Damien Gonot

# Mathematics

Homepage / Notes / Mathematics

## Notation

### 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
}


"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

by Daniel Lakens

## 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

## Equational Logic

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

## Category Theory

### Functor

Mapping between categories.

## Euclidian Geometry

### Scalar

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

### Vector

An element of a vector space

A set of vectors

## 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

### So You Want to Study Mathematics…

https://www.susanrigetti.com/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