📚 Resources

https://www.randomservices.org

Independence

• Visual intuition of independence by @whuber

• Visual intuition of independence

Markov chains

• Intuitive explanation of the reversibility condition

• https://www.randomservices.org/random/expect/Kernels.html

Markov chain Monte Carlo

• https://stats.stackexchange.com/questions/165/how-would-you-explain-markov-chain-monte-carlo-mcmc-to-a-layperson

• https://jeremykun.com/2015/04/06/markov-chain-monte-carlo-without-all-the-bullshit/

• Hui Wang: Snell envelope and optimal stopping

• David Pollard: Optimal stopping

• Michel Goemans: Chernoff bounds

• Motivation behind large deviations

• Djalil Chafaï: Tutorial on large deviation principles

• Tim van Erven - Cramér vs Sanov

• Frank den Hollander's lectures in ISI, Bangalore

• Dominic Yeo - Large Deviations 1: Motivation and Cramér's theorem

• Nick Alger: physical meaning of the Legendre transform

• Jonathan Manton: introduction to the Legendre transform

• Frank Nielsen: Legendre transformation and information geometry

Basics

• Alon Amit: nonexistence of locally constant analytic functions

Operator theory

• Jordan Bell - Trace class operators and Hilbert-Schmidt operators (2016)

• http://bjlkeng.github.io/posts/the-calculus-of-variations

• MathSx: Why is analysis called analysis?

• Aaron Meurer - The Risch Algorithm: Part 1

• Alon Amit: What is π?

• MathSx: differential vs derivative

• Set Theory on Math24

• Peter Suber: A Crash Course in the Mathematics of Infinite Sets

• MathSx195517: Definition of the infinite Cartesian product

• Alon Amit: Gödel's incompleteness theorem in a nutshell

• Jeremy Kun: Primers

• Brian Keng's blog

• Unicode character search

• Unicode emoji modifiers

• Useful Unicode symbols

• Top-down vs bottom-up, recursion, memoization, dynamic programming

• Michael Verdi: Use dynamic programming to improve recursive solutions

• Dimitrios Kosmopoulos: Recursion and Dynamic Programming

• Fabian Robaina: A Systematic Approach to Dynamic Programming

• SO11632516: ANN vs SVMs

• Software Foundations (series)

• https://playground.tensorflow.org

• Google: How to do a code review

• https://www.quantamagazine.org/with-category-theory-mathematics-escapes-from-equality-20191010

• Category Theory Notes

• Kevin deLaplante - Reasoning with Probabilities

• http://thedailyidea.org/best-books-philosophy-mathematics

• https://www.newyorker.com/culture/annals-of-inquiry/the-myth-and-magic-of-generating-new-ideas

• Quine - Two Dogmas of Empericism

• Michael O'Rourke: The Meaning of the Material Conditional

• A mathematician's response to the philosophy of mathematics

• PhilSx: Was mathematics invented or discovered?

• Alon Amit: Cardano's method for solving cubic equations

• Alon Amit: constructible numbers

• MathSx: ℝ is ∞-dimensional vector space over ℚ

• Quora: normal subgroups

• Theory of everything (Wiki)

• PhysSx: path integral vs measure on infinite-dimensional spaces

• MO19495: mathematics of path integral

Spin glass

• 3blue1brown: neural networks

• Lucas Souza (Numenta): the case for sparsity in neural networks (pruning)

• Nolan Dey: Breaking down the Lottery Ticket Hypothesis

• David Donoho: 50 Years of Data Science

• QuantSX: List of Quantitative Finance books

Giving talks

• John McCarthy - How to Give a Good Colloquium

• Tips on giving talks

Teaching

• Differential Calculus Teaching Plans

• Lee Lady: How Does One Do Mathematical Research?

• IMA: public lectures

• IMA: graduate student training resources

• IMA: programs

• A list of podcasts for mathematics people

• Why is Mathematics?

• Edward Frenkel - Mathematics: The Language of Nature (WorldScienceU)

• Edward Frenkel - Mathematics: The Language of Nature (YouTube)

• Gian-Carlo Rota: Ten Lessons I wish I had been Taught

• Gian-Carlo Rota: Ten lessons I wish I had learned before I started teaching differential equations

• Gian-Carlo Rota: Ten lessons of an MIT Education

• Cosma Shalizi's blog

• David Aldous: "Probability and the Real World" project