Mathematics Colloquium by Prof. Steven J. Miller, Williams College, Wednesday, October 13, 1:00 pm

Why I Love Monovariants: From Zombies to Conway’s Soldiers Via the Golden Mean by Prof. Steven J. Miller, Williams College, Mathematics Colloquium, Wednesday, October 13, 1:00 pm, North Science Building 113, Wachenheim

Abstract: A monovariant is a quantity which is either non-increasing or non-decreasing (such as the number of primes up to x or the volume of a sphere of radius r, but not the number of factors of n). Amazingly, many challenging problems can easily be solved by associating the right monovariant to it; unfortunately it is often challenging to ‘see’ the right quantity to study. We’ll explore three interesting cases: understanding the growth of the Zombie apocalypse, the famous Conway checker problem, and if time permits Zeckendorf’s Theorem that every integer can be written uniquely as a sum of non-adjacent Fibonacci numbers (if we define them by F=_{n+1} = F_n+ F_{n-1} with F_1=1, F₂₌₂). This leads to a game I created based on the Fibonacci problem, with a $500 reward for a solution!