Textbooks
Math at Undergrad and Grad Level
Calculus
- Thomas’ Calculus
- Stewart’s Calculus
- Lax & Terrell - Calculus and Multivariable Calculus with Applications
Linear Algebra
- Lay, Lay, & McDonald - Linear Algebra and Its Applications
- Trefethen & Bau - Numerical Linear Algebra
- Sheldon Axler - Linear Algebra Done Right
- Friedberg, Insel, Spence - Linear Algebra
Real and Functional Analysis
- Steven Krantz – Real Analysis and Foundations
- Walter B. Rudin - Principles of Mathematical Analysis
- Thomas Apostol - Mathematical Analysis
- Luigi Ambrosio, Giuseppe Da Prato and Andrea Mennucci - Introduction to Measure Theory and Integration
- Donald Cohn - Measure Theory
- Vladimir I. Bogachev - Measure Theory, Vol. 1 and 2
- Bogachev, Smolyanov - Real and Functional Analysis
- Gerald B. Folland - Real Analysis: Modern Techniques and Their Applications
- Haïm Brezis - Functional Analysis, Sobolev Spaces and Partial Differential Equations
Algebra
- John B. Fraleigh - A First Course in Abstract Algebra
- Dummit & Foote - Abstract Algebra
Advanced Undergraduate Probability
- Anirban DasGupta - Fundamentals of Probability: A First Course
- Grimmett & Welsh - Probability: An Introduction
- Gregory Lawler - Introduction to Stochastic Processes
- James Norris - Markov Chains
Graduate Probability
- Grimmett & Stirzaker - Probability and Random Processes
- Jean-François Le Gall - Measure Theory, Probability, and Stochastic Processes
- Rick Durrett - Probability: Theory and Examples
- Patrick Billingsley - Probability and Measure
- Richard M. Dudley - Real Analysis and Probability
- Olav Kallenberg - Foundations of Modern Probability
Markov Chains on countable state space
- Levin, Peres, & Wilmer - Markov Chains and Mixing Times
Brownian Motion and Stochastic Analysis
- Jean-François Le Gall - Brownian Motion, Martingales, and Stochastic Calculus
- Mörters & Peres - Brownian Motion
- Revuz & Yor - Continuous Martingales and Brownian Motion
- Karatzas & Shreve - Brownian Motion and Stochastic Calculus
Ergodic Theory
- Patrick Billingsley - Ergodic Theory and Information
- Einsiedler & Ward - Ergodic Theory, with a view towards Number Theory
High-Dimensional Probability
- Roman Vershynin - High-Dimensional Probability: An Introduction with Applications to Data Science
- Ramon van Handel - Lecture Notes for APC 550: Probability in High Dimension
Statistics
- A.W. van der Vaart - Asymptotic Statistics
- Martin Wainwright - High-dimensional Statistics: A Non-asymptotic Viewpoint
Information Theory
- Cover and Thomas - Elements of Information Theory
- Polyanskiy and Wu - Information Theory: from Coding to Learning
Game Theory
- Thomas Ferguson - A Course in Game Theory
- Karlin & Peres - Game Theory, Alive
Probability Research Texts
High-Dimensional Probability: an Introduction with Applications to Data Science (Roman Vershynin)
APC550 High-Dimensional Probability (Ramon van Handel)
Concentration of Measure Phenomenon (Michel Ledoux)
Probability in Banach Spaces (Michel Ledoux and Michel Talagrand)
Concentration Inequalities: a Nonasymptotic Theory of Independence (Stéphane Boucheron, Gábor Lugosi, and Pascal Massart)
Concentration Inequalities and Model Selection (Saint-Flour 2003, Pascal Massart)
Random Fields and Geometry (Robert Adler and Jonathan Taylor)
Spectral Analysis of Large Dimensional Random Matrices (Zhidong Bai and Jack Silverstein)
Percolation (Geoffrey Grimmett)
50 Years of First-Passage Percolation (Antonio Auffinger, Michael Damron, and Jack Hanson)
Proceedings of Symposia in Applied Mathematics Vol.79: Random Growth Models (AMS Short Course January 2–3, 2017; edited by Michael Damron, Firas Rassoul-Agha, and Timo Seppäläinen)
Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction (Sacha Friedli and Yvan Velenik)
A Course on Large Deviations with an Introduction to Gibbs Measures (GSM 162; Firas Rassoul-Agha and Timo Seppäläinen)
Analysis and Geometry of Markov Diffusion Operators (Dominique Bakry, Ivan Gentil, and Michel Ledoux)