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
Math church
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 GĂĽnter 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
Better Explained
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