Modular arithmetic

Modular Arithmetic: Under the Hood

Modular arithmetic visually! For aspiring mathematicians already familiar with modular arithmetic, this video describes how to formalize the concept mathematically: to define the integers modulo n, to define the operations of addition and multiplication, and check that these are well-def

From playlist Modular Arithmetic Visually

Discrete Math - 4.1.2 Modular Arithmetic

Introduction to modular arithmetic including several proofs of theorems along with some computation. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

From playlist Discrete Math I (Entire Course)

Number Theory | Modular Inverses: Example

We give an example of calculating inverses modulo n using two separate strategies.

From playlist Modular Arithmetic and Linear Congruences

Modular forms: Introduction

This lecture is part of an online graduate course on modular forms. We introduce modular forms, and give several examples of how they were used to solve problems in apparently unrelated areas of mathematics. I will not be following any particular book, but if anyone wants a suggestion

From playlist Modular forms

Modular Arithmetic: User's Manual

Modular arithmetic visually! How to compute modulo n, efficiently and with intuition. We rely heavily on visual intuition. This video is appropriate for anyone interested in modular arithmetic! It could be used in high school, for an introduction to proof course, for undergraduate math

From playlist Modular Arithmetic Visually

What is Modular Arithmetic - Introduction to Modular Arithmetic - Cryptography - Lesson 2

Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Cryptography

Modular Arithmetic: In Motion

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

From playlist Modular Arithmetic Visually

Discrete Structures: Modular arithmetic

A review of modular arithmetic. Congruent values; addition; multiplication; exponentiation; additive and multiplicative identity.

From playlist Discrete Structures

The modular inverse via Gauss not Euclid

We demonstrate a lesser-known algorithm for taking the inverse of a residue modulo p, where p is prime. This algorithm doesn't depend on the extended Euclidean algorithm, so it can be learned independently. This is part of a larger series on modular arithmetic: https://www.youtube.com/pl

From playlist Modular Arithmetic Visually

Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences

Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know

From playlist 2022 Summer School on the Langlands program

Mod By A Group: Generalized Modular Arithmetic, from Basic Modular Arithmetic Congruence to 'Normal'

This time I wanted to tackle what it means to Mod by a Group (or rather by a subgroup) and how that can give rise to generalized modular arithmetic. I start from basic modular arithmetic congruence in the integers and used that as a vehicle to build up to the idea of 'Normal' in Abstract a

From playlist The New CHALKboard

How does Modular Arithmetic work?

Question 6 from Tom Rocks Maths and I Love Mathematics - answering the questions sent in and voted for by YOU. This time we explore modular arithmetic through the familiar example of the 12-hour clock. Full playlist: https://www.youtube.com/watch?v=by8Mf6Lm5I8&list=PLMCRxGutHqfmb00xXx9n0

From playlist I Love Mathematics

Modular Arithmetic in Mathematica & the Wolfram Language

𝙒𝘼𝙉𝙏 𝙈𝙊𝙍𝙀? https://snu.socratica.com/mathematica To be notified of when our first Pro Course "Mathematica Essentials" is available, join our mailing list at: https://snu.socratica.com/mathematica In this video, we introduce modular arithmetic and how it can be visualized as "circular arit

From playlist Mathematica & the Wolfram Language

Bergeron Nicolas "Les "invariants arithmétiques" de H. Poincaré"

Note(s) Biographique(s) Nicolas Bergeron est né en 1975. Elève de l'ENS Lyon il obtiendra son doctorat en 2000. Lauréat de la Médaille de bronze du C.N.R.S. en 2007, il a également été membre junior de l'IUF en 2010. Il est actuellement professeur de mathématiques à l'Université Pierre

From playlist Colloque Scientifique International Poincaré 100

What are Reed-Solomon Codes?

An introduction to Modular Arithmetic, Lagrange Interpolation and Reed-Solomon Codes. Sign up for Brilliant! https://brilliant.org/vcubingx Fund future videos on Patreon! https://patreon.com/vcubingx The source code for the animations can be found here: https://github.com/vivek3141/videos

From playlist Other Math Videos

Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 1

In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

Math for Liberal Studies - Lecture 3.8.1 Affine and Multiplicative Ciphers

This is the first video lecture for Math for Liberal Studies, Section 3.8: More Modular Arithmetic and Public-Key Cryptography. In this lecture, I talk about how we can use multiplication in modular arithmetic to construct new ciphers. I also discuss the difficulty in finding the decryptio

From playlist Math for Liberal Studies Lectures

Modular Forms | Modular Forms; Section 1 2

We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)

From playlist Modular Forms

Arithmetic theta series - Stephan Kudla

Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: Arithmetic theta series Speaker: Stephan Kudla Affiliation: University of Toronto Date: March 8, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics