Daily Syllabus, Math 221 Linear Algebra, Fall 2021
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 onCourse
- PS due refers to Problem Sets uploaded to onCourse
| 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 |
8/31 |
1.1 Systems of Linear Equations 1.2 Row Reduction and Echelon Forms Background Questionnaire due Wed 9/1 @ midnight |
9/2 | 1.3 Vector Equations |
| 2 | Describing all solutions to a system
PCA due Monday 9/6 @ midnight |
9/7 |
1.4 The Matrix Equation Ax=b 1.5 Solution Sets of Linear Systems |
9/9 |
1.7 Linear Independence
PS #1 due Thursday 9/9 @ midnight PS #1 partner eval due Friday 9/10 @ midnight |
| 3 | Matrices as functions
PCA due Monday 9/13 @ midnight |
9/14 | 1.8 Introduction to Linear Transformations | 9/16 |
1.9 The Matrix of a Linear Transformation
PS #2 due Thursday 9/16 @ midnight PS #2 partner eval due Friday 9/17 @ midnight |
| 4 | Multiplying and inverting matrices
PCA due Monday 9/20 @ midnight |
9/21 |
2.1 Matrix Operations 2.2 Inverse of a Matrix |
9/23 |
2.3 Characterizations of Invertible Matrices
PS #3 due Thursday 9/23 @ midnight PS #3 partner eval due Friday 9/24 @ midnight |
| 5 | Using matrices to shift, rotate, and skew graphics; The determinant function
PCA due Monday 9/27 @ midnight |
9/28 |
2.7 Applications to Computer Graphics
Cheat Sheet for Exam 1 due @ 8:00 am Exam 1 covers thru 2.3 |
9/30 |
3.1 Introduction to Determinants 3.2 Properties of Determinants Exam 1 due @ midnight |
| 6 | Identifying underlying structural similarities
PCA due Monday 10/4 @ midnight |
10/5 | 4.1 Vector Spaces and Subspaces | 10/7 | 4.2 Null Spaces, Column Spaces, and Linear Transformations |
| 7 | No class meetings this week due to Fall Break and MAP Day | 10/12 | Fall Break | 10/14 | MAP Day |
| 8 | Minimal generating sets
PCA due Monday 10/18 @ midnight |
10/19 | 4.3 Linearly Independent Sets; Bases | 10/21 |
4.3 Linearly Independent Sets; Bases (cont.)
PS #4 due Thursday 10/21 @ midnight PS #4 partner eval due Friday 10/22 @ midnight |
| 9 | Adjusting your reference; An invariant of vector spaces
PCA due Monday 10/25 @ midnight |
10/26 |
4.4 Coordinate Systems 4.5 The Dimension of a Vector Space |
10/28 |
4.6 Rank
PS #5 due Friday 10/29 @ midnight PS #5 partner eval due Friday 10/29 @ midnight |
| 10 | Understanding longterm behavior; Directions fixed by matrix functions
PCA due Monday 11/1 @ midnight |
11/2 | 4.9 Applications to Markov Chains | 11/4 |
5.1 Eigenvectors and Eigenvalues 5.2 The Characteristic Equation PS #6 due Thursday 11/4 @ midnight PS #6 partner eval due Friday 11/5 @ midnight |
| 11 | Extending geometric intuition to higher dimensions
PCA due Monday 11/8 @ midnight |
11/9 |
6.1 Inner Product, Length, and Orthogonality
Cheat Sheet for Exam 2 due @ 8:00 am Exam 2 covers thru 5.2 |
11/11 |
6.2 Orthogonal Sets
Exam 2 due @ midnight |
| 12 | Finding the closest vector
PCA due Monday 11/15 @ midnight |
11/16 |
6.3 Orthogonal Projections 6.4 The Gram-Schmidt Process |
11/18 | 6.5 Least-Squares Problems |
| 13 | A factorization of certain square matrices
PCA due Monday 11/22 @ midnight |
11/23 | 5.3 Diagonalization | 11/25 | Thanksgiving Break |
| 14 | A factorization of m x n matrices
PCA due Monday 11/29 @ midnight |
11/30 | 7.1 Diagonalization of Symmetric Matrices | 12/2 | 7.4 The Singular Value Decomposition |
| 15 | The power of the singular value decomposition
PCA due Monday 12/6 @ midnight |
12/7 |
Applications of the SVD
PS #7 due Tuesday 12/7 @ midnight Cheat Sheet for Exam 3 due Wednesday 12/8 @ 8:00 am |
12/9 | The BIG Picture |
| Finals Period | 12/14 | 12/16 | Exam 3 due Thursday 12/16 @ midnight |