Textbook Suggestions

Calculus

• Thomas’ Calculus
• Stewart’s Calculus

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

Markov Chains on general state space

• Bakry, Gentil, & Ledoux - Analysis and Geometry of Markov Diffusion Operators

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