| Num | Date | Topic |
| 1 | Sept 11 |
Introduction and Course topics, Introduced Graph Laplacian, Effective Resistance, and Random Walks.
See: Dole and Snell: Scribe: Sue Ann Hong |
| 2 | Sept 13 | Resistance, Energy and Rayleigh's Monotonicity Law. Random Walks the symmetric case. |
| 3 | Sept 18 | Laplacian of Graphs and some examples |
| 4 | Sept 20 |
Eigenvalues of directed graphs and the Perron-Frobenius Theorem
See: Godsil and Royle: |
| 5 | Sept 25 |
More on Perron-Frobenius |
| 6 | Sept 27 |
Random Walks on Undirected Graphs: Mixing time Coupling and Eigenvalues See: (1) Wikipedia: (2) Lovasz Survey: (3) Spielman Lecture 7: |
| 7 | Oct 2 | |
| 8 | Oct 4 |
Solutions to Spring and Mass Systems and the Normalized Laplacian |
| 9 | Oct 9 | Computing Mixing Rates using coupling |
| 10 | Oct 11 |
Cutting a graph evenly: Proof of Cheeger Inequality Guattery's notes |
| 11 | Oct 16 |
No Class IMR Conference |
| 12 | Oct 18 |
No Class IMR Conference |
| 13 | Oct 23 |
Cholesky decomposition, Gaussian elimination, and Nested Dissection See: (1) Gilbert and Tarjan (2) Survey |
| 14 | Oct 25 |
Nested Dissection continued |
| 15 | Oct 30 |
Minimum Degree heuristic and Fractals |
| 16 | Nov 1 |
Iterative Methods Richardson's method and rates of convergence See: (1) Yousef Saad's Book |
| 17 | Nov 6 | Polynomial acceleration and Chebyshev polynomials |
| 18 | Nov 8 |
Steepest descent and Conjugate Gradient See: (1) Hageman and Young (2) Trefethen and Bau |
| 19 | Nov 13 |
Introduction to Preconditioned Conjugate Gradient See: (1) Bern, Gilbert, Hendrickson, Nguyen and Toledo |
| 20 | Nov 15 | No Class Out of Town |
| 21 | Nov 20 | |
| Nov 22 | Thanksgiving | |
| 22 | Nov 27 | |
| 23 | Nov 29 | |
| 24 | Dec 4 | |
| 25 | Dec 6 |