Particle Collisions, Hypergroups and Quadratic Residues - Diffusion Symmetry 3

This lecture introduces discrete hypergroups through a probabilistic particle-collision model and connects them to complete graphs, bipartite graphs, and quadratic residues. It reviews prime fields and primitive roots while developing examples related to algebraic combinatorics.

Syllabus

Intro
Overview
Describing Particle Collisions
The Golden Hypergroup
Complete Graphs
Complete Bipartite Graphs
Quadratic Residues and Non-Residues
Structure of R and N via Primitive Roots
Additive Arithmetic of R and N
Moving to a Multiplicative Arithmetic
A Different Example of Multiplicative Arithmetic