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Dates |
Topics |
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8/23, 8/25 |
Reading - Dweck's article. There is some background available here (Cornell NetID needed).
1 - Properties of numbers, greatest common divisors.
2 - GCDs, Euclidean algorithm, Integers mod n. Handout on modular arithmetic. |
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8/30, 9/1 |
Reading - §1.1- beginning of 1.4 (through page 20)
3 - More on integers mod n. Fields. Handout on complex numbers.
4 - Vector spaces. Subspaces. Quite a few examples |
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9/6, 9/8 |
Reading - §1.5 - 1.6
5 - Direct sums. Span and linear independence.
6 - Bases and finite-dimensional vector spaces. Your group work. |
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9/13, 9/15 |
Reading - §1.7 - 1.8 and the end of 1.4 (pages 20 - 24)
7 - Infinite-dimensional subspaces (mentioning the Axiom of Choice, for which you are not responsible)
8 - Quotient spaces with examples. Definition of linear transformation with examples. |
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9/20, 9/22 |
Reading - §2.1 - 2.3
9 - Linear transformations, kernel, image. Handout and your group work.
10 - The isomorphism theorems. |
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9/27, 9/29 |
Reading - §2.4 - 2.6
11 - The algebra of linear transformations and the algebra of matrices.
12 - Invertible transformations and matrices |
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10/4, 10/6 |
Reading - Review Chapters 1 and 2
13 - Catching up and review.
14 - PRELIM 1 in class!!!! |
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Fall Break 10/8 – 10/11 |
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10/13 |
Reading - §3.1
15 - The algebra of polynomials |
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10/18, 10/20 |
Reading - §3.2 and this handout
16 - Roots of polynomials, irreducibility
17 - Constructing finite fields via irreducible polynomials |
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10/25, 10/27 |
Reading - §4.1, Alternative treatment on diagonalizability
18 - A single linear operator. Invariant subspaces.
19 - Diagonalizability |
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11/1, 11/3 |
Reading - § 4.2 - 4.3
20 - Cyclic transformations.
21 - Maximal vectors |
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11/8, 11/10 |
Reading - § 4.4 - 4.5. I wrote up some notes of my own.
22 - Canonical forms.
23 - Canonical forms. |
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11/15, 11/17 |
Reading - § 4.6, bits of Chapters 5 and 6
24 - Canonical forms.
25 - "Jordan canonical form is not continuous." Inner products. |
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11/22 |
Reading - bits of Chapters 5 and 6. I wrote up some notes of my own.
26 - Inner products and adjoint transformations. Self-adjoint operators. |
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Thanksgiving Break 11/23 – 11/27 |
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11/29, 12/1 |
Reading - § 6.1, 6.2, 6.5, 7.2. My handwritten notes. Some other SVD notes.
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.
27 - Spectral Theorems over R and C. Singular Value Decomposition. Some SVD pictures.
28 - A whirlwind on Determinants. Final thoughts. |
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Final Exam DECEMBER 9, 2-4:30pm, 406 Malott |