Modular Arithmetic: Multiplication in Motion

Modular arithmetic visually! We explore multiplication modulo n, and discover and prove that the multiplication-by-a map f(z) = az mod n is bijective if and only if a and n are coprime. We use a visualization tool called a "dynamical portrait."

This treatment is inspired by Martin H. Weissman's beautiful book, An Illustrated Theory of Numbers.

This video is appropriate for an introduction to proof course, for undergraduate mathematics majors, or for the mathematically inclined, especially those interested in cryptography or number theory.

This is part of a series on modular arithmetic:    • Modular Arithmetic Visually  

For associated materials:
proofofconcept.katestange.net/