Mathematics

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Notation

https://twitter.com/ZMatuszewski/status/1446179776495034376

Sum

\(\sum_{n=0}^{4} = 3n\)

sum = 0
for (n=0, n<=4, n++) {
  sum += 3*n
}

Product

\(\prod_{n=1}^{4} = 2n\)

prod = 1
for (n=1, n<=4, n++) {
  prod *= 2*n
}

Iff

"If and only if"

Calculus

Calculus For The People – Season 1 https://www.geogebra.org/m/x39ys4d7

Tensor Calculus

https://grinfeld.org/books/An-Introduction-To-Tensor-Calculus/

Algebra

Basics

Exponent properties

• \(x^n x^m = x^{n+m}\)
• \(\dfrac{x^n}{x^m} = x^{n-m}\)
• \({x^n}^m = x^{nm}\)
• \((xy)^n = x^n y^n\)
• \(x^{-n} = \dfrac{1}{x^n}\)

Linear Algebra

https://pabloinsente.github.io/intro-linear-algebra

Intermediate Algebra

https://saylordotorg.github.io/text_intermediate-algebra/index.html

Statistics

Probabilities

Singleton

A set with exactly one element.

Linear Regression

https://www.simonwardjones.co.uk/posts/linear_regression/

https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average

Resources

Statistics in a Nutshell, 2nd Edition

by Sarah Boslaugh

Statistics without Tears: An Introduction for Non-Mathematicians

by Derek Rowntree

Improving your statistical inferences

by Daniel Lakens

Introduction to Modern Statistics (2nd Ed)

https://openintro-ims2.netlify.app/

Statistical Rethinking

A Bayesian Course with Examples in R and Stan https://xcelab.net/rm/statistical-rethinking/

Stastistical Rethinking Recoded

Statistical Rethinking with brms, ggplot2, and the tidyverse https://bookdown.org/ajkurz/Statistical_Rethinking_recoded/

Decision Theory

Loss Function

A function that maps an event or values to a real number representing some "cost". Typically, the difference between estimated values and true values. To optimize is to seek to minimize a loss function.

Operations

Unary Operations

https://en.wikipedia.org/wiki/Unary_operation

Probabilities

https://en.wikipedia.org/wiki/Kelly_criterion

https://seeing-theory.brown.edu/basic-probability/index.html

Number Sets

https://thinkzone.wlonk.com/Numbers/NumberSets.htm

Combinatory Logic

https://en.wikipedia.org/wiki/Combinatory_logic

Resources

To Mock a Mockingbird

by Raymond Smullyan

John's Lambda Calculus and Combinatory Logic Playground

https://tromp.github.io/cl/cl.html

Combinatory Logic table

https://combinatorylogic.com/table.html

Equational Logic

https://en.wikipedia.org/wiki/Equational_logic

Fibonacci sequence

A sequence in which each number is the sum of the two preceding ones

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

Category Theory

Categories

Morphisms

Functor

Mapping between categories.

Monad

Monoid

Resources

• https://www.logicmatters.net/categories/
• https://news.ycombinator.com/item?id=29734482
• https://github.com/bgavran/Category_Theory_Machine_Learning

Euclidian Geometry

Scalar

An element of a vector space. Multiple scalars form a vector.

Vector

An element of a vector space

Vector Space

A set of vectors

Glossary

Singularity

A point at which the mathematical object is not defined.

Resources

Math equations to LaTeX OCR

https://mathpix.com/

Math church

http://nanar.com/

Math cheatsheet

https://ourway.keybase.pub/mathematics_cheat_sheet.pdf

MIT Mathlets

https://mathlets.org/mathlets/

Math as code

https://github.com/Jam3/math-as-code

MIT Applied Math curriculum

https://math.mit.edu/academics/undergrad/major/course18/applied.php

So You Want to Study Mathematics…

https://www.susanrigetti.com/math

Why Math?

by R.D. Driver

e: The Story of a Number by Eli Maor (Level: Easy)

"A fun, accessible book that will get you excited about mathematics."

The Joy Of X: A Guided Tour of Math, from One to Infinity by Steven H. Strogatz (Level: Easy)

"A lot of fun to read, but make sure you get the paperback or hardcover version for readability purposes."

Fermat’s Enigma by Simon Singh (Level: Easy)

"A beautifully-written book about Fermat’s Last Theorem."

The Man Who Loved Only Numbers by Paul Hoffman (Level: Easy)

"A compulsively-readable biography of Paul Erdős."

The Man Who Knew Infinity by Robert Kanigel (which was also made into a film) (Level: Easy)

"A wonderful biography of Srinivasa Ramanujan."

Flatland by Edwin A. Abbott (Level: Easy)

"A classic. I highly recommend the annotated version, which adds extra joy to the reading experience."

A Mathematician’s Apology by G.H. Hardy (Level: Medium)

"One of the most beautiful things ever written about mathematics, by one of the greatest mathematicians of all time."

Fearless Symmetry by Avner Ash and Robert Gross (Level: Difficult)

"One of my all-time favorites."

Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler (Level: Difficult)

"This book is an absolute joy to read in small bits and pieces. The more math you learn, the more you will fall in love with it."

Mathspp

https://mathspp.com/blog

Better Explained

https://betterexplained.com/

Approximation Theory

https://xn--2-umb.com/22/approximation/index.html

Free Math Textbooks by Xah Lee

http://xahlee.info/math/math_books.html

Paul's Online Math Notes

https://tutorial.math.lamar.edu/

Linear Algebra by Jim Hefferon

https://hefferon.net/linearalgebra/index.html

Everything You Always Wanted To Know About Mathematics

https://www.math.cmu.edu/~jmackey/151_128/bws_book.pdf