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  GramSchmidt 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 

31  13 Nov 2020  Optimization, Least squares,
Machine learning notes 

16 Nov 2020  no class!  semifinals  
18 Nov 2020  no class!  semifinals  
20 Nov 2020  no class!  semifinals  
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 