The videos below are the lectures for Math 432 – Applied Combinatorics which I taught as a flipped class in Spring 2021.

This course surveys a variety of topics in combinatorics, beginning with basic counting techniques and elementary proof techniques. We apply these to enumeration of subsets, arrangements, and derangements. We develop advanced counting techniques of generating functions and solving recurrence relations. We study fundamentals of graph theory and algorithms on graphs, including graph colorings and matchings. We conclude with an exploration advanced topics in probabilistic methods.

Each lecture has 3 associated videos following the content of Miklos Bona’s textbook, A Walk Through Combinatorics.

Unit 1 – Counting Basics





Unit 2 – Order and Choice

Unit 3 – The Binomial Theorem

Unit 4 – Sequences

Unit 5 – Permutation

Unit 6 – Generating Functions

Unit 7 – Graph Theory

Unit 8 – Trees

Unit 9 – Graph Properties

Unit 10 – Graph Theorems

Unit 11 – Ramsey Theory

Unit 12 – Discrete Probability