vectors]]
* [[The Derivative as a Function]]
* [[The Limit of a Function]]
* [[Continuity]]
* [[The Dot Product]]
* [[The Cross Product]]

||

* Vector functions
* Limits of vector functions
* Continuity of vector functions
* Differentiation rules for vector functions
* Curves and paths in space

|-

|Week 4

||

3.3

||

[[Arc Length]]

||

* '''[[Distance Formula| The Length of a Line Segment]]'''
* [[Curves in Space and Vector-Valued Functions|Vector Functions]]
* [[Line Integrals|Integrals of Vector Functions]], [[Derivatives of Vector Functions]]

||

* The arc Length of a vector function
* Arc length parameterization

|-

|Weeks 4/5

||

3.4

||

[[Motion in Space]]

||
* [[Vectors]]
* [[Parametric Equations]]
* [[The Cross Product]]
* [[Derivatives of Vector Functions]]
||
* The Unit tangent vector
* The curvature
* The Principal Unit Normal Vector
* The Binormal Vector
* The tangential and normal components of acceleration
* The Torsion

|-

|Week 5/6

||

4.1

||

[[Functions of Several Variables]]

||

* [[Domain of a Function]]
* [[Range of a Function]]
* [[Solving Equations and Inequalities]]
* [[Graphs| Graphing a Function]]

||
* Functions of two variables
* Functions of three variables
* Domain and range of multivariable functions
* Bounded regions
* Graphs and level curves of two variable functions
* Level surfaces of three variable functions
|-

|Week 6

||

4.2

||

[[Limit and Continuity of Function of Several Variables]]

||

* [[Continuity]]
* [[The Limit Laws]]
* [[Composition of Functions]]
* [[The Dot Product]]

||

* Limits of functions of two variables
* Limits of functions of more than two variables
* Properties of limits of functions of several variables
* Two path test of non-existing of a limit
* Continuity for functions of several variables
* Continuity of composition
* Extreme values on closed and bounded domains
|-

|Week 6

||

4.3

||

[[Partial Derivatives]]

||

* [[The Derivative as a Function|The first]] and [[The Second Derivative|second derivative]] of a function
* [[Limit and Continuity of Function of Several Variables]]

||
* Partial derivatives for functions of two variables
* Partial derivatives for functions of more than two variables
* Partial derivatives and continuity
* Second order partial derivatives
* Mixed derivative theorem
|-

|Week 7

||

4.4

||

[[Directional Derivatives and Gradient Vectors]]

||
* [[Trigonometric Functions]]
* [[Vectors, Unit Vectors]]
* [[Partial Derivatives]]
* [[Gradients]]
* [[The Dot Product]]
||
* Directional derivatives for functions of two variables
* Gradients
* Properties of directional derivatives
* Tangents to level curves
* Directional derivatives for functions of three variables
|-

|Week 7

||

4.5

||
[[Tangent Plane]],
[[Differentiability]]

||
* [[Partial Derivatives]]
* [[Parametric Equations]] of Lines
* [[Equations of Lines, Planes and Surfaces in Space]]

||
* Determine the equation of a plane tangent to a given surface at a point
* Determine the parametric equation of a normal line to a given surface at a point
* The linear approximation of a function of two variables at a point
* The definition of differentiability for a function of two variables
* Differentiability implies Continuity
* Continuity of First Partial Derivatives implies Differentiability
* The definition of total differentiability for a function of two variables
* Use the total differential to approximate the change in a function of two variables
|-

|Week 7

||

4.6

||

[[The Chain Rule for Functions of more than One Variable]]

||
* [[Differentiation Rules]]
* [[The Chain Rule]]
* [[Partial Derivatives]]

||
* Chain rule for functions of one independent variable and several intermediate variables.
* Chain rule for functions of two independent variable and several intermediate variables.
* Method for implicit differentiation.
* The general chain rule for functions of several independent variables
|-
|Week 8

||

4.7

||

[[Maxima and Minima Problems]]

||
* [[Extreme values on closed and bounded domains]]
* [[Partial Derivatives]]
* [[Maxima and Minima|Maxima, Minima and Critical Points of a Function]]
* [[Limit and Continuity of Function of Several Variables]]

||
* The derivative test for local extreme values
* Extreme values on closed and bounded domains
* Critical points and saddle points for functions of two variables
* Second derivative test for local extreme values
* Absolute maxima and minima on closed and bounded regions
|-
|Week 8/9

||

4.8

||

[[Lagrange Multipliers]]

||

* [[Partial Derivatives]]
* [[Critical Points of a Function]]

||
* Lagrange Multipliers with One Constraint
* Lagrange Multipliers with Two Constraints
|-

|Week 9/10

||

5.1

||

[[Multiple Integrals|Double Integrals over Rectangular Regions]]

||

* [[Approximating Areas]]
* [[The Definite Integral|Limits of Riemann Sums]]

||
* Double Integral is the limit of Double Sums.
* Double Integrals over Rectangular Regions.
* Interated Integrals.
* Fubini's Theorem (part 1).
|-

|Week 10

||

5.2

||

[[Multiple Integrals|Double Integrals over General Regions]]

||

* [[Continuity]]
* [[Determining Volumes by Slicing]]
* [[Multiple Integrals|Double and Iterated Integrals over Rectangular regions]]

||
* Double integrals over bounded, general regions.
* Properties of double Integrals.
* Fubini's theorem (part 2)
* Changing the order of Integration.
* Calculating Volumes, Areas and Average Values
|-

|Week 11

||

5.3

||

[[Multiple Integrals|Double Integrals in Polar Coordinates]]

||

* [[Multiple Integrals|Double Integrals over General Regions]]
* [[Polar Coordinates]]

||
* Double Integrals over rectangular polar regions.
* Double Integrals over general polar regions.
* Changing Cartesian Integrals into Polar Integrals.
* Using Double Integrals in Polar Coordinates to find Volumes, Areas.
|-

|Week 11

||

5.4

||

[[Multiple Integrals|Triple Integrals in Rectangular Coordinates]]

||

* [[Multiple Integrals|Double Integrals]]
* [[Multiple Integrals|Area by Double Integration]]
* '''[[Change of Variables]]'''

||

* Triple Integrals over general bounded regions.
* Finding Volumes by evaluating Triple Integrals.
* Average value of a function in space.
* Changing Integration Order and Coordinate systems.
|-

|Week 12

||

5.5

||

[[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]]

||

* [[Multiple Integrals|Double Integrals in Polar Form]]
* [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]]

||

* Integrations in Cylindrical Coordinates.
* Equations relating rectangular and cylindrical coordinates.
* Changing Cartesian integrations into Cylindrical integrations.
* Integrations in Spherical coordinates.
* Equations relating spherical coordinates to Cartesian and cylindrical coordinates.
* Changing Cartesian integrations into Cylindrical integrations.
|-

|Week 13

||

5.6

||

[[Multiple Integrals|Applications of Multiple Integrals]]

||

* [[Multiple Integrals|Double Integral]]
* [[Multiple Integrals|Triple Integrals]]

||

* Finding Masses, Moments, Centers of Masses, Moments of Inertia in Two Dimensions.
* Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions.
|-
|Week 13/14

||

5.7

||

[[Multiple Integrals|Change of Variables in Multiple Integrals]]

||

* [[Multiple Integrals|Double Integral]]
* [[Multiple Integrals|Triple Integrals]]

||

* Determine the image of a region under a given transformation of variables.
* Compute the Jacobian of a given transformation.
* Evaluate a double integral using a change of variables.
* Evaluate a triple integral using a change of variables.
|-
|Week 14

||

6.1

||

[[Vector Fields]]

||

* [[The Dot Product]] 
* [[Directional Derivatives and Gradient Vectors]]
||
* Vector Fields in a plane.
* Vector Fields in Space.
* Potential Functions.
* Gradient Fields, Conservative Vector Fields.
* The Cross-Partial Test for Conservative Vector Fields.
* Determining Whether a Vector Field is conservative.
|-

|Week 14

||

6.2

||

[[Line Integrals]]

||

* [[Parametric Equations]]
* [[Curves in Space and Vector-Valued Functions]]
* [[Arc Length]]

||
* Line Integrals of functions a long a smooth curves in a planer or in space
* Line Integrals of of vector fields along an oriented curves in a plane or space..
* Properties of Vector Line Integrals.
* Evaluating Line Integrals.
* Applications of line integrals: Calculating Arc Length, the Mass of a wire, Work done by a force, Flux across a curve, Circulation of a force.
|-

|Week 14/15

||

6.3

||

[[Conservative Vector Fields]]

||

* [[Vector Fields and Line Integrals]]
* [[Partial Derivatives]]

||
* Describe simple and closed curves
* Define connected and simply connected regions.
* Explain how to test a vector field to determine whether it is conservative.
* Find a potential function for a conservative vector field.
* Use the Fundamental Theorem for Line Integrals to evaluate a line integral of a vector field.
|-

|Weeks 14/15

||

6.4

||

[[Green's Theorem]]

[[Stokes' Theorem]]

||

* [[Vector Fields]]
* [[Line Integrals]]
* [[Partial Derivatives]]
* [[The Dot Product]]
* [[Line Integrals|Path Independence]]
* [[Conservative Vector Fields]]

||

* Circulation form of Green's Theorem.
* Flux Form of Green’s Theorem.
* Applying Green's Theorem to find Work, Flux.

|}

MAT2214

2023-03-31T21:17:30Z

Juan.gutierrez3: /* Topics List */ Removed HTML formatting

MAT1213

2023-03-31T20:28:41Z

Juan.gutierrez3: Changed content to match a 3-CH course with instructors' input

MAT1213

2023-03-31T19:58:27Z

Juan.gutierrez3: /* Topics List */ removed html formatting

MAT1214

2023-03-31T19:57:34Z

Juan.gutierrez3: /* Topics List */ removed HTML formatting

MAT1223

2023-03-31T19:46:51Z

Juan.gutierrez3: /* Topics List */ Changed content with instructors' input

MAT1223

2023-03-31T19:38:19Z

Juan.gutierrez3: Undo revision 5172 by Juan.gutierrez3 (talk)

The textbook for this course is
[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history].

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">1.5</div>

||

[[Integration by Substitution]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Antiderivatives]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 

||

* Recognize when to use integration by substitution.
* Use substitution to evaluate indefinite integrals.
* Use substitution to evaluate definite integrals.

|-

|Week 2

||

<div style="text-align: center;">2.1</div>

||

[[Area between Curves]]

||

* [[Toolkit Functions|Graphing Elementary Functions]] 
* [[The Definite Integral]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the area of a region between two curves by integrating with respect to the independent variable.
* Find the area of a compound region.
* Determine the area of a region between two curves by integrating with respect to the dependent variable.

|-

|Week 2

||

<div style="text-align: center;">2.2</div>

||

[[Determining Volumes by Slicing]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the volume of a solid by integrating a cross-section (the slicing method).
* Find the volume of a solid of revolution using the disk method.
* Find the volume of a solid of revolution with a cavity using the washer method

|-

|Week 3

||

<div style="text-align: center;">2.3</div>

||

[[Volumes of Revolution, Cylindrical Shells]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[Determining Volumes by Slicing]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Calculate the volume of a solid of revolution by using the method of cylindrical shells.
* Compare the different methods for calculating a volume of revolution.

|-

|Week 3
||

<div style="text-align: center;">2.4</div>

||

[[Arc Length and Surface Area]]

||

* [[Differentiation Rules]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the length of a plane curve between two points.
* Find the surface area of a solid of revolution.

|-

|Week 4

||

<div style="text-align: center;">2.5</div>

||

[[Physical Applications]]

||

* '''[[Areas of basic shapes]]''' 
* '''[[Volume of a cylinder]]''' 
* '''[[Basic Physics (Mass, Force, Work, Newton's Second Law, Hooke's Law)]]''' 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Determine the mass of a one-dimensional object from its linear density function.
* Determine the mass of a two-dimensional circular object from its radial density function.
* Calculate the work done by a variable force acting along a line.
* Calculate the work done in stretching/compressing a spring.
* Calculate the work done in lifting a rope/cable.
* Calculate the work done in pumping a liquid from one height to another.
* Find the hydrostatic force against a submerged vertical plate.

|-

|Week 4

||

<div style="text-align: center;">2.6</div>

||

[[Moments and Center of Mass]]

||

* [[Toolkit Functions|Graphing elementary functions]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Find the center of mass of objects distributed along a line.
* Find the center of mass of objects distributed in a plane.
* Locate the center of mass of a thin plate.
* Use symmetry to help locate the centroid of a thin plate.

|-

|Week 5

||

<div style="text-align: center;">3.1</div>

||

[[Integration by Parts]]

||

* [[Differentiation Rules]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 

||

* Recognize when to use integration by parts.
* Use the integration-by-parts formula to evaluate indefinite integrals.
* Use the integration-by-parts formula to evaluate definite integrals.
* Use the tabular method to perform integration by parts.
* Solve problems involving applications of integration using integration by parts.

|-

|Week 5

||

<div style="text-align: center;">3.2</div>

||

[[Trigonometric Integrals]]

||

* [[Trigonometric Functions]] 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 

||

* Evaluate integrals involving products and powers of sin(x) and cos(x).
* Evaluate integrals involving products and powers of sec(x) and tan(x).
* Evaluate integrals involving products of sin(ax), sin(bx), cos(ax), and cos(bx).
* Solve problems involving applications of integration using trigonometric integrals.

|-

|Week 6

||

<div style="text-align: center;">3.3</div>

||

[[Trigonometric Substitution]]

||

* [[Completing the Square]] 
* [[Trigonometric Functions]] 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 

||

* Evaluate integrals involving the square root of a sum or difference of two squares.
* Solve problems involving applications of integration using trigonometric substitution.

|-

|Week 6

||

<div style="text-align: center;">3.4</div>

||

[[Partial Fractions]]

||

* [[Factoring Polynomials]] 
* [[Completing the Square]] 
* [[Dividing Polynomials|Long Division of Polynomials]] 
* [[Systems of Linear Equations]] 
* [[Antiderivatives]] 
* [[Integration by Substitution]] 

||

* Integrate a rational function whose denominator is a product of linear and quadratic polynomials.
* Recognize distinct linear factors in a rational function.
* Recognize repeated linear factors in a rational function.
* Recognize distinct irreducible quadratic factors in a rational function.
* Recognize repeated irreducible quadratic factors in a rational function.
* Solve problems involving applications of integration using partial fractions.

|-

|Week 7

||

<div style="text-align: center;">3.7</div>

||

[[Improper Integrals]]

||

* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 
* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Recognize improper integrals and determine their convergence or divergence.
* Evaluate an integral over an infinite interval.
* Evaluate an integral over a closed interval with an infinite discontinuity within the interval.
* Use the comparison theorem to determine whether an improper integral is convergent or divergent.

|-

|Week 8

||

<div style="text-align: center;">4.3</div>

||

[[Separation of Variables]]

||

* [[Factoring Polynomials]] 
* [[Exponential Properties]] 
* [[Logarithmic Properties]] 
* [[Linear Approximations and Differentials|Differentials]] 
* [[Initial Value Problem]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 
* [[Trigonometric Integrals]] 
* [[Trigonometric Substitution]] 
* [[Partial Fractions]] 

||

* Recognize separable differential equations.
* Use separation of variables to solve a differential equation.
* Develop and analyze elementary mathematical models.

|-

|Week 8

||

<div style="text-align: center;">4.5</div>

||

[[First-Order Linear Equations]]

||

* [[Separation of Variables]] 

||

* Write a first-order linear differential equation in standard form.
* Find an integrating factor and use it to solve a first-order linear differential equation.
* Solve applied problems involving first-order linear differential equations.

|-

|Week 9

||

<div style="text-align: center;">5.1</div>

||

[[Sequences]]

||

* [[The Limit Laws| The Limit Laws and Squeeze Theorem]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 

||

* Find a formula for the general term of a sequence.
* Find a recursive definition of a sequence.
* Determine the convergence or divergence of a given sequence.
* Find the limit of a convergent sequence.
* Determine whether a sequence is bounded and/or monotone.
* Apply the Monotone Convergence Theorem.

|-

|Week 10

||

<div style="text-align: center;">5.2</div>

||

[[Infinite Series]]

||

* '''[[Sigma notation]]''' 
* [[Sequences]] 
* [[Partial Fractions]] 

||

* Write an infinite series using sigma notation.
* Find the nth partial sum of an infinite series.
* Define the convergence or divergence of an infinite series.
* Identify a geometric series.
* Apply the Geometric Series Test.
* Find the sum of a convergent geometric series.
* Identify a telescoping series.
* Find the sum of a telescoping series.

|-

|Week 10

||

<div style="text-align: center;">5.3</div>

||

[[The Divergence and Integral Tests]]

||

* [[The Limit Laws]] 
* [[Limits at Infinity and Asymptotes| Limits at Infinity]] 
* [[Continuity]] 
* [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Improper Integrals]] 

||

* Use the Divergence Test to determine whether a series diverges.
* Use the Integral Test to determine whether a series converges or diverges.
* Use the p-Series Test to determine whether a series converges or diverges.
* Estimate the sum of a series by finding bounds on its remainder term.

|-

|Week 11

||

<div style="text-align: center;">5.4</div>

||

[[Comparison Tests]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 

||

* Use the Direct Comparison Test to determine whether a series converges or diverges.
* Use the Limit Comparison Test to determine whether a series converges or diverges.

|-

|Week 11

||

<div style="text-align: center;">5.5</div>

||

[[Alternating Series]]

||

* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] 
* [[L’Hôpital’s Rule]] 
* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests|The p-Series Test]] 
* [[Comparison Tests]] 

||

* Use the Alternating Series Test to determine the convergence of an alternating series.
* Estimate the sum of an alternating series.
* Explain the meaning of absolute convergence and conditional convergence.

|-

|Week 12

||

<div style="text-align: center;">5.6</div>

||

[[Ratio and Root Tests]]

||

* '''[[Factorials]]''' 
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] 
* [[L’Hôpital’s Rule]] 

||

* Use the Ratio Test to determine absolute convergence or divergence of a series.
* Use the Root Test to determine absolute convergence or divergence of a series.
* Describe a strategy for testing the convergence or divergence of a series.

|-

|Week 12

||

<div style="text-align: center;">6.1</div>

||

[[Power Series and Functions]]

||

* [[Infinite Series|The Geometric Series Test]] 
* [[The Divergence and Integral Tests]] 
* [[Comparison Tests]] 
* [[Alternating Series]] 
* [[Ratio and Root Tests]] 

||

* Identify a power series.
* Determine the interval of convergence and radius of convergence of a power series.
* Use a power series to represent certain functions.

|-

|Week 13

||

<div style="text-align: center;">6.2</div>

||

[[Properties of Power Series]]

||

* [[Differentiation Rules]] 
* [[Antiderivatives]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Power Series and Functions]] 

||

* Combine power series by addition or subtraction.
* Multiply two power series together.
* Differentiate and integrate power series term-by-term.
* Use differentiation and integration of power series to represent certain functions as power series.

|-

|Week 14

||

<div style="text-align: center;">6.3</div>

||

[[Taylor and Maclaurin Series]]

||

* [[The Derivative as a Function|Higher-Order Derivatives]] 
* [[Power Series and Functions]] 
* [[Properties of Power Series]] 

||

* Find a Taylor or Maclaurin series representation of a function.
* Find the radius of convergence of a Taylor Series or Maclaurin series.
* Finding a Taylor polynomial of a given order for a function.
* Use Taylor's Theorem to estimate the remainder for a Taylor series approximation of a given function.

|-

|Week 15

||

<div style="text-align: center;">7.1</div>

||

[[Parametric Equations]]

||

* [[Toolkit Functions|Sketching Elementary Functions]] 
* '''[[Equation of a Circle]]''' 
* '''[[Equation of an Ellipse]]''' 
* [[Trigonometric Functions]] 
* [[Properties of the Trigonometric Functions|Trigonometric Identities]] 

||

* Plot a curve described by parametric equations.
* Convert the parametric equations of a curve into the form y=f(x) by eliminating the parameter.
* Recognize the parametric equations of basic curves, such as a line and a circle.

|-

|Week 15

||

<div style="text-align: center;">7.2</div>

||

[[The Calculus of Parametric Equations]]

||

* [[Parametric Equations]] 
* [[Differentiation Rules]] 
* [[The Derivative as a Function|Higher-Order Derivatives]] 
* [[The Fundamental Theorem of Calculus]] 
* [[Integration by Substitution]] 
* [[Integration by Parts]] 

||

* Find the slope of the tangent line to a parametric curve at a point.
* Use the second derivative to determine the concavity of a parametric curve at a point.
* Determine the area bounded by a parametric curve.
* Determine the arc length of a parametric curve.
* Determine the area of a surface obtained by rotating a parametric curve about an axis.

|}

MAT1223

2023-03-31T19:37:39Z

Juan.gutierrez3: /* Topics List */ Modifed content per input by Calc II instructors

MAT1223

2023-03-31T19:25:03Z

Juan.gutierrez3: /* Topics List */