Science on Tap: Exploring Combinatorial Puzzles, Games, and Counting

Mathematicians use logic to understand the behavior and connections of abstract objects and collections. We use the power of mathematical proof to form statements that we know with certainty to be true. We also, on occasion, enjoy applying mathematics towards slightly more playful things! While mathematics is often viewed as daunting, complex, and terrifying, my hope is to present a side of rigorous mathematics that's inviting, entertaining, and perhaps even fun! In this talk, we'll apply combinatorial game theory to examine some combinatorial games, i.e. sequential games or puzzles with perfect information given. On this tour, we'll thoroughly examine a number of simple games, and will encounter surprising results and satisfying proofs. We'll also provide a taste of enumerative combinatorics, seeing examples of things common sequences count.

Speaker: Sam Miller, UC Santa Cruz