MAT1073

From Department of Mathematics at UTSA
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Course Catalog

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

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 2

Module 0.1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of order of operations

Review of:

  • PEMDAS
Week 2

Module 0.1

  • Basic mathematical symbols and terminology
  • Basic understanding of Order of Operations (Module 0.1)
  • Basic understanding of exponents and radicals
  • Basic understanding of factoring polynomials and definition of a factor
  • Understanding operations with fractions

Review the following radical expression concepts:

  • evaluate square roots
  • use the product rule to simplify square roots
  • use the quotient rule to simplify square roots
  • add and subtract square roots
Week 3

Module 0.2

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations (Module 0.1)
  • Basic prime factorization
  • Basic understanding of factoring

Review factoring techniques for the following type of polynomials:

  • factor the greatest common factor of a polynomial
  • factor a trinomial
  • factor by grouping
  • factor a perfect square trinomial
  • factor a difference of squares
Week 3

Module 0.3

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations (Module 0.1)
  • Basic understanding of factoring

Review the following linear equation topics:

  • Basic mathematical symbols and terminology
  • solving linear equations in one variable
  • finding a linear equation
  • write and interpret a linear equation
Week 3

Module 0.4

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of factoring
  • Basic understanding of Solving Equations and Inequalities (Module 0.3)
Week 3

Module 0.4

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of order of operations
  • Basic understanding of factoring
  • Basic understanding of solving Linear Equations (Module 0.4)
  • Understanding of the Cartesian coordinate system
Week 4

Module 1.1

  • 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 1.2

  • Solve systems of equations in three variables
  • Identify inconsistent systems of equations containing three variables
  • Express solutions of a system of dependent equations containing three variables
Week 5

Module 2.1

  • Determine whether a relation represents a function.
Week 5

Module 2.2

  • Basic understanding of Graphs (Module 0.4)
  • Basic understanding of Functions (Module 2.1)
  • 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 5

Module 2.2

  • Find the domain of a function defined by an equation.
  • Graph piecewise-defined functions.
Week 5

Module 2.2

  • Find the range of a function defined by an equation.
  • Graph piecewise-defined functions.
Week 5

Module 2.2

  • Basic understanding of Cartesian coordinate system (Module 0.4: Graphs)
  • Identify the basic toolkit functions
  • Determine Domain and Range for the basic toolkit functions (Module 1.2)
  • Graph the basic toolkit functions. (Module 0.4)
Week 6

Module 3.1

  • Basic understanding of power expressions.
  • The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 2.2).
  • Identify power functions.
  • Identify end behavior of power functions.
Week 6

Module 3.1

  • Basic understanding of a polynomial expression.
  • The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 2.2).
  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
Week 6

Module 3.2

  • Fundamentals of Polynomials (Module 2.1)
  • The student understands the difference between a maximum and minimum.
  • 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 7

Module 4.1

  • Basic understanding of multiplying and dividing fractions.
  • Basic understanding of simplifying fractions by common factors.
  • Basic understanding of Factoring Polynomials (Module 0.2)
  • Use long division to divide polynomials
  • Use synthetic division to divide polynomials
Week 7

Module 4.2

  • 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 8

Module 5.1

  • The student understands that zero in the denominator of a fraction is undefined.
  • Basic understanding of Polynomial Functions (Module 3.1)
Week 8

Module 5.2

  • The student understands that zero in the denominator of a fraction is undefined.
  • The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2).
  • Solving applied problems involving Polynomial Functions. (Module 2.1)
  • Use arrow notation.
  • Solve applied problems involving rational functions.
  • Find the Domain of rational functions.
  • Identify vertical asymptotes.
  • Identify horizontal asymptotes.
Week 9

Module 6.1

  • Recognize characteristics of graphs of polynomial functions
  • Use factoring to find zeros of polynomial functions
  • Identify zeros and their multiplicities
  • Determine end behavior
  • Understand the relationship between degree and turning points
  • Graph polynomial functions
Week 9

Module 6.2

  • Identify and graph vertical asymptotes
  • Identify and graph horizontal asymptotes
  • Determine behavior of rational functions around vertical asymptotes
  • Graph rational functions
Week 10

Module 7.1

  • Graph functions using vertical and horizontal shifts
  • Graph functions using reflections about the x-axis and the y-axis
  • Determine whether a function is even, odd, or neither from it's graph
  • Graph functions using compressions and stretches
  • Combine transformations
Week 10

Module 7.2

  • Combine transformations
Week 11

Module 8.1

  • Combine functions using algebraic operations
  • 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 11

Module 8.2

  • Verify inverse functions
  • 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 12

Module 9.1

  • Understanding Order of Operations. (Module 0.1)
  • Use the product rule for exponents.
  • Use the quotient rule for exponents.
  • Use the power rule for logarithms.
Week 12

Module 9.2

  • Evaluate exponential functions.
  • Find the equation of an exponential function.
  • Use compound interest formulas.
  • Evaluate exponential functions with base e.
Week 13

Module 10.1

  • Rewriting from exponential form to logarithmic form and vice versa
-y=b^x\equiv\log_b(y)=x
  • Evaluate logarithms.
  • Use common logarithms.
  • Use natural logarithms.
Week 13

Module 10.2

  • 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 14

Module 11

  • Solve direct variation problems
  • Solve inverse variation problems
  • Solve problems involving joint variation
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