Most of the readings are assigned from the required textbook Bona, Miklos. A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory. World Scientific Publishing Company, 2011. ISBN: 9789814335232. [Preview with Google Books]
| SES # | TOPICS | READINGS |
|---|---|---|
| 1 | Pigeonhole Principle | Chapter 1 |
| 2 | Induction, Elementary Counting | Chapter 2 and start Chapter 3. |
| 3 | Elementary Counting (concluded) | Chapter 3 (continued) |
| 4 | Binomial Theorem, Compositions | Chapter 4 |
| 5 | Compositions (concluded), Integer Partitions | Chapter 5 |
| 6 | Integer Partitions (concluded) | |
| 7 | Set Partitions | |
| 8 | Permutations, Cycle Type | Chapter 6 |
| 9 | Permutations (cont.), Stirling Numbers of the First Kind | |
| 10 | Permutations (concluded) | |
| 11 | The Sieve | Chapter 7 |
| 12 | The Sieve (cont.), Generating Functions | |
| 13 | Generating Functions (continued) | Chapter 8 |
| 14 | Generating Functions (concluded) | |
| 15 | Catalan Numbers | |
| 16 | Midterm One-Hour Exam 1 (Chapters 1–7, omitting pp. 123–24) | |
| 17 | Partitions | Chapter 8 (continued) |
| 18 | Exponential Generating Functions | |
| 19 | Exponential Generating Functions (concluded) | |
| 20 | Vertex Degree, Eulerian Walks | Chapter 9 |
| 21 | Isomorphism, Hamiltonian Cycles | |
| 22 | Tournaments, Trees | Chapter 10 |
| 23 | Counting Trees | |
| 24 | Minimum Weight Spanning Trees |
Matrix-Tree Theorem (PDF) More on Matrix-Tree Theorem (PDF) |
| 25 | Matrix-Tree Theorem | Chapter 10 (continued) |
| 26 | Matrix-Tree Theorem (concluded), Bipartite Graphs | Finish Chapter 10 and start Chapter 11. |
| 27 | Bipartite Graphs (concluded) | Chapter 11 |
| 28 | Matchings in Bipartite Graphs | Chapter 11 (continued) |
| 29 | Midterm One-Hour Exam 2 (Chapters 8–10.2) | |
| 30 | Latin Rectangles, Konig-Egervary Theorem | Chapter 11 (continued) |
| 31 | Matchings in Bipartite Graphs (concluded) | |
| 32 | Chromatic Polynomials | |
| 33 | Planar Graphs | Chapter 12 |
| 34 | Polyhedra | |
| 35 | Polyhedra (concluded) | |
| 36 | Coloring Maps | |
| 37 | Ramsey Theory | Chapter 13 |
| 38 | A Probabilistic Proof | |
| 39 | Discussion of Final Exam, Answering Questions | |
| 40 | Final Exam (Chapters 1–12) | |