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 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 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-SchmidtOrthogonal 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 31 13 Nov 2020 Optimization, Least squares, Machine learning notes 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 38 14 Dec 2020 Jordan canonical form Axler: § 8.B,C 39 16 Dec 2020 Jordan canonical form Axler: § 8.C,D