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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 non-examples.
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
IN-CLASS 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, Gram-Schmidt.
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. Gram-Schmidt 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 2-D 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