Particle collisions, hypergroups and quadratic residues | Diffusion Symmetry 3 | N J Wildberger скачать в хорошем качестве

Particle collisions, hypergroups and quadratic residues | Diffusion Symmetry 3 | N J Wildberger

We introduce a simple particle collision model for the algebraic structure called a hypergroup, which is a normalization of a fusion rule algebra, and closely connected also to Bose Messner algebras and association schemes from algebraic combinatorics. In this model, the results of particle collisions are probabilistic, there is a distinguished particle called a photon which is absorbed in any collision, and each particle has a unique antiparticle (which might in fact coincide with the given particle), characterized by the condition on yielding a photon when collided with the original particle. We will be introducing the "Golden hypergroup", along with hypergroups coming from complete graphs, and also from complete bi-partite graphs. A further interesting family of such algebraic objects goes back in some sense to C. F. Gauss and his study of quadratic residues and non-residues. For that we will need to review some basic facts about prime fields, including the idea of primitive roots. Video Contents (thanks to Lucas Lofaro) 0:00 Intro 0:08 Overview 1:53 Describing Particle Collisions 5:39 The Golden Hypergroup 9:05 Complete Graphs 11:30 Complete Bipartite Graphs 20:30 Quadratic Residues and Non-Residues 22:52 Structure of R and N via Primitive Roots 26:03 Additive Arithmetic of R and N 29:59 Moving to a Multiplicative Arithmetic 37:00 A Different Example of Multiplicative Arithmetic The Playlist for this series is at    • Плейлист   ************************ This is closely related to the Exceptional Structures in Mathematics and Physics lectures which are part of the Explore Research Level Mathematics video lectures. These are designed for motivated amateur, or professional, mathematicians wanting to delve into pure maths research without the abstraction and complexity that currently besets much of the subject. We will aim to always connect our abstract musings to computational reality by focusing on examples and explicit, concrete calculations --- naturally without any pretense of being "able to do an infinite number of things"! To access more Explore Research Level Mathematics, please join Norman's Wild Egg Maths channel at    / @wildeggmathematicscourses  , or become a Patron at   / njwildberger   . There are already dozens of videos there, and many more will appear over the next months and years. One additional advantage: you get to access pdf summaries of some of the videos along with GeoGebra worksheets. *********************** Here are all the Insights into Mathematics Playlists: Elementary Mathematics (K-6) Explained:    / playlist   list=PL8403C2F0C89B1333 Year 9 Maths:    • Плейлист   Ancient Mathematics:    • Плейлист   Wild West Banking:    • Плейлист   Sociology and Pure Mathematics:    • Плейлист   Old Babylonian Mathematics (with Daniel Mansfield):    / playlist   list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov Math History:    • Плейлист   Wild Trig: Intro to Rational Trigonometry:    • Плейлист   MathFoundations:    • Плейлист   Wild Linear Algebra:    • Плейлист   Famous Math Problems:    • Плейлист   Probability and Statistics: An Introduction:    • Плейлист   Boole's Logic and Circuit Analysis:    • Плейлист   Universal Hyperbolic Geometry:    • Плейлист   Differential Geometry:    • Плейлист   Algebraic Topology:    • Плейлист   Math Seminars:    • Плейлист   ************************ And here are the Wild Egg Maths Playlists: Solving Polynomial Equations:    • Плейлист   Exceptional Structures in Maths and Physics via Dynamics on Graphs"    • Плейлист   Triangle Centres:    • ENCYCLOPEDIA OF TRIANGLE CENTERS   Six: An elementary course in pure mathematics:    • Плейлист   Algebraic Calculus One:    • Плейлист   Algebraic Calculus Two:    • Плейлист