| Date | Topic | Textbook sections | Supplemental materials |
| Wed, Jan 27 | Course overview; introduction to proofs, divisibility of integers. | Some background
reading on proofs and integers (requires a Cornell NetID) - this
covers the sort of things I'll be talking about the first few classes.
A book on proofs; the first couple chapters may be a helpful supplement on learning to write proofs. |
|
| Fri, Jan 29 | GCDs and more on proofs | Sections 1.1, 1.2, 1.3 of the background reading above. | |
| Mon, Feb 1 | Primes, congruences and the integers modulo n. | Sections 1.2, 1.3, 1.4 of the background reading above. | |
| Wed, Feb 3 | Equivalence relations and the integers modulo n | Equivalence relations handout | |
| Fri, Feb 5 | Fields and vector spaces. | Chapters 1 and 2 | Fields handout |
| Mon, Feb 8 | Examples of vector spaces | Chapter 3 | |
| Wed, Feb 10 | Subspaces and quotient spaces | Chapter 4 | Quotient vector spaces handout |
| Fri, Feb 12 | Spans and linear independence | Chapters 4 and 5 | |
| Mon, Feb 15 | No class - February break | ||
| Wed, Feb 17 | Linear independence and bases | Chapters 5 and 6 | |
| Fri, Feb 19 | Bases and some examples | Chapters 6 and 7 | |
| Mon, Feb 22 | Linear Transformations | Sections 8.1-8.4 and Chapter 9 | |
| Wed, Feb 24 | Linear Transformations | Sections 8.4-8.6 and Chapter 9 | |
| Fri, Feb 26 | Quotient spaces and the first isomorphism theorem | Isomorphism theorems handout | |
| Mon, Feb 29 | Matrices and linear transformations | Chapter 10 | |
| Wed, Mar 2 | Review | ||
| Fri, Mar 4 | Prelim #1 - In Class | ||
| Mon, Mar 7 | Matrices and linear transformations | Chapter 11 | |
| Wed, Mar 9 | Examples of linear transformations | Chapters 11 and 12 | |
| Fri, Mar 11 | Special types of matrices/transformations | Chapters 10.4 and 12 | |
| Mon, Mar 14 | Solving linear systems | Chapter 13 | |
| Wed, Mar 16 | Eigenvalues and Eigenvectors | Sections 14.1 and 14.2 | |
| Fri, Mar 18 | Determinants | Section 14.3 and Appendix A | Another reference for determinants |
| Mon, Mar 21 | Determinants again | Section 14.3 and Appendix A | Determinants reference above |
| Wed, Mar 23 | Determinants and characteristic polynomials | Sections 14.3-14.5 | Determinants reference |
| Fri, Mar 25 | More on determinants + signs of permutations | ||
| Mon, Mar 28 | No class this week - Spring break | ||
| Mon, Apr 4 | Inner products | Sections 15.1-15.2 | |
| Wed, Apr 6 | Inner product spaces | Sections 15.2-15.4 | |
| Fri, Apr 8 | Inner products | Sections 15.4-15.5 | |
| Mon, Apr 11 | No class because of power outage Prelim #2 - Take-home exam assigned |
||
| Wed, Apr 13 | Adjoints | Section 16.1 | |
| Fri, Apr 15 | The Spectral Theorem Prelim #2 - Take-home exam due |
Section 16.2 | |
| Mon, Apr 18 | The Principal Axis Theorem | Section 16.3 | |
| Wed, Apr 20 | Proof of the Spectral Theorem | Section 16.4 | |
| Fri, Apr 22 | Singular value decompositions | Reference 1 on SVD Reference 2 on SVD |
|
| Mon, Apr 25 | Invariant subspaces and direct sums | Section 17.1 | |
| Wed, Apr 27 | Jordan canonical form - nilpotent transformations | Section 17.2 | |
| Fri, Apr 29 | Jordan canonical form - general case | Section 17.3 | |
| Mon, May 2 | Jordan canonical form - proof of existence | ||
| Wed, May 4 | Jordan canonical form - uniqueness and examples | ||
| Fri, May 6 | Some applications of the JCF | Sections 17.4-17.6 | |
| Mon, May 9 | Systems of differential equations | Chapter 18 | |
| Wed, May 11 | Continuation of previous class and/or review |