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Schedule for Math 433, Fall 2006 (tentative)
(in pdf format,
ready to print)
| Week |
Day |
Ch. |
Sec. |
Topics |
| 8/24
– 25 |
1 |
1 |
1, 2 |
Problems leading to linear algebra,
mathematical induction. |
| 8/28 – 9/1 |
2 |
2 |
3, 4 |
Fields, Vector spaces, examples;
Subspaces, Linear dependence. |
|
3 |
2 |
5, 6 |
Basis and dimension; Row equivalence of
matrices. |
|
4 |
2 |
6, 7 |
Finish row equiv.; General theorems. |
| 9/3
– 9/8 |
5 |
2 |
7, 8 |
General theorems; Systems of linear
equations. |
|
6 |
2 |
9, 10 |
Systems of homogeneous linear equations;
Linear manifolds. |
|
7 |
3 |
11 |
Linear Transformations |
| 9/11 – 9/15 |
8 |
3 |
11, 12 |
Linear Transformations and operations with
matrices. |
|
9 |
3 |
13 |
The matrix of a linear transformation. |
|
10 |
4 |
14 |
Concept of symmetry |
| 9/18 – 9/22 |
11 |
4 |
14, 15 |
Inner Products |
|
12 |
4 |
15 |
Inner Products, orthonormal basis,
Gram-Schmidt process |
|
13 |
5 |
16, 17 |
Definition, existence and uniqueness of
determinants |
| 9/25 – 9/29 |
14 |
5 |
17, 18 |
Existence, uniqueness, multiplication
theorem |
|
15 |
5 |
18 |
Multiplication theorem |
|
16 |
5 |
19 |
Properties of determinants |
| 10/2 – 10/6 |
17 |
5 |
19 |
Properties of determinants |
|
18 |
6 |
20, 21 |
Polynomials and Complex Numbers |
|
19 |
6 |
21 |
Polynomials and Complex Numbers |
| 10/9 – 13 |
|
|
|
FALL BREAK |
|
20 |
7 |
22 |
Basic concepts: minimal polynomial,
eigenvalues, eigenvectors |
|
21 |
7 |
23 |
Invariant Subspaces, diagonalizable
transformations |
| 10/16 – 20 |
22 |
7 |
23, 24 |
Diagonalization, the triangular form
theorem |
|
23 |
7 |
24 |
Triangular forms |
|
24 |
7 |
25 |
Rational and Jordan Canonical forms |
| 10/23 – 27 |
25 |
7 |
25 |
Rational and Jordan Canonical forms |
|
26 |
8 |
25, 26 |
Canonical forms; Quotient spaces |
|
27 |
8 |
26 |
Quotient spaces |
| 10/30 – 11/3 |
28 |
8 |
26 |
Dual vector spaces |
|
29 |
8 |
27 |
Bilinear forms and duality |
|
30 |
8 |
28 |
Direct sums and tensor products |
| 11/6 – 10 |
31 |
8 |
28 |
Tensor products |
|
32 |
8 |
29 |
A proof of the elementary divisor theorem |
|
33 |
8 |
29 |
A proof of the elementary divisor theorem |
| 11/13 – 17 |
34 |
9 |
30 |
Orthogonal transformations |
|
35 |
9 |
30, 31 |
Orthogonal transformations and the
principal axis theorem. |
|
36 |
9 |
31 |
The principal axis theorem |
| 11/20 – 24 |
37 |
9 |
32 |
Unitary transformations |
|
38 |
9 |
32 |
The spectral theorem |
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THANKSGIVING |
| 11/27 – 12/1 |
39 |
9 |
32 |
The spectral theorem |
|
40 |
10 |
33 |
Applications of linear algebra |
|
41 |
10 |
34 |
Applications of linear algebra |
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