Math 239
Introduction
Week 1-A Examples
Week 1-B Counting Binomial Theorem & Coefficients
Week 1-C Binomial Theorem & Combinatorial Proofs
Week 2-A Combinatorial Proofs & Generating Functions
Week 2-B Generating Functions
Week 2-C Power Series
Week 2-D Inverses, Recurrences, Sum Lemma
Week 3-A Sum Lemma, Product Lemma
Week 3-B Product Lemma, Integer compositions
Week 4-A Integer Compositions
Week 4-B Binary Strings, Generating functions for binary strings
Week 4-C String ambiguity, Basic decompositions, Restrictions on substrings
Week 5-A Restriction on subsets & String recursion
Week 5-B String recursion & Coefficients from rational expressions
Week 5-C Coefficients from Rational Expressions & Solving Homogeneous Recurrences
Week 6-A Solving nonhomogeneous recurrences
Week 6-B Graph theory, Graph models & problems, Graph isomorphism
Week 6-C Isomorphism, Degrees & Special Graphs
Week 7-A Bipartite Graphs
Week 7-B Walks and Paths
Week 7-C Hamilton Cycles
Week 8-A Components and Cuts, Eulerian circuits
Week 8-B Eulerian Circuit & Bridges
Week 8-C Bridges & Trees
Week 9-B Trees & Spanning Trees
Week 9-C Spanning trees, Bipartite characterization
Week 10-A Minimum Spanning Tree, Prim's Algorithm
Week 10-B Euclidean TSP, Planarity
Week 10-C Planarity, Euler's formula
Week 12-A Euler's Formula & Platonic Solids
Week 12-B Kuratawski's Theorem & Colouring
Week 12-C Colouring
Week 13-A Duality, Matching
Week 13-B Matchings & Vertex Covers
Week 13-C Kӧnig's Theorem
Week 14-A Kӧnig's Theorem & Hall's Theorem
Week 14-B Hall's Theorem, Stable Marriage
Final Boss Tips/Tricks
Tutorials
Tutorial #1
Tutorial #2
Tutorial #3
Tutorial #4
Tutorial #5
Tutorial #6
Tutorial #7
Tutorial #8
Tutorial #9