Difference between revisions of "MAT2253"

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

Latest revision as of 14:44, 24 August 2026

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

Week Section Topic Prerequisites SLOs
1 2.1 Systems of Linear Equations
2 2.2 Matrices
2.3 Solving systems of linear equations
3 2.4 Vector spaces
4 2.5 Linear Independence
2.6 Basis & Rank
5 Exam 1
2.7 Linear Mappings
6 2.7 Linear Mappings (examples)
4.1 Determinant and Traces
7 4.2 Eigenvalues & Eigenvectors
4.3, 4.4 Matrix Factorizations (Diagonalization)
8 3.1, 3.2, 3.3 Norms, Inner Products, Lengths & Distances
3.4 Angles & orthogonality
9 3.5 *Orthonormal Basis
3.7 *Inner Product of Functions
Project 1
10 5.1 Vector Calculus Intro and Taylor Series
5.1, 5.2 Differentiation Rules Review and Partial Derivatives
5.2 Gradients- Examples, visualizations, computation
11 5.3 Gradients of Vector-Valued Functions
5.4, Dhrymes 78 Gradients of Matrices
12 Exam 2
5.5, Dhrymes 78 Useful Identities for Computing Gradients
13 5.7 Higher-Order Derivatives
Notes Minimization via Newton's Method & Backpropagation
Project 2
14 5.8 Multivariate Taylor Series
Notes Linear optimization: Simplex method
7.1 Optimization Using Gradient Descent
15 7.2 and Notes *Constrained Optimization and Lagrange Multipliers: PCA
Bishop, Duda et al. Feed-forward Artificial Neural Networks
Bishop, Duda et al. Backpropagation in ANNs
16 Bishop, Duda et al. Activation Functions: Linear & Nonlinear
Bishop, Duda et al. Step-by-step simple ANN
Final Project
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