The following lecture schedule is tentative and could change as the term proceeds. Practice problems will appear as topics are covered in class. Any electronic materials displayed in class will be linked to the corresponding lecture.

Week 1, Sept. 4 - 6

- Review material: Complex numbers - appendix B and supplementary material
- Lecture 1; from the supplementary material, try 10.1 #3 b), 4 e), f), 5, 8, 10, 13, 16; 10.2 #4, 6
- Lecture 2; from the supplementary material, 10.2, #5, 7, 9, 11, 18, 23; 10.3 #5, 7, 15

- Chapter 4 - 5: Review of vector spaces and introduction to complex vector spaces
- Lecture 3; section 4.1, #3 - 11, 27
- Lecture 4; section 4.2, #9 - 13, 16, 17; section 4.3, #3 - 5, 11, 24 - 27
- Lecture 5; section 4.4, #5, 9, 14, 25, 26; section 4.5, #9, 17, 11, 22

- Chapter 5: sections 5.1, 5.2, review of eigenvalues and eigenvectors; chapter 6, inner product spaces
- Lecture 6; section 5.3, 15 - 18
- Lecture 7; section 5.1, #9, 11, 13, 17, 25; section 5.2, #5, 7, 17, 27

- Chapter 6; inner product spaces, sections 6.1, 6.2, cont'd
- Lecture 8; section 6.1 #4, 10, 11, 14, 30, 31, 43, 44
- Lecture 9; section 6.2, #3, 11, 13, 17, 21, 23, 35, 39 (very important example; we will eventually do this one in class but take a shot at this; remember trig substitutions), 41
- Lecture 10 will just use the slides
from Lecture 9

- Sections 6.2 - 6.3
- Lecture 11
- Lecture 12; section 6.3, #3, 4, 7, 10, 11, 14
- Lecture 13; section 6.3, #21, 23, 31, 41, 42, 43, 53

Week 6, Oct. 7 - 11; first test on Oct. 9; no class on Oct. 11

- Lecture 14 section 6.4, #3, 7, 17, 24

- section 6.4, Fourier series, Linear transformations, section 8.1
- Lecture 15 section 6.6, #2, 8
- Lecture 16 (I used these slides in lecture 15 to explain the integral calculations.)
- Lecture 17 section 8.1, #1, 7, 10, 11, 19, 21, 25, 27, 31, 33

- Sections 8.2 - 8.3
- Lecture 18 section 8.2, #1, 3, 7, 17, 19, 21, 29, 31
- Lecture 19 section 8.3, #3, 5, 9, 15, 21
- No new slides for Friday

- Sections 8.4 - 8.5

- Lecture 21
- Lecture 22; section 8.4, #1, 5, 13, 17, 21, 23

- Chapter 7, orthogonal diagonalization, section 7.1 - 7.2, 7.5
- Lecture 23;
section 8.5, #5, 9, 15, 21, 25, 27

- Lecture 24; section 7.1, #7, 12, 21, 22, 26, 30 (this one might take some work but explains what is going on in 3 dimensions)
- We will use the slides from Lecture 24; section 7.2, #11, 12, 17, 19, 21, 26, 29

- Normal and hermitian diagonalization, section 7.3 - 7.5
- Lecture 26; section 7.5, #7, 11, 13, 17, 39, 41
- Lecture 27
- We
will use the slides from Lecture 27

- Optimization of quadratic forms and canonical forms, section 7.4; section 9.4
- Lecture 28 section 7.3, #2, 5, 8, 13, 15
- Lecture 29 section 7.4, #3, 5, 7, 13, 15, 21
- Dec. 2 slides are contained in Lecture 29
- Final lecture slides; the theorems on SVD are from lecture 29, the theorem of Tao et al is here and here is the SVD example.
- References: Here is a link to the article
by Tao; the blog
post by Andrew Gibiansky (nice hat) and the book on Deep
Learning by Goodfellow, Bengio and Courville - check
out chapter 2.