This is an archived course. A more recent version may be available at ocw.mit.edu.

Readings

The readings are assigned in the required textbook: Buy at Amazon Bona, M. A Walk through Combinatorics. 1st ed. Singapore, SG: World Scientific Publishing Company, 2002. ISBN: 9810249012.

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