The topics in the following syllabus are tentative, and might change. Check back here often for new versions!
Version 1.5 (Last changed 11/6/2020)| Lec | Date | Topic | Read | Problem sets |
| 1 | 2 Sep 2020 | Intro; Fields notes | FIS Appendix C, D | |
| 2 | 4 Sep 2020 | Fields notes | Axler, § 1.A; FIS Appendix C, D | |
| 3 | 7 Sep 2020 | Fields; Vector spaces notes | Axler, § 1.A; 1.B | |
| 4 | 9 Sep 2020 | Vector spaces notes | Axler, § 1.B | HW#1 Dweck reading |
| 5 | 11 Sep 2020 | Subspaces notes | Axler § 1.C | |
| 6 | 14 Sep 2020 | Span, Linear dependence notes | Axler: § 2.A | |
| 7 | 16 Sep 2020 | Bases notes | Axler: § 2.B | HW#2 latex |
| 8 | 18 Sep 2020 | Bases and Dimension notes | Axler: § 2.B, 2.C | |
| 9 | 21 Sep 2020 | Examples notes | ||
| 10 | 23 Sep 2020 | Vector space of Linear maps (transformations) notes | Axler: § 3.A | HW#3 latex |
| 11 | 25 Sep 2020 | Linear maps 2 notes | Axler: § 3.A | |
| 12 | 28 Sep 2020 | Kernels and images notes | Axler: § 3.B | |
| 13 | 30 Sep 2020 | Kernel and image Fundamental theorem of linear maps notes |
Axler: § 3.B | |
| 14 | 2 Oct 2020 | Matrix of a linear map
Matrix multiplication Change of basis notes |
Axler: § 3.C | HW#4 latex |
| 15 | 5 Oct 2020 | Invertibility, isomorphisms notes | Axler: § 3.D | |
| 16 | 7 Oct 2020 | Gaussian elimination, LU decomposition notes |
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| 17 | 9 Oct 2020 | LU continued,
notes
julia code |
Axler: § 3.E. Read about products |
HW#5 latex |
| 18 | 12 Oct 2020 | Quotient vector spaces notes | Axler: § 3.E | |
| 14 Oct 2020 | no class! | Fall break | ||
| 19 | 16 Oct 2020 | Dual vector space notes | Axler: § 3.F | |
| 18 Oct 2020 | Test #1 | covers thru lecture 16 | practice | |
| 20 | 19 Oct 2020 | Polynomials, fundamental thm of algebra notes | Axler: § 4 | |
| 21 | 21 Oct 2020 | Polynomials and matrices notes | Axler: § 4 | |
| 22 | 23 Oct 2020 | Eigenvalues and eigenvectors notes | Axler: § 5.A | |
| 23 | 26 Oct 2020 | Eigenvalues and diagonalizability notes | Axler: § 5.B | |
| 24 | 28 Oct 2020 | Eigenspaces notes | Axler: § 5.C | |
| 25 | 30 Oct 2020 | Examples: Markov chains notes |
HW#6, HW#7 latex |
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| 26 | 2 Nov 2020 | Examples: Markov chains, continued notes | ||
| 27 | 4 Nov 2020 | Inner products notes | Axler: § 6.A | |
| 28 | 6 Nov 2020 | Orthonormal bases notes | Axler: § 6.B |
HW#8 latex |
| 29 | 9 Nov 2020 | Gram-Schmidt Orthogonal complements notes |
Axler: § 6.C | |
| 30 | 11 Nov 2020 | Orthogonal complements and projection notes | Axler: § 6.B,C | |
| 12 Nov 2020 |
HW#9 latex pic |
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| 31 | 13 Nov 2020 | Optimization, Least squares,
Machine learning notes |
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| 16 Nov 2020 | no class! | semi-finals | ||
| 18 Nov 2020 | no class! | semi-finals | ||
| 20 Nov 2020 | no class! | semi-finals | ||
| 23 Nov 2020 | Test #2 | Covers thru lecture 29 | 9:30 am - 12:00 pm | |
| 25 Nov 2020 | no class! | |||
| 27 Nov 2020 | no class! | Thanksgiving | ||
| 32 | 30 Nov 2020 | Symmetric matrices, spectral theorems | Axler: § 7.B | |
| 33 | 2 Dec 2020 | Examples, review and consolidate! | ||
| 34 | 4 Dec 2020 | SVD (Singular value decomposition) | Axler: § 7.D |
HW#10 latex |
| 35 | 7 Dec 2020 | SVD, part 2 | Axler: § 7.D | |
| 36 | 9 Dec 2020 | Applications of SVD | ||
| 37 | 11 Dec 2020 | Jordan canonical form | Axler: § 8.A,B |
HW#11 latex |
| 39 | 13 Dec 2020 | Test #3 | covers through and including SVD |
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| 38 | 14 Dec 2020 | Jordan canonical form | Axler: § 8.B,C | |
| 39 | 16 Dec 2020 | Jordan canonical form | Axler: § 8.C,D |
