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Math 301 - Introduction to Combinatorics

1

Triangular Numbers

2

Factorials

3

Binomial coefficients

4

Graphs in Combinatorics

5

Arithmetic of counting I

6

Arithmetic of Counting II - Division

7

Combinations

8

Sets

9
10
11

Sequences

12
13

Pascal's Triangle

14

The Binomial Theorem

15

Multinomial coefficients

16

Problem Solving Techniques

17

Proof Techniques in Combinatorics

18

Induction

19

Combinatorial Proofs

20

Bijections and Cardinality

21

Pigeonhole Principle

22

Recursions and Fibonacci Numbers

23

The Tower of Hanoi

24

Introduction to Sage Math

25

Linear Recurrences

26

Regions of the Plane

27

Recurrence relations with SAGE

28

Derangements

29

Catalan numbers

30

Generating Functions

31
32

Operations on generating functions

33

Solving recursions using generating functions

34

Solving Recurrences with Generating Functions Part II

35

Graph Theory Basics

36

Walks and Adjacency Matrices

37

Eulerian and Hamiltonian walks

38

Introduction to Trees

39

The Language of Trees

40

Cayley's theorem

41

Graph Optimization

42

Matchings on graphs

43

Planar Graphs

44

Planar Graphs and the Euler Characteristic

45

Platonic Solids

46

Partitions

47

Chromatic Number and Chromatic Polynomial