Modular Arithmetic: In Motion

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Modular arithmetic visually! We use a visualization tool called a "dynamical portrait." We explore addition and multiplication modulo n, and discover and prove the portrait is made of cycles if and only if the function (f(z) = z+a mod n or f(z) = az mod n) is bijective.

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.

For associated materials:
  1. Proof of Concept
  2. modular arithmetic
  3. dynamical portrait
  4. cryptography
  5. discrete mathematics
  6. number theory
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Комментарии
Автор

I've never thought modular arithmetic in a graph form. Beautiful. Alwo thanks for clean representation.

XahhaTheCrimson
Автор

Thanks for the video! l really enjoyed seeing connections to graph theory.. taking abstract algebra and graph theory right now and this visualization helped:) Also the interactive modular dynamics activity on your site! amazing

jessiemeanwell
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Really nice! I teach an Algebra in Argentina. I´ll try to incorporate some of the visuals. I think students are gonna like it!

TheSanmanju