Daily Syllabus, Math 221 Linear Algebra, Fall 2024
Be sure to check back, because this will be updated during the semester.
- All section numbers refer to the 3rd and 4th editions of Linear Algebra and Its Applications by Lay.
- PCA due refers to Pre-Class Assignments submitted through Canvas
- PS due refers to Problem Sets uploaded to Canvas
| Week | Major Topics |
Tuesday 11:00 - 12:20 |
Thursday 11:00 - 12:20 |
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|---|---|---|---|---|---|
| 1 |
Welcome to Linear Algebra!
Systems of linear equations Background Questionnaire due |
8/27 | 1.1 Systems of Linear Equations | 8/29 | 1.2 Row Reduction and Echelon Forms |
| 2 |
Equivalent systems of vector equations Describing all solutions to a system PCA due Monday 9/2 @ 11:59 pm |
9/3 |
1.3 Vector Equations 1.4 The Matrix Equation Ax=b |
9/5 |
1.5 Solution Sets of Linear Systems
PS #1 due Friday 9/6 @ 12:30 pm |
| 3 | Matrices as functions PCA due Monday 9/9 @ 11:59 pm |
9/10 |
1.7 Linear Independence 1.8 Introduction to Linear Transformations |
9/12 |
1.8 Introduction to Linear Transformations 1.9 The Matrix of a Linear Transformation PS #2 due Friday 9/13 @ 12:30 pm |
| 4 |
Multiplying and inverting matrices PCA due Monday 9/16 @ 11:59 pm |
9/17 | 2.1 Matrix Operations | 9/19 |
2.2 Inverse of a Matrix 2.3 Characterizations of Invertible Matrices PS #3 due Friday 9/20 @ 12:30 pm |
| 5 |
Using matrices to shift, rotate, and skew graphics
The determinant function Do the reading, but no PCA to submit |
9/24 |
Exam 1, In-Class part
Covers thru Section 2.3 |
9/26 |
2.7 Applications to Computer Graphics 3.1 Introduction to Determinants
Exam 1, Takehome part due Friday 9/27 @ 11:59 pm |
| 6 |
Identifying underlying structural similarities PCA due Monday 9/30 @ 11:59 pm |
10/1 |
3.2 Properties of Determinants 4.1 Vector Spaces and Subspaces |
10/3 |
4.1 Vector Spaces and Subspaces 4.2 Null Spaces, Column Spaces, and Linear Transformations |
| 7 | Minimal generating sets PCA due Monday 10/7 @ 11:59 pm |
10/8 | 4.3 Linearly Independent Sets; Bases | 10/10 |
4.3 Linearly Independent Sets; Bases (cont.)
PS #4 due Friday 10/11 @ 12:30 pm |
| 8 | No class meetings this week due to Fall Break and MAP Day | 10/15 | Fall Break | 10/17 | MAP Day |
| 9 |
An invariant of vector spaces
Understanding longterm behavior PCA due Monday 10/21 @ 11:59 pm |
10/22 |
4.5 The Dimension of a Vector Space 4.6 Rank |
10/24 |
4.9 Applications to Markov Chains
PS #5 due Friday 10/25 @ 12:30 pm |
| 10 |
Directions fixed by matrix functions PCA due Monday 10/28 @ 11:59 pm |
10/29 |
5.1 Eigenvectors and Eigenvalues 5.2 The Characteristic Equation |
10/31 |
6.1 Inner Product, Length, and Orthogonality
PS #6 due Friday 11/1 @ 12:30 pm |
| 11 |
Extending geometric intuition to higher dimensions PCA due Monday 11/4 @ 11:59 pm |
11/5 | 6.2 Orthogonal Sets | 11/7 |
6.3 Orthogonal Projections 6.4 The Gram-Schmidt Process PS #7 due Friday 11/8 @ 12:30 pm |
| 12 | Finding the closest vector Do the reading, but no PCA to submit |
11/12 |
Exam 2, In-Class part
Covers thru Section 6.2 |
11/14 |
6.5 Least-Squares Problems
Exam 2, Takehome part due Friday 11/15 @ 11:59 pm |
| 13 |
A factorization of certain square matrices PCA due Monday 11/18 @ 11:59 pm |
11/19 | 5.3 Diagonalization | 11/21 | 7.1 Diagonalization of Symmetric Matrices |
| 14 |
A factorization of m x n matrices PCA due Monday 11/25 @ 11:59 pm |
11/26 | 7.4 The Singular Value Decomposition | 11/28 | Thanksgiving Break |
| 15 |
The power of the singular value decomposition
Do the reading, but no PCA to submit |
12/3 | Applications of the SVD | 12/5 | Applications of the SVD |
| Finals Week |
Final Assignment due Tuesday 12/10 @ 11:59 pm |
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