Difference between revisions of "MAT2253"

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Prerequisite: [[MAT1214]]/[[MAT1213]] Calculus I
 
Prerequisite: [[MAT1214]]/[[MAT1213]] Calculus I
  
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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.
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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.
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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
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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
  
 
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| 3 || 2.3 || Solving systems of linear equations ||  ||  
 
| 3 || 2.3 || Solving systems of linear equations ||  ||  
 
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| 4 || 3.1, 3.2, 3.3 || Norms, Inner Products, Lengths & Distances ||  ||  
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| 4 || 2.4 || Vector spaces ||  ||  
 
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| 5 || 3.4 || Angles & orthogonality ||  ||  
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| 5 || 2.5 ||Linear Independence ||  ||  
 
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| 6 || 2.4, 2.5 || Vector spaces & Linear Independendence ||  ||  
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| 6 || 2.6 || Basis & Rank ||  ||  
 
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| 7 || Mini-test ||  ||  ||  
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| 7 || Exam 1 ||  ||  ||  
 
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| 8 || 2.6 || Basis & Rank ||  ||  
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| 8 || 2.7 || Linear Mappings ||  ||  
 
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| 9 || 2.7 || Linear Mappings ||  ||  
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| 9 || 2.7 || Linear Mappings (examples) ||  ||  
 
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| 10 || 4.1 || Determinant and Traces ||  ||  
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| 10 || 3.1, 3.2, 3.3 || Norms, Inner Products, Lengths & Distances ||  ||  
 
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| 11 || 4.2 || Eigenvalues & Eigenvectors ||  ||  
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| 11 || 3.4 || Angles & orthogonality ||  ||  
 
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| 12 || 4.3, 4.4 || Matrix Factorization ||  ||  
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| 12 || 3.5 || Orthonormal Basis ||  ||  
 
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| 13 || 3.5 || Orthonormal Basis ||  ||  
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| 13 || 3.7 || Inner Product of Functions ||  ||  
 
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| 14 || 3.7 || Inner Product of Functions ||  ||  
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| 14 || Project 1 || ||  ||  
 
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| 15 || 3.9 || Rotations ||  ||  
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| 15 || 4.1 || Determinant and Traces ||  ||  
 
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| 16 || Mini-test || ||  ||  
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| 16 || 4.2 || Eigenvalues & Eigenvectors ||  ||  
 
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| 17 || 5.1 || Vector Calculus ||  ||  
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| 17 || 4.3, 4.4 || Matrix Factorization ||  ||
 
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| 18 || 5.1 || Taylor Series ||  ||  
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| 18 || 5.1 ||Vector Calculus Intro and Taylor Series ||  ||  
 
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| 19 || 5.1 || Differentiation Rules Review ||  ||  
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| 19 || 5.1, 5.2 || Differentiation Rules Review and Partial Derivatives ||  ||  
 
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| 20 || 5.2 || Partial Derivatives ||  ||  
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| 20 || 5.2 || Gradients- Examples, visualizations, computation ||  ||  
 
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| 21 || 5.2 || Gradients - Examples, visualizations, computaiton ||  ||  
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| 21 || 5.3 || Gradients of Vector-Valued Functions ||  ||  
 
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| 22 || 5.2 || Rules for Partial Differentiation & Chain Rule ||  ||  
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| 22 || 5.4, Dhrymes 78 || Gradients of Matrices ||  ||  
 
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| 23 || Mini-test ||  ||  ||  
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| 23 || Exam 2 ||  ||  ||  
 
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| 24 || 5.3 || Gradients of Vector-Valued Functions ||  ||  
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| 24 || 5.5, Dhrymes 78 || Useful Identities for Computing Gradients ||  ||  
 
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| 25 || 5.3 || Gradients of Vector-Valued Functions ||  ||  
 
| 25 || 5.3 || Gradients of Vector-Valued Functions ||  ||  
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| 29 || Notes || Minimization via Newton's Method & Backpropagation ||  ||  
 
| 29 || Notes || Minimization via Newton's Method & Backpropagation ||  ||  
 
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| 30 || Min-test ||  ||  ||  
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| 30 ||Project 2 ||  ||  ||  
 
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| 31 || 5.8 || Linearization & Multivariate Taylor Series ||  ||  
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| 31 || 5.8 || Multivariate Taylor Series ||  ||  
 
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| 32 || Notes || Linear optimization: Simplex method ||  ||  
 
| 32 || Notes || Linear optimization: Simplex method ||  ||  
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| 33 || 7.1 || Optimization Using Gradient Descent ||  ||  
 
| 33 || 7.1 || Optimization Using Gradient Descent ||  ||  
 
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| 34 || 7.2 || Constrained Optimization and Lagrange Multipliers ||  ||
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| 34 || 7.2 and Notes || Constrained Optimization and Lagrange Multipliers: PCA ||  ||  
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| 35 || 7.3 || Convex Optimization ||  ||  
 
 
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| 36 || Mini-Test || ||  ||  
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| 35 || 7.3 || Convex Optimization (time permitting) ||  ||  
 
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| 37 || Bishop, Duda et al. || Feed-forward Artificial Neural Networks ||  ||  
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| 36 || Bishop, Duda et al. || Feed-forward Artificial Neural Networks ||  ||  
 
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| 38 || Bishop, Duda et al. || Backpropagation in ANNs ||  ||  
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| 37 || Bishop, Duda et al. || Backpropagation in ANNs ||  ||  
 
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| 39 || Bishop, Duda et al. || Activation Functions: Linear & Nonlinear ||  ||  
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| 38 || Bishop, Duda et al. || Activation Functions: Linear & Nonlinear ||  ||  
 
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| 40 || Bishop, Duda et al. || Step-by-step simple ANN ||  ||  
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| 39 || Bishop, Duda et al. || Step-by-step simple ANN ||  ||  
 
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| 41 || Bishop, Duda et al. || Measures of performance ||  ||  
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| 40 || Bishop, Duda et al. || Measures of performance ||  ||  
 
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| 42 || Bishop, Duda et al. || More complex architectures of ANNs ||  ||  
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| 41 || Bishop, Duda et al. || More complex architectures of ANNs ||  ||  
 
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| 43 || Mini-test ||  ||  ||  
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| 42 || Final Project Introduction ||  ||  ||  
 
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| 44 || Final project ||  ||  ||  
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| 43 || Final project||  ||  ||  
 
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| 45 || Review ||  ||  ||  
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| 44 || Review ||  ||  ||  
 
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Latest revision as of 09:55, 19 September 2025

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

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 2.4 Vector spaces
5 2.5 Linear Independence
6 2.6 Basis & Rank
7 Exam 1
8 2.7 Linear Mappings
9 2.7 Linear Mappings (examples)
10 3.1, 3.2, 3.3 Norms, Inner Products, Lengths & Distances
11 3.4 Angles & orthogonality
12 3.5 Orthonormal Basis
13 3.7 Inner Product of Functions
14 Project 1
15 4.1 Determinant and Traces
16 4.2 Eigenvalues & Eigenvectors
17 4.3, 4.4 Matrix Factorization
18 5.1 Vector Calculus Intro and Taylor Series
19 5.1, 5.2 Differentiation Rules Review and Partial Derivatives
20 5.2 Gradients- Examples, visualizations, computation
21 5.3 Gradients of Vector-Valued Functions
22 5.4, Dhrymes 78 Gradients of Matrices
23 Exam 2
24 5.5, Dhrymes 78 Useful Identities for Computing Gradients
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 Project 2
31 5.8 Multivariate Taylor Series
32 Notes Linear optimization: Simplex method
33 7.1 Optimization Using Gradient Descent
34 7.2 and Notes Constrained Optimization and Lagrange Multipliers: PCA
35 7.3 Convex Optimization (time permitting)
36 Bishop, Duda et al. Feed-forward Artificial Neural Networks
37 Bishop, Duda et al. Backpropagation in ANNs
38 Bishop, Duda et al. Activation Functions: Linear & Nonlinear
39 Bishop, Duda et al. Step-by-step simple ANN
40 Bishop, Duda et al. Measures of performance
41 Bishop, Duda et al. More complex architectures of ANNs
42 Final Project Introduction
43 Final project
44 Review
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