Schedule — subject to change — check back and reload for updates!
Dates 
Topics 
8/26, 8/28 
Reading  There is some background available here (Cornell NetID needed).
1  Proofs.
2  Euclidean algorithm, greatest common divisors. 
8/31, 9/2, 9/4 
Reading  Skim §1, Read §2
3  Fields. "Integers mod n" are a field if and only if n is prime.
4  Examples and catch up
5  Vector spaces. 
9/9, 9/11 
Reading  §§ 3 to 4
6  Examples of Vector Spaces
7  Subspaces 
9/14, 9/16, 9/18 
Reading  §§ 5 to 7
8  Linear combinations and linear independence
9  Bases and dimension
10  More examples, catch up. 
9/21, 9/23, 9/25 
Reading  §§ 8
11  Last bits on bases; linear transformations
12  Images, Kernels, Dimensions Class cancelled
13  Images, Kernels, Dimensions: Rank nullity theorem 
9/28, 9/30, 10/2 
Reading  §§ 8 and 9
14  Linear extensions, Isomorphisms
15  Isomorphisms. Equivalence relations.
16  Equivalence relations and quotient vector spaces. 
10/5, 10/7, 10/9 
Reading  Supplementary notes
17  Quotient vector spaces and the BetterThanRankNullity Theorem (First Isomorphism Thm)
18  Second Isomorphism Theorem, Review for Prelim
19  INCLASS PRELIM 1, 10/9 
Fall Break 10/10 – 10/13 
10/14, 10/16 
Reading  § 1011
20  Finish up isomorphism theorems. The mechanics of matrices.
21  Matrices and linear transformations. 
10/19, 10/21, 10/23 
Reading  § 1213
22  Change of basis
23  Solving systems of equations
24  Solving systems of equations 
10/26, 10/28, 10/30 
Reading  § 14, handout
25  Eigenvalues and eigenvectors
26  Eigenvalues continued. Determinants.
27  Rings, solving polynomials, finite fields. 
11/2, 11/4, 11/6 
Reading  § 14 and Reference on Det
28  Determinants via properties
29  Determinants via properties
30  Det(AB) = Det(A)Det(B); More on polynomials and complex numbers 
11/9, 11/11, 11/13 
Reading  § 1516 (NOT ON PRELIM 2!)
31  Inner Products
32  Inner Products
33  Selfadjoint operators 
11/16, 11/18, 11/20 
Reading  § 16. You can find some notes about SVD here. Wikipedia also has a reasonable description.
34  The Spectral Theorem
35  Singular Value Decomposition
36  INCLASS PRELIM 2, 11/20 
11/23 
37  Applications of SVD. Read about SVD in the NYT. It's also described nicely for the public in the Fueling Innvation and Discovery report on pages 710. There's also a nice description of applications here. 
Thanksgiving Break 11/25 – 11/29 
11/30, 12/2, 12/4 
Reading  § 17
38  The Jordan Canoncial Form
39  The Jordan Canoncial Form
40  General overview 
Final Exam 12/14, time 2:00pm–4:30pm, 228 Malott — comprehensive 
