The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.
| Date | Sections in Text | Description | Practice Problems |
|---|---|---|---|
| (M) Sep 11 | 1.1 |
Systems of Linear Equations Row reduction slides SageMath plots |
§1.1: #3, 16 |
| (W) Sep 13 | 1.2 |
Row Reduction and Echelon Forms Row reduction worksheet |
§1.2: #3, 17, 19 |
| (Th) Sep 14 x-hour |
Computing session Sage CoCalc notebook Sage text file |
||
| (F) Sep 15 | 1.3 |
Vector Equations Classwork |
§1.3: #11, 13 |
| (M) Sep 18 | 1.4 - 1.5 |
The Matrix Equation Ax=b Solution Sets of Linear Systems |
§1.4: #1, 3, 13 §1.5: #15, 25, 35 |
| (W) Sep 20 | 1.7 | Linear Independence |
§1.7: #1, 7, 33, 34, 35 |
| (Th) Sep 21 x-hour |
Proofs Methods of proof handout Cheat sheet for proofs |
More proof resources | |
| (F) Sep 22 | 1.8 |
Introduction to Linear Transformations Linear transformations worksheet, Solutions HW 1 due 3:30 pm |
§1.8: #5, 19, 36 |
| (M) Sep 25 | 1.9 | The Matrix of a Linear Transformation | §1.9: #11, 21, 27 |
| (W) Sep 27 | 2.1 | Matrix Operations | §2.1: #5, 12, 22, 26 |
| (Th) Sep 28 x-hour |
Exam 1 review Practice Exam 1, Solutions Practice Exam 2, Solutions |
Past exams |
|
| (F) Sep 29 | 2.2 |
The Inverse of a Matrix HW 2 due 3:30 pm |
§2.2: #15, 31, 37 |
| (M) Oct 2 | 2.3 | Characterizations of Invertible Matrices | §2.3: #29, 33, 35 |
| (Tu) Oct 3 | Exam 1: 4:30 - 6:30 pm, Moore Hall B13, Filene Auditorium | ||
| (W) Oct 4 | 3.1 - 3.2 |
Introduction to Determinants Properties of Determinants |
§3.1: #9, 37 §3.2: #5, 9, 29 |
| (F) Oct 6 | 4.1 |
Vector Spaces and Subspaces HW 3 due 3:30 pm |
§4.1: #2, 3, 5, 6 |
| (M) Oct 9 | 4.2 |
Null Spaces (aka Kernels), Column Spaces, and Linear Transformations |
§4.2: #15, 23, 27 |
| (W) Oct 11 | 4.3 | Linearly Independent Sets and Bases Basis worksheet |
§4.3: #9, 13, 15 |
| (Th) Oct 12 x-hour |
Discussion of solutions to Exam 1 | ||
| (F) Oct 13 | 4.4 |
Coordinate Systems Coordinate vector worksheet HW 4 due 3:30 pm |
§4.4: #23, 24, 27 |
| (M) Oct 16 | 4.5 |
The Dimension of a Vector Space Dimension worksheet |
§4.5: #13, 17, 31 |
| (W) Oct 18 | 4.6 |
Rank Rank-nullity worksheet |
§4.6: #5, 14, 17 |
| (Th) Oct 19 x-hour |
Exam 2 review Practice Exam 1, Solutions Practice Exam 2, Solutions |
Past exams |
|
| (F) Oct 20 | 4.7 |
Change of Basis Change of basis worksheet HW 5 due 3:30 pm |
§4.7: #2, 7, 13 |
| (M) Oct 23 | 5.1 |
Eigenvectors and Eigenvalues Eigenvector demo Eigenvectors and eigenvalues worksheet |
§5.1: #1, 15, 19 |
| (Tu) Oct 24 |
Exam 2: 4:30 - 6:30 pm, Moore Hall B13, Filene Auditorium |
||
| (W) Oct 25 | 5.2 | The Characteristic Equation Characteristic polynomial worksheet |
§5.2: #1, 9, 25 |
| (Th) Oct 26 x-hour |
Discussion of solutions to Exam 2 | ||
| (F) Oct 27 | 5.3 |
Diagonalization Diagonalization worksheet HW 6 due 3:30 pm |
§5.3: #7, 10, 27 |
| (M) Oct 30 | 6.1 | Inner Product, Length, and Orthogonality | §6.1: #28, 31 |
| (W) Nov 1 | 6.2 | Orthogonal Sets Orthogonal sets worksheet |
§6.2: #12, 17, 19 |
| (Th) Nov 2 x-hour |
4.9, 10.1 |
Applications to Markov Chains Chapter 10: Markov Chains |
§4.9: #2; §10.2: #15, 17 |
| (F) Nov 3 | 6.3 |
Orthogonal Projections Orthogonal projections worksheet HW 7 due 3:30 pm |
§6.3: #7, 19, 23 |
| (M) Nov 6 | 6.4 |
The Gram-Schmidt Process Gram-Schmidt worksheet |
§6.4: #9, 15, 19, 20 |
| (W) Nov 8 | 7.1 |
Diagonalization of Symmetric Matrices Orthogonal diagonalization worksheet |
§7.1: #13, 15, 35 |
| (Th) Nov 9 x-hour |
10.2 |
Google's PageRank Chapter 10: Markov Chains PageRank article |
§10.2: #25 |
| (F) Nov 10 | 7.4 |
Singular Value Decomposition (SVD) SVD worksheet HW 8 due 3:30 pm |
§7.4: #5, 7, 9, 19 |
| (M) Nov 13 | 7.5 |
Applications of SVD: The Four Fundamental Spaces and Principal Component Analysis (PCA) |
|
| (W) Nov 15 |
Review session, 7 - 9 pm, Kemeny 008 Practice Exam 1, Solutions Practice Exam 2, Solutions |
Past exams Textbook review resources |
|
|
(F) Nov 17 |
Final Exam: 3:00 pm, Class of 1978 Life Sciences Center, Room 100 |
