Daily Syllabus, Math 221 Linear Algebra, Fall 2023
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 9:30 - 11:50 |
Thursday 9:30 - 11:50 |
||
|---|---|---|---|---|---|
| 1 | Welcome to Linear Algebra!
Systems of linear equations and equivalent vector equations Background Questionnaire due Upload photo to profile in Canvas |
8/29 |
1.1 Systems of Linear Equations 1.2 Row Reduction and Echelon Forms |
8/31 | 1.3 Vector Equations |
| 2 | Describing all solutions to a system
PCA due Monday 9/4 @ 11:59 pm |
9/5 |
1.4 The Matrix Equation Ax=b 1.5 Solution Sets of Linear Systems |
9/7 |
1.7 Linear Independence
PS #1 & partner eval due @ 11:59 pm |
| 3 | Matrices as functions
PCA due Monday 9/11 @ 11:59 pm |
9/12 | 1.8 Introduction to Linear Transformations | 9/14 |
1.9 The Matrix of a Linear Transformation
PS #2 & partner eval due @ 11:59 pm |
| 4 | Multiplying and inverting matrices
PCA due Monday 9/18 @ 11:59 pm |
9/19 |
2.1 Matrix Operations 2.2 Inverse of a Matrix |
9/21 |
2.3 Characterizations of Invertible Matrices
PS #3 & partner eval due @ 11:59 pm |
| 5 | Using matrices to shift, rotate, and skew graphics; The determinant function
Do the reading, but no PCA to submit |
9/26 |
Cheat Sheet for Exam 1 due @ 8:00 am Exam 1, In-Class part, 9:30 - 10:15 Exam 1 covers thru 2.3 |
9/28 |
2.7 Applications to Computer Graphics
3.1 Introduction to Determinants
Exam 1, Takehome part, due Fri 9/29 @ 11:59 pm |
| 6 | Identifying underlying structural similarities
PCA due Monday 10/2 @ 11:59 pm |
10/3 | 3.2 Properties of Determinants 4.1 Vector Spaces and Subspaces | 10/5 | 4.2 Null Spaces, Column Spaces, and Linear Transformations |
| 7 | No class meetings this week due to Fall Break and MAP Day | 10/10 | Fall Break | 10/12 | MAP Day |
| 8 | Minimal generating sets
PCA due Monday 10/16 @ 11:59 pm |
10/17 | 4.3 Linearly Independent Sets; Bases | 10/19 |
4.3 Linearly Independent Sets; Bases (cont.)
PS #4 & partner eval due @ 11:59 pm |
| 9 | Adjusting your reference; An invariant of vector spaces
PCA due Monday 10/23 @ 11:59 pm |
10/24 |
4.4 Coordinate Systems 4.5 The Dimension of a Vector Space |
10/26 |
4.6 Rank
PS #5 & partner eval due @ 11:59 pm |
| 10 | Understanding longterm behavior; Directions fixed by matrix functions
PCA due Monday 10/30 @ 11:59 pm |
10/31 | 4.9 Applications to Markov Chains | 11/2 |
5.1 Eigenvectors and Eigenvalues 5.2 The Characteristic Equation PS #6 & partner eval due @ 11:59 pm |
| 11 | Extending geometric intuition to higher dimensions
PCA due Monday 11/6 @ 11:59 pm |
11/7 |
6.1 Inner Product, Length, and Orthogonality
Cheat Sheet for Exam 2 due @ 8:00 am Exam 2, In-Class part, 9:30 - 10:00 Exam 2 covers thru 5.2 |
11/9 |
6.2 Orthogonal Sets
Exam 2, Takehome part, due @ 11:59 pm |
| 12 | Finding the closest vector
PCA due Monday 11/13 @ 11:59 pm |
11/14 |
6.3 Orthogonal Projections 6.4 The Gram-Schmidt Process |
11/16 | 6.5 Least-Squares Problems |
| 13 | A factorization of certain square matrices
PCA due Monday 11/20 @ 11:59 pm |
11/21 | 5.3 Diagonalization | 11/23 | Thanksgiving Break |
| 14 | A factorization of m x n matrices
PCA due Monday 11/27 @ 11:59 pm |
11/28 | 7.1 Diagonalization of Symmetric Matrices | 11/30 |
7.4 The Singular Value Decomposition
PS #7 (individual) due @ 11:59 pm |
| 15 | The power of the singular value decomposition
PCA due Monday 12/4 @ 11:59 pm |
12/5 |
Applications of the SVD
Cheat Sheet for Exam 3 due Wednesday 12/6 @ 8:00 am |
12/7 | The BIG Picture |
| Finals Period | 12/12 | Exam 3 due Wednesday 12/13 @ 11:59 pm | 12/14 |