Explore the fascinating world of hypergroups and particle collisions in this 41-minute lecture. Delve into a simple particle collision model for hypergroups, a normalized form of fusion rule algebra connected to Bose Messner algebras and association schemes. Learn about probabilistic collision results, the unique "photon" particle, and antiparticles. Discover the "Golden hypergroup" and hypergroups derived from complete and complete bi-partite graphs. Investigate quadratic residues and non-residues, reviewing prime fields and primitive roots. Examine the structure and arithmetic of residues and non-residues, transitioning from additive to multiplicative arithmetic. Gain insights into research-level mathematics through concrete calculations and examples, bridging abstract concepts with computational reality.