Wolfram MathWorld: The Web's Most Extensive Mathematics Resource
Eddie Woo - YouTube - YouTube High School
MathHelp.com - YouTube
Math | Khan Academy
AMATH 301 - YouTube
Wolfram MathWorld: The Web's Most Extensive Mathematics Resource
Math of the impossible - YouTube TED-Ed playlist
The Langlands Program, Explained - YouTube connecting harmonic analysis and number theory
Math with Bad Drawings – Lover of math. Bad at drawing.
Mathstopia | Share your Knowledge
Math is Fun
The Map of Mathematics - YouTube
The story of mathematical proof – with John Stillwell - YouTube geometric -> algebraic (including calculus) proof, unsolvability
Permutations/Combinations Algorithms Cheat Sheets - DEV Community 👩💻👨💻
Pauls Online Math Notes
Machine learning leads mathematicians to unsolvable problem
CalmCode Blog: An Inverse Turing Test
3Blue1Brown - YouTube
Another Roof - YouTube
eigenchris - YouTube Linear Algebra, Physics
Mathemaniac - YouTube
Mathologer - YouTube
MindYourDecisions - YouTube
Primer - YouTube
VisualMath - YouTube
Zach Star - YouTube
妈咪说 MommyTalk - YouTube
黑筆紅筆 - YouTube
Understanding Wavelets - YouTube
The Secret of Synchronization - YouTube
Lockdown math - YouTube 3Blue1Brown
Calculation
Wolfram|Alpha: Computational Intelligence
DLMF: NIST Digital Library of Mathematical Functions
Invented or Discovered
Is math discovered or invented? - Jeff Dekofsky - YouTube
Roger Penrose - Is Mathematics Invented or Discovered? - YouTube
Was maths invented or discovered? - BBC Science Focus Magazine
Infinity
Aristotle's Wheel Paradox - To Infinity and Beyond - YouTube
Cantor's Infinity Paradox | Set Theory - YouTube Cantor's Diagonalization Proof
Countably infinite: 1-1 correspondence with Natural Numbers, enumerable infinity
Uncountably infinite: 1-1 correspondence with Real Numbers, non-enumerable infinity
Why can't you divide by zero? - TED-Ed - YouTube
Gödel's Incompleteness Theorems
Gödel's incompleteness theorems - Wikiwand
What's the easiest way to understand Gödel's Incompleteness Theorems? Are there statements that have truth values which cannot be determined except meta-mathematically? - Quora
Gödel's Incompleteness Theorem - Numberphile - YouTube
Gödel's Incompleteness (extra footage 1) - Numberphile - YouTube
Math Has a Fatal Flaw - YouTube
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy - YouTube
Encode mathematics operation as numbers, one can create a number (statement) that cannot be proved within the system
哥德尔不完备定理到底说了啥？为什么希尔伯特的数学梦因此破灭？ - YouTube
Alan Turing Publishes "On Computable Numbers," Describing What Came to be Called the "Turing Machine" : History of Information
Turing_Paper_1936.pdf
Linear Algebra
Linear algebra - Wikiwand
Eigenvalues and eigenvectors - Wikiwand
What's a Tensor? - YouTube
Mathematics for Machine Learning: Linear Algebra - YouTube
兩小時學會線性代數 - YouTube
如何证明 3=0？推翻数学大厦！ - YouTube 增根
折磨了人類三百年的難題 | 老高與小茉 Mr & Mrs Gao - YouTube 費馬最後定理
Immersive Math
immersivemath - YouTube
Dear linear algebra students, This is what matrices (and matrix manipulation) really look like - YouTube
Matrix Multiplication Explained (with Python examples): Complete Guide
The fastest matrix multiplication algorithm - YouTube
Covariance and contravariance of vectors - Wikiwand
Variance-covariance matrix using matrix notation of factor analysis - YouTube
6.5.4.1. Mean Vector and Covariance Matrix
Lecture: Eigenvalues and Eigenvectors - YouTube
Lecture: Eigen-decompositions and Iterations - YouTube
What are Eigenvalues and Eigenvectors? - FinTechExplained - Medium
[1908.03795v2] Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra
Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra | What's new
Neutrinos Lead to Unexpected Discovery in Basic Math | Quanta Magazine
Linear Algebra Essentials with Numpy (part 1) - Towards Data Science
Linear Algebra Essentials with Numpy (part 2) - Towards Data Science
Essence of linear algebra - YouTube 3Blue1Brown
Why is Linear Algebra Taught So Badly? - Towards Data Science
Linear Algebra makes sense - YouTube Looking Glass Universe
Solving your first linear program in Python | by Bhaskar Agarwal | Towards Data Science
Hands-On Linear Programming: Optimization With Python – Real Python
Project Point to Plane
c++ - How to project a point onto a plane in 3D? - Stack Overflow
Projection of point onto a plane - YouTube
Point-Plane Distance -- from Wolfram MathWorld
PCA
PCA: Principal Component Analysis, finding direction of maximum variance
MDS: Multidimensional scaling
SVD: Singular Value Decomposition, Singular value = sq rt of Eigenvalue
Eigenvalue = sum of squared distances of projected points on principal component to origin
Principal Component Analysis (PCA) - YouTube
A Comparison of PCA and MDS on a Simple Example - Towards Data Science
Principal Components Analysis - Georgia Tech - Machine Learning - YouTube
StatQuest: Principal Component Analysis (PCA), Step-by-Step - YouTube
StatQuest: PCA main ideas in only 5 minutes!!! - YouTube
Principal Component Analysis (PCA) clearly explained (2015) - YouTube
Lecture: The Singular Value Decomposition (SVD) - YouTube
Lecture: Principal Componenet Analysis (PCA) - YouTube
Lecture: PCA for Face Recognition - YouTube
Daniel Pyrathon - A practical guide to Singular Value Decomposition in Python - PyCon 2018 - YouTube slide
淺談降維方法中的 PCA 與 t-SNE. 在機器學習當中，如果特徵數過多時，有可能會造成一些問題，像是： | by 愷開 | De-Magazine | Medium
Discrete Mathematics
Introduction to Discrete Mathematics for Computer Science | Coursera
Markov Chains
probabilistic state transition
Markov chain - Wikiwand
Markov Chains Clearly Explained! - YouTube
Markov Decision Processes - Computerphile - YouTube
equilibrium probability = left eigen vector of the adjacency matrix
Combinatorics
Group Theory
Group (mathematics) - Wikiwand Set with binary operation defined
Simple group - Wikiwand "prime numbers" of group
Composition series - Wikiwand Jordan-Hölder theorem
List of finite simple groups - Wikiwand
Classical group - Wikiwand
Ring (mathematics) - Wikiwand Group closed in addition, subtraction and multiplication
Field (mathematics) - Wikiwand Ring closed also in division
Explanaria - Groups & Clear Crystal Conundrums
Galois theory - Wikiwand
从五次方程到伽罗瓦理论 - YouTube
Why you can't solve quintic equations (Galois theory approach) SoME2 - YouTube
What is the square root of two? | The Fundamental Theorem of Galois Theory - YouTube
But why is there no quintic formula? | Galois Theory - YouTube
Why There's 'No' Quintic Formula (proof without Galois theory) - YouTube
Galois Theory Explained Simply - YouTube
Group theory, abstraction, and the 196,883-dimensional monster - YouTube
Monster Group (John Conway) - Numberphile - YouTube
Group theory, abstraction, and the 196,883-dimensional monster - YouTube group theory and simple groups
Euler's formula with introductory group theory - YouTube
Group Theory — Introduction to Higher Mathematics - YouTube
Steiner system - Wikiwand
What are...Steiner systems? - YouTube
The Most Powerful Diagram in Mathematics - YouTube S(5,8,24) and MOG
Category Theory
A Sensible Introduction to Category Theory - YouTube
27 Unhelpful Facts About Category Theory - YouTube parody
Intuitive Introduction to Category Theory - YouTube
A Crash Course in Category Theory - Bartosz Milewski - YouTube
Calculus
頂級數學家之間的微積分撕逼大戰有多可怕？生前被牛頓打壓，死後居然躺贏 | 雅桑了嗎 - YouTube
3Blue1Brown
Essence of calculus - YouTube
Vector fields, introduction | Multivariable calculus | Khan Academy - YouTube
Divergence and curl: The language of Maxwell's equations, fluid flow, and more - YouTube
Khan Academy
Multivariable Calculus | Khan Academy
Multivariable calculus - YouTube
3 Paradoxes That Gave Us Calculus - YouTube
Understand Calculus in 10 Minutes - YouTube
Why is calculus so ... EASY ? - YouTube
This Is the Calculus They Won't Teach You #SoME2 - YouTube
Pi
Why pi? - YouTube
Why π^π^π^π could be an integer (for all we know!). - YouTube
Probability
The mathematical foundations of probability - Towards Data Science
Monte Carlo Methods, Made Simple. Using Chaos to Find Clarity | by Andre Ye | Sep, 2020 | Towards Data Science
The Forgotten Algorithm. Exploring Monte Carlo Simulation with… | by Ian Xiao | Towards Data Science
The Beauty of Bayesian Optimization, Explained in Simple Terms | by Andre Ye | Sep, 2020 | Towards Data Science
Exploring Bayesian Optimization
Statistical hypothesis testing - Wikiwand
Frequentist inference - Wikiwand
Overview of Frequentist Hypothesis Testing
class17-slides-all.pdf
How To Catch A Cheater With Math - YouTube explains probabilistic tests, statistical power (sensitivity), p-value
3Blue1Brown
Binomial distributions | Probabilities of probabilities, part 1 - YouTube
Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2 - YouTube Probability Density Function, where the area under the function is 1
But what is a convolution? - YouTube
妈咪说 MommyTalk
概率也能骗人？什么是伯特兰悖论？用数学告诉你为什么说话要严谨 - YouTube
一个反直觉的硬币游戏，伯特兰箱子悖论 - YouTube
充满争议的概率论问题星期二男孩悖论，你能算对吗？ - YouTube
Bayes Theorem
How Bayes Theorem works - YouTube
A visual guide to Bayesian thinking - YouTube
The Bayesian Trap - YouTube
Bayes theorem, the geometry of changing beliefs - YouTube 3Blue1Brown
Bayes Theorem and some of the mysteries it has solved - YouTube
The Mathematics Used to Solve Crime - YouTube
How Bayes Theorem works - YouTube
Causal Bayesian Networks: A flexible tool to enable fairer machine learning | DeepMind
A Gentle Introduction to Bayes Theorem for Machine Learning
The Math Problem I Was NEVER Able to Understand - YouTube "unrelated info"
Statistics
Simple Statistics
StatQuest with Josh Starmer - YouTube
Normalized Nerd - YouTube
This is How Easy It Is to Lie With Statistics - YouTube
This is how easy it is to manipulate public perception - YouTube
Does math belong in the courtroom? - YouTube
Three Statistical Tests Every Game Developer Should Know - YouTube
淘宝“双 11”2684 亿销售额造假了吗？用本福特定律检验一下 - YouTube
Think Stats 2e – Green Tea Press
data set that creates same simple statistics but are totally different
Data visualisation, reporting, and processing with R
Anscombe's quartet - Wikiwand
The Datasaurus Dozen - Same Stats, Different Graphs | Autodesk Research
articles/basic_measures_of_descriptive_statistics.md at master · Dobiasd/articles
articles/mechanical_analogies_for_basic_measures_of_descriptive_statistics.md at master · Dobiasd/articles
p-value
p-value is the probability that random chance generated the data, or something else that is equal or rarer.
Everything you Ever Wanted to Know About P-Value from Scratch
P-value Explained Simply for Data Scientists - Towards Data Science
5 ways to Increase Statistical Power | by Alison Yuhan Yao | Nov, 2021 | Towards Data Science
StatQuest: P Values, clearly explained - YouTube
False Discovery Rates, FDR, clearly explained - YouTube
p-hacking and power calculations - YouTube
Central Limit Theorem
Central limit theorem - Wikiwand
But what is the Central Limit Theorem? - YouTube
Benford's Law
Why do Biden's votes not follow Benford's Law? - YouTube
Differential Equations
Differential equations - YouTube 3Blue1Brown
Machine learning meets math: Solve differential equations with new Julia library - JAXenter
JuliaDiffEq/DiffEqTutorials.jl: Tutorials for using the DiffEq ecosystem
Home · DifferentialEquations.jl
A Comparison Between Differential Equation Solver Suites In MATLAB, R, Julia, Python, C, Mathematica, Maple, and Fortran - Stochastic Lifestyle
Spurious Correlations
Spurious relationship - Wikiwand
Spurious Correlations
Spurious Correlation: Definition, Examples & Detecting - Statistics By Jim
Beware Spurious Correlations
Topology
Visual Topology & Geometry - YouTube
Who cares about topology? (Inscribed rectangle problem) - YouTube
Sneaky Topology | The Borsuk-Ulam theorem and stolen necklaces - YouTube
Why does this balloon have -1 holes? - YouTube
3N+1 Collatz Conjecture
The Simplest Math Problem No One Can Solve - Collatz Conjecture - YouTube
UNCRACKABLE? The Collatz Conjecture - Numberphile - YouTube
民科盛宴冰雹猜想：小学生都能看懂，专业数学家 80 年都证不出来 - YouTube
Poincaré Conjecture
Poincaré conjecture - Wikiwand
庞加莱猜想为何价值 100 万美元？宇宙到底是什么形状？ - YouTube
Programming
math.js | an extensive math library for JavaScript and Node.js
Numeral.js formatting and manipulating numbers
SymPy
SymPy Tutorial - Tutorialspoint
Euler's Formula (e^(πi) = -1)
3Blue1Brown
e^(iπ) in 3.14 minutes, using dynamics | DE5 - YouTube
Euler's formula with introductory group theory - YouTube
e to the pi i for dummies - YouTube
Number Theory
如何快速筛选质数？费马素性检验和米勒-拉宾测试 - YouTube
Fermat's little theorem - Wikiwand
Fermat's little theorem - GeeksforGeeks
Carmichael number - Wikiwand exceptions to Fermat's little theorem
P-adic number - Wikiwand
Mathematicians Use Numbers Differently From The Rest of Us - YouTube
Geometry
Byrne’s Euclid The first 6 books of "The Elements of Euclid" in HTML
Euclidean geometry - Wikiwand
Volume word problems — Basic example (video) | Khan Academy
11 岁的爱因斯坦如何证明勾股定理？跟中国古人比谁的方法好？ - YouTube
How many ways are there to prove the Pythagorean theorem? - Betty Fei - YouTube
But why is a sphere's surface area four times its shadow? - YouTube
How to lie using visual proofs - YouTube
Rhapsody on the Proof of Pi = 4 - YouTube
This Problem Broke Math (and led to quantum physics) - YouTube
- geometric solutions to quadratic and cubic formula
$e^ix$showing up in Schrödinger’s Equations
Penrose Tiles
The Infinite Pattern That Never Repeats - YouTube
Why Penrose Tiles Never Repeat - YouTube
Pattern Collider
Constructible Numbers
Straight edge and Compass Construction
古希腊三大尺规不能问题 高斯为何说正十七边形可以尺规作图？ - YouTube
高斯如何做出正 17 边形？李永乐老师讲数学神器【尺规作图 1/2】 - YouTube
史上最悲惨的数学家是谁？为什么不能三等分任意角？【尺规作图 2/2】 - YouTube
uses complex number and group theory
教你如何不用计算器徒手开平方！《孙子算经》中的开平方术 - YouTube
如何快速徒手开立方？当我没有计算器的时候…… - YouTube
以下問題為尺規不可解
立方體體積倍增
三等分位意角
化圓為方
Fractal
Fractal - Wikiwand
Mandelbrot set - Wikiwand bounded set of simple function on complex number to generate fractal
Draw the Mandelbrot Set in Python – Real Python
Prover
The story of mathematical proof – with John Stillwell - YouTube
Lean
Lean (proof assistant) - Wikiwand
Lean
Automated Mathematical Proofs - Computerphile - YouTube
EXTRA BITS: Automated Proofs - Computerphile - YouTube
TLA+
The TLA+ Home Page
Introduction :: Learn TLA+
Designing Distributed Systems with TLA+
TLA+: The Best Debugger/ Optimizer You’ve Never Heard of – The New Stack
The Temporal Logic of Actions
Leslie Lamport's The TLA+ Video Course - YouTube
Leslie Lamport: Thinking Above the Code - YouTube
Lamport TLA+ Course Lecture 1: Introduction to TLA+ (HD) - YouTube
Lamport TLA+ Course Lecture 2: State Machines in TLA+ (HD) - YouTube
A gentle intro to TLA+ - YouTube
YOW! 2019 - Hillel Wayne - Designing Distributed Systems with TLA+ - YouTube
"Tackling Concurrency Bugs with TLA+" by Hillel Wayne - YouTube
Inductive invariance
Thinking at a more abstract level will improve your code
PlusCal - Wikiwand
PlusCal :: Learn TLA+
A Simple Example
quux00/PlusCal-Examples: Algorithm examples in PlusCal, the algorithm language of Lamport's TLA+
muratdem/PlusCal-examples: Pluscal/TLA+ modeling of distributed systems/protocols
How Amazon Web Services Uses Formal Methods | April 2015 | Communications of the ACM
TLA+ with Leslie Lamport - Software Engineering Daily