Summer 2, 2021
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Lecture |
Date |
Lecture Topics |
Readings and Resources |
Optional Resources |
Homeworks/Labs |
| 1 | W 7/7 | Administrative matters; Goals of the course; Math review; Systems of Equations (as time permits) |
Reading: Math Review: PDF Required Reading: Systems of Linear Equations |
Python Resources CS 132: HTML |
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| Th 7/8 | Lab: Introduction to Jupyter Notebooks and Numpy | Look at Python, Jupyter, Latex, and Numpy tutorials in the tutorials directory linked above as needed. | Optional video: As listed above under Useful Links |
HW 01: IPYNB HW 01 zipped: ZIP |
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| 2 | F 7/9 | Gaussian Elimination; Parametric Forms of Solutions (if time) |
Required Reading: 1.2 Row Reduction, 1.3 Parametric Forms |
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| 3 | M 7/12 |
Vectors, Vector Equations, and Span |
Required Readings: Vectors, Vector Equations and Span | Supplementary videos: | |
| 4 | W 7/14 |
Matrix Equations, Solution Sets (Homogeneous Sets of Equations) |
Matrix Equations, Solution Sets | ||
| Th 7/15 | Lab: | Look at Python, Jupyter, Latex, and Numpy tutorials in the tutorials directory linked above as needed. |
HW 02: IPYNB HW 02 zipped: ZIP |
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| 5 | F 7/16 |
Solution Sets (In-homogeneous Sets of Equations); Linear Independence, Subspaces (if time) |
Linear Independence, Subspaces | ||
| 6 | M 7/19 |
Subspaces continued; Basis and Dimension; Bases as Coordiate Systems (if time) |
Basis and Dimension, Bases as Coordinate Systems | ||
| 7 | W 7/21 |
The Rank Theorem; Matrix Transformations: One-to-one and Onto Transformations; Linear Transformations |
The Rank Theorem, Matrix Transformations, One-to-one and Onto Transformations, Linear Transformations | Optional videos:
Linear Transformation Visualizer (Geogebra) HTML |
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| Th 7/22 | Lab: | Look at Python, Jupyter, Latex, and Numpy tutorials in the tutorials directory linked above as needed. |
HW 03A: IPYNB HW 03A zipped: ZIP HW 03B: IPYNB HW 03B zipped: ZIP |
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| 8 | F 7/23 |
Matrix Multiplication and Matrix Algebra; Matrix inverses; The Invertible Matrix Theorem |
Matrix Multiplication, Matrix Inverse, The Invertible Matrix Theorem |
Optional videos: Inverse Matrices; column space and null space |
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| 9 | M 7/26 |
Matrix Decomposition: The LU Decomposition; The Determinate and its properties; Determinants and Volumes |
LU Factorization, Determinants: Definition, Determinants and Volumes |
Optional videos: Determinants |
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| 10 | W 7/28 | Eigenvectors and Eigenvalues; The Characteristic Polynomial
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Eigenvalues and Eigenvectors, The Characteristic Polynomial | Optional video: Eigenvectors and Eigenvalues | |
| Th 7/29 | Lab: Calculating the LU decomposition, Determinates, and Eigenspaces using Gaussian Elimination |
HW 04A: IPYNB HW 04A zipped: ZIP HW 04B: IPYNB HW 04B zipped: ZIP |
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| 11 | F 7/30 |
Similarity; Diagonalization |
Similarity, Diagonalization | ||
| 12 | M 8/2 |
Dot Products and Orthogonality; Orthogonal Complements |
Dot Products and Orthogonality, Orthogonal Complements | ||
| 13 | W 8/4 |
Orthogonal Projection; Orthogonal Sets |
Orthogonal Projection, Orthogonal Sets | ||
| Th 8/5 | Lab: Stochastic Matrices, Difference Equations, and Markov Chains | Stochastic Matrices |
HW 05A: IPYNB HW 045A zipped: ZIP HW 05B: IPYNB HW 05B zipped: ZIP |
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| 14 | F 8/6 | Orthogonal Projections, Orthogonal Bases
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Orthogonal Projection, Orthogonal Sets | ||
| 15 | M 8/9 |
Least Squares Solutions |
Least Squares Solutions | f | |
| 16 | W 8/11 | Singular Value Decompositions
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Singular Value Decomposition | ||
| F 8/13 |
Final Exam Handed out |