Media Summary: This is a graduate course that I taught at Sungkyunkwan University in 2017. We closely follow the book: Proofs and Confirmations ... This week we learn about the different kinds of induction: weak induction and strong induction. Sean explains why math is useful and talks about visualizing the Fibonacci sequence through
Topics In Combinatorics Lecture 9 - Detailed Analysis & Overview
This is a graduate course that I taught at Sungkyunkwan University in 2017. We closely follow the book: Proofs and Confirmations ... This week we learn about the different kinds of induction: weak induction and strong induction. Sean explains why math is useful and talks about visualizing the Fibonacci sequence through We prove several partition identities, including Euler's pentagonal number theorem. Let F be a family of subsets of {1,2,...,n} such that every set in F has size that satisfies some congruence condition mod p and every ... Here I show how to use the Borsuk-Ulam theorem to find a graph with no short odd cycles but with very high chromatic number, ...
This is an introduction to mathematical probability. A result that has played a central role in additive Having presented some (but by no means all) of the basic theory of entropy, I give an application to the following problem: let G be ...