| Lec. | Date | Sections/pages covered | Topics |
|---|---|---|---|
| 1 | 1/12 | Sec.2, pp.16-19 | Review: Notations, math. induction, fields. Vector spaces: definition and examples. |
| 2 | 1/14 | pp. 19-23, 26-28, Sec.4 #7,8 |
Vector spaces: properties, a geometric interpretation. Subspaces, generators, intersections and unions of subspaces. |
| - | 1/19 | - MLK Day - | |
| 3 | 1/21 | pp. 29-32, Sec. 5 | Linear dependence and independence. Basis and dimension. |
| 4 | 1/26 | p.35, Sec.6 | Basis and dimension. Row equivalence of matrices -- definition and applications. |
| 5 | 1/28 | Sec.6, 7 | Row equivalence of matrices -- general statements. Some theorems about finitely generated vector spaces. |
| 6 | 2/2 | Sec.8: pp.53-56 | Systems of linear equations. Nonhomogeneous case: general statements. |
| 7 | 2/4 | Sec.8: pp.57-61; Sec.9 |
Nonomogeneous case: examples. Systems of homogeneous equations. |
| 8 | 2/9 | Sec.9 Sec.10: p.69-71 |
Systems of homogeneous equations. Linear manifolds: definition and statements. |
| 9 | 2/11 | Sec.10: p.71-73, Ex.3,4 Sec.11: p.75-77 |
Linear manifolds: proofs and examples; hyperplanes and lines. Functions. Linear transformations. |
| 10 | 2/16 | Sec.11 p.77-83 | Linear transformations. |
| 11 | 2/18 | Sec.11 p.84-86 Sec.12 |
Isomorphism of vector spaces. Matrices: review. |
| 12 | 2/23 | Sec.13 p.99-105 | Linear transformations and matrices. |
| 13 | 2/25 | Sec.13: p.106 Sec.14 |
Range and null space of a linear transformation. The concept of symmetry. |
| 14 | 3/1 | Review | |
| 15 | 3/3 | Midterm Exam | Covers Chapters 1-3 |
| 16 | 3/8 | Sec.15: p.119-122 | Inner products. |
| 17 | 3/10 | Sec.15: p.123-128 | Orthonormal sets, orthogonal transformations. |
| - | 15-21 | - Spring Break - | |
| 18 | 3/22 | p.128-129, p.130 #8, etc. | Orthogonal matrices. Isometries. |
| 19 | 3/24 | Sec.16 Sec.17 - statements. |
Area and volume. Determinants: definition, properties, calculations; existence and uniqueness. |
| 20 | 3/29 | Sec.18 | Multiplication theorem for determinants. |
| 21 | 3/31 | Sec.19 p.150-152,154-160 | Further properties of determinants. Permutations |
| 22 | 4/5 | Sec.19 p.152-153 Sec.20 |
Determinants and systems of equations. Polynomials. |
| 23 | 4/7 | Sec.21 | Complex numbers. |
| 24 | 4/12 | p. 184-185 |
Proofs of the fundamental theorem of algebra. The space L(V,V): dimension and basis. |
| 25 | 4/14 | Sec.22 | Minimal polynomial. Eigenvalues and eigenvectors. |
| 26 | 4/19 | Characteristic polynomial. Diagonalizable transformations. | |
| 27 | 4/21 | Jordan canonical form. | |
| 28 | 4/26 | Jordan canonical form. | |
| 29 | 4/28 | Review |