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

Calendar

Lec # Topics KEY DATES
1

Introduction

Pigeonhole Principle

  
2 Mathematical Induction  
3 Permutations  
4 Binomial Theorem Problem set 1 due
5

Compositions

Integer Partitions

  
6 Set Partitions  
7

Cycles in Permutations

Stirling Numbers

  
8 Exam 1 Problem set 2 due
9 Inclusion-exclusion Principle  
10

Inclusion-exclusion (cont.)

Mobius Inversion

  
11 Recurrence Relations Problem set 3 due
12 Generating Functions  
13 Generating Functions (cont.)  
14 Catalan Numbers  
15 Generating Functions (cont.) Problem set 4 due
16 Exam 2  
17

Graphs

Eulerian Walks

Hamiltonian Cycles

  
18

Trees

Counting Trees

 Problem set 5 due
19 Matrix-tree Theorem  
20 Matrix-tree Theorem (cont.)  
21 Matrix-tree Theorem and Eulerian Digraphs  
22 Bipartite Graphs and Matchings Problem set 6 due
23

Planar Graphs

Polyhedra

Maps

  
24 Chromatic Polynomials  
25 Exam 3  
26

Polya Counting

Ramsey Theory

Probabilistic Method

 Problem set 7 due