Modular Arithmetic in Mathematica & the Wolfram Language

Mathematica Essentials - the first PRO COURSE from Socratica

In this video, we introduce modular arithmetic and how it can be visualized as "circular arithmetic" or "clock arithmetic." Mathematica has many built-in functions that help you do modular arithmetic, including the Mod function, the PowerMod function, the ModularInverse function, and many more. We show several examples to help you get started.

Thank you to our VIP Patreon Members who helped make this video possible! Robert Fulbright, Marko Popovic, Scott Dreblow, Marcos Silveira, Christopher Kemsley, Philip Rice, Eric Eccleston, Jeremy Shimanek, Michael Shebanow, Kavon Johnson, Alvin Khaled, Kevin B, John Krawiec, Umar Khan, MdeG, Carlos Araujo, and Tracy Karin Prell.

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MATHEMATICA ESSENTIALS by Socratica
Modular Arithmetic

0:00 Intro to Modular Arithmetic
2:17 Mod function
3:21 Number Theory/ Fermat's Little Theorem
3:43 Euler totient function
4:31 PowerMod function
5:41 ModularInverse function
6:34 Using Solve with modular equations
7:34 PolynomialMod function
7:46 PrimitiveRoot & PrimitiveRootList functions
7:58 EulerPhi
8:09 MultiplicativeOrder function
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We recommend the following (affiliate links):
The Wolfram Language

The Mythical Man Month - Essays on Software Engineering & Project Management

Innumeracy: Mathematical Illiteracy and Its Consequences

Mindset by Carol Dweck

How to Be a Great Student (our first book!)

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Written & Produced by Michael Harrison & Kimberly Hatch Harrison
Edited by Megi Shuke

About our Instructors:

Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.

Kimberly earned her BS in Biology and another BS in English at Caltech. She did her graduate work in Molecular Biology at Princeton, specializing in Immunology and Neurobiology. Kimberly spent 16+ years as a research scientist and a dozen years as a biology and chemistry instructor.

Michael and Kimberly Harrison co-founded Socratica.
Their mission? To create the education of the future.

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PLAYLISTS

#Mathematica #Wolfram #WolframLanguage

[Socratica]

Mathematica Essentials - the first PRO COURSE from Socratica

[tracykarinp]

Mathematica is a *Beautiful* way to find solutions! Thank you for creating this wonderful video!

[cykkm]

The 3rd argument to Mod[] is worth mentioning: the lower bound of the result range. E.g., if you want the representative range around 0, Mod[a, b, -b/2] does the trick:
Table[Mod[n, 7, -3], {n, 0, 7}] ⇒ {0, 1, 2, 3, -3, -2, -1, 0}
7:22: Ughhh... :) Ctrl+L copies closest input cell's contents from above and inserts at point if inside a cell, or to a new input cell if the point is between cells.

[thamilanban]

1:24 is this explanation correct for 1(mod 7). 34 divided by 7 gives 6 remainders. I am confused.

[martinnyberg]

0:13 Why do some people put arrows at both ends? 🤔 The arrow is there to point in the direction of increase. (And, no, it is not an exclusively american thing; I went to uni in the US and my profs did not do this, but I have seen brits and south-asians on YT who do).

[kirbymarchbarcena]

I guess I have to re-watch this again and again to better understand it.

[williamjordan]

Second @Battery

Like a negative post on a battery @Battery.

All good.

Positive!