Schedule — subject to change — check back and reload for updates!
Dates 
Topics 
8/22, 8/24 
Reading  § 1 and 2
1  Proofs. We did less than I hoped. Here is another example of a direct proof.
2  Induction. Fields.

8/27, 8/29, 8/31 
Reading  § 3 and 4
4  Properties of fields, more examples and nonexamples.
5  "Integers mod n" are a field if and only if n is prime
6  Vector spaces. 
9/5, 9/7 
Reading  § 4 and 5
7  Vector spaces and subspaces
8  Linear dependence

9/10, 9/12, 9/14 
Reading  § 5 and 6
9  Linear dependence and independence
10  Bases, dimension
11  Elementary row operations, row equivalence of matrices 
9/17, 9/19, 9/21 
Reading  § 6, 7 and 8
12  Row equivalence and its implications in general vector spaces
13  Facts about finitely generated vector spaces  PLEASE READ THE END OF § 7 and bring any questions to class on Friday!
14  Systems of linear equations

9/24, 9/26, 9/28 
Reading  § 9 and 10
15  Homogeneous systems of linear equations
16  Linear manifolds / Affine subspaces
17  Linear manifolds

10/1, 10/3, 10/5 
Reading  § 11
19  Linear transformations  L(V,V) is a ring
20  Linear transformations  the set of invertible transformations in L(V,V) is a group
INCLASS PRELIM 10/5

Fall
Break 10/6 – 10/9 
10/10, 10/12 
Reading  § 12 and 13
21  Matrix Multiplication
22  Linear transformations and matrices

10/15, 10/17, 10/19 
Reading  § 13 and 14
23  Linear transformations and matrices
24  Linear transformations and matrices
25  Symmetries of the plane

10/22, 10/24, 10/26 
Reading  § 15 and 16
26  Symmetry groups. Inner products on real vector spaces.
27  Orthogonal vectors, GramSchmidt.
28  Complex inner products.

10/29, 10/31, 11/2 
Reading  Not based on course text. For reference, check out Axler, available to Cornell students here.
29  More on complex inner products.
30  The adjoint of a linear transformation.
31  More on adjoints. Orthogonal projection.

11/5, 11/7, 11/9 
Reading  § 17 and 18
32  Taylor series versus orthogonal projection. GramSchmidt revisited.
33  Properties of determinants.
34  Existence and uniqueness of determinants.

11/12, 11/14, 11/16 
Reading  § 18 and 19
35  Further properties of determinants.
36  The multiplication theorem for determinants. The determinant of a linear transformation.
37  Properties of polynomials

11/19, 11/21 
Reading  § 22 and 23
38  Factoring polynomials
39  Invariant subspaces, eigenvalues and eigenvectors

Thanksgiving Break 11/21 – 11/25 
11/26, 11/28, 11/30 
Reading  § 23 and 24
40  Polynomials and linear transformations. Complex eigenvectors for 2D rotation.
41  Invariant subspaces, more on polynomials and linear transformations
42  Comments on Triangular form and Jordan Canonical Form 
Final Exam 12/10, time 2:00pm–4:30pm, 406 Malott — comprehensive

