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Schedule — subject to change — check back and reload for updates!
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Dates |
Topics |
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8/26, 8/28 |
Reading - There is some background available here (Cornell NetID needed).
1 - Proofs.
2 - Euclidean algorithm, greatest common divisors. |
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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. |
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9/9, 9/11 |
Reading - §§ 3 to 4
6 - Examples of Vector Spaces
7 - Subspaces |
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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. |
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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 |
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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. |
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10/5, 10/7, 10/9 |
Reading - Supplementary notes
17 - Quotient vector spaces and the Better-Than-Rank-Nullity Theorem (First Isomorphism Thm)
18 - Second Isomorphism Theorem, Review for Prelim
19 - IN-CLASS PRELIM 1, 10/9 |
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Fall Break 10/10 – 10/13 |
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10/14, 10/16 |
Reading - § 10-11
20 - Finish up isomorphism theorems. The mechanics of matrices.
21 - Matrices and linear transformations. |
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10/19, 10/21, 10/23 |
Reading - § 12-13
22 - Change of basis
23 - Solving systems of equations
24 - Solving systems of equations |
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10/26, 10/28, 10/30 |
Reading - § 14, handout
25 - Eigenvalues and eigenvectors
26 - Eigenvalues continued. Determinants.
27 - Rings, solving polynomials, finite fields. |
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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 |
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11/9, 11/11, 11/13 |
Reading - § 15-16 (NOT ON PRELIM 2!)
31 - Inner Products
32 - Inner Products
33 - Self-adjoint operators |
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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 - IN-CLASS PRELIM 2, 11/20 |
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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 7-10. There's also a nice description of applications here. |
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Thanksgiving Break 11/25 – 11/29 |
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11/30, 12/2, 12/4 |
Reading - § 17
38 - The Jordan Canoncial Form
39 - The Jordan Canoncial Form
40 - General overview |
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Final Exam 12/14, time 2:00pm–4:30pm, 228 Malott — comprehensive |
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