Home Page of Alistair Savage | Department of Mathematics and Statistics | Virtual Campus | Sessional Dates |
The syllabus will be updated as the course progresses.
Date | Sections of the notes | Material |
Sep 7 | Ch. 1 | Review of vector spaces |
Sep 11 | Ch. 2 | Review of linear maps |
Sep 14 | Ch. 2 | Review of linear maps (cont.) (Students should review Ch. 3 on their own.) |
Sep 18 | Ch. 4 | Polynomials, linear operators and matrices |
Sep 21 | 5.1 | Divisibility in integral domains |
Sep 25 | 5.2–5.4 | Euclidean domains |
Sep 28 | 5.4–5.6 | The Unique Factorization Theorem, the Fundamental Theorem of Algebra |
Oct 2 | 6.1–6.2 | Modules, submodules |
Oct 5 | 6.2–6.5 | Submodules (cont.), free modules, direct sum of modules, module homomorphisms |
Oct 9 | 7.1 | Annihilators |
Oct 12 | 7.2 | Modules over a euclidean domain, rational canonical form |
Oct 16 | 7.3–7.4 | Primary decomposition, Jordan canonical form |
Oct 19 | 8.1 | Submodules of free modules |
Oct 22–26 | ||
Oct 30 | N/A | Midterm exam (covers up to and including Ch. 7) |
Nov 2 | 8.2, 8.3 | The Cayley-Hamilton Theorem, submodules of free modules |
Nov 6 | 8.4 | The column module of a matrix |
Nov 9 | 8.5, 9.1 | Smith normal form, duality |
Nov 13 | 9.1–9.2 | Duality, bilinear maps |
Nov 16 | 9.2–9.3 | Bilinear maps, tensor products |
Nov 20 | 9.4–9.5 | Course evaluations. The Kronecker product, multiple tensor products |
Nov 23 | 10.1 | Review of inner product spaces |
Nov 27 | 10.2–10.3 | Orthogonal operators, adjoint operators |
Nov 30 | 10.4 | Spectral theorems |
Dec 4 | Notes | Review |