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The readings are assigned in the required textbook: Bona, M. A Walk through Combinatorics. 1st ed. Singapore, SG: World Scientific Publishing Company, 2002. ISBN: 9810249012.
Course readings.
| Lec # |
Topics |
Readings |
| 1 |
Introduction
Pigeonhole Principle |
Chapter 1 |
| 2 |
Mathematical Induction |
Chapter 2 |
| 3 |
Permutations |
Chapter 3 |
| 4 |
Binomial Theorem |
Chapter 4 |
| 5 |
Compositions
Integer Partitions |
Chapter 5 |
| 6 |
Set Partitions |
|
| 7 |
Cycles in Permutations
Stirling Numbers |
Chapter 6 |
| 8 |
Exam 1 |
|
| 9 |
Inclusion-exclusion Principle |
Chapter 7 |
| 10 |
Inclusion-exclusion (cont.)
Mobius Inversion |
|
| 11 |
Recurrence Relations |
|
| 12 |
Generating Functions |
Chapter 8 |
| 13 |
Generating Functions (cont.) |
|
| 14 |
Catalan Numbers |
|
| 15 |
Generating Functions (cont.) |
|
| 16 |
Exam 2 |
|
| 17 |
Graphs
Eulerian Walks
Hamiltonian Cycles |
Chapter 9 |
| 18 |
Trees
Counting Trees |
Chapter 10 |
| 19 |
Matrix-tree Theorem |
|
| 20 |
Matrix-tree Theorem (cont.) |
|
| 21 |
Matrix-tree Theorem and Eulerian Digraphs |
|
| 22 |
Bipartite Graphs and Matchings |
Chapter 11 |
| 23 |
Planar Graphs
Polyhedra
Maps |
Chapter 12 |
| 24 |
Chromatic Polynomials |
|
| 25 |
Exam 3 |
|
| 26 |
Polya Counting
Ramsey Theory
Probabilistic Method |
|