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Some mathematical bibliography
Algebra and number theory
- Algebra 2, Jay Abramson et al.
- Algebra: Abstract and Concrete, Frederick M. Goodman
- Algebra: Chapter 0, Paolo Aluffi
- Basic Algebra, Anthony W. Knapp
- Basic Category Theory, Tom Leinster
- Basic Mathematics, Serge Lang
- A Computational Introduction to Number Theory and Algebra, Victor Shoup
- A Course in Universal Algebra, Stanley N. Burris, H. P. Sankappanavar
- Elementary Number Theory: Primes, Congruences, and Secrets, William Stein
- Foundations of Module and Ring Theory: A Handbook for Study and Research, Robert Wisbauer
- Group Theory, J. S. Milne
- Introduction to Modern Algebra, David Joyce
Algorithms and computation
- Algorithms and Complexity, Herbert S. Wilf
- Applied Combinatorics, Mitchel T. Keller, William T. Trotter
- Discrete Structures, Andreas Klappenecker, Hyunyoung Lee
- Exploring Combinatorial Mathematics, Richard Grassl, Oscar Levin
- Foundations of Applied Mathematics, Jeffrey Humpherys, Tyler J. Jarvis
- Foundations of Computation, Carol Critchlow, David Eck
- Foundations of Data Science, Avrim Blum, John Hopcroft, Ravindran Kannan
- Graph Theory, Reinhard Diestel
- Graph Theory, Christopher Griffin
- Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein
- Mathematical Methods for Computer Vision, Robotics, and Graphics, Justin Solomon
- Mathematics for Computer Science, Eric Lehman, F. Thomson Leighton, Albert R. Meyer
- Open Data Structures, Pat Morin
- Scientific Computing, Jeffrey R. Chasnov
Calculus and real analysis
- Active Calculus: Single Variable, Matthew Boelkins, David Austin, Christina Safranski, Steven Schlicker
- Advanced Calculus, Lynn H. Loomis, Shlomo Sternberg
- Analysis of Functions of a Single Variable, Lawrence W. Baggett
- Basic Real Analysis, Anthony W. Knapp
- Calculus, Michael Spivak
- Calculus, Gilbert Strang
- Calculus in Context, James Callahan, David Cox, Kenneth Hoffman, Donal O’Shea, Harriet Pollatsek, Lester Senechal
- Calculus: Early Transcendentals, David Guichard
- Elementary Calculus: An Infinitesimal Approach, H. Jerome Keisler
- Honors Calculus, Pete L. Clark
- Integral Calculus: Mathematics 103, Leah Edelstein-Keshet
- Introduction to Analysis, John K. Hunter
- An Introduction to Measure Theory, Terence Tao
- Introduction to Real Analysis, Jiří Lebl
- Lecture Notes in Calculus I, Jakob Streipel
- Lecture Notes on Mathematical Analysis, Hsuan-Yi Liao
- Measure, Integration & Real Analysis, Sheldon Axler
- Methods of Real Analysis, Richard R. Goldberg
- Univariate Real Analysis, Martin Klazar
Complex analysis
- Complex Variables, Robert B. Ash, W. P. Novinger
- A First Course in Complex Analysis, Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
- Visual Complex Analysis, Tristan Needham
Foundations and general references
- Algebra, Topology, Differential Calculus, and Optimization Theory for Computer Science and Machine Learning, Jean Gallier, Jocelyn Quaintance
- The Architecture of Mathematics, Nicholas Bourbaki
- Book of Proof, Richard Hammack
- Everything You Always Wanted to Know About Mathematics (But Didn’t Even Know to Ask), Brendan W. Sullivan
- Handbook of Mathematical Functions, Milton Abramowitz, Irene A. Stegun
- An Introduction to Formal Logic, Richard Zach
- Introduction to University Mathematics, James Munro
- Klotz Online Math Notes, Richard G. Klotz
- Maths 1, Andrew Rees
- The Princeton Companion to Mathematics, Timothy Gowers, June Barrow-Green, Imre Leader
- Proofs and Concepts, Dave Witte Morris, Joy Morris
- Pure Mathematics, Stuart Parsonson
Geometry
- Analytic Geometry, Lewis Parker Siceloff, George Wentworth, David Eugene Smith
- Beginning in Algebraic Geometry, Emily Clader, Dustin Ross
- Differential Geometry: From Elastic Curves to Willmore Surfaces, Ulrich Pinkall, Oliver Gross
- Elementary Geometry from an Advanced Standpoint, Edwin E. Moise
- Plane Geometry, George Wentworth, David E. Smith
- The Rising Sea: Foundations of Algebraic Geometry, Ravi Vakil
- Trigonometry, Michael Corral
Linear algebra
- Advanced Linear Algebra, Steven Roman
- Fundamentals of Linear Algebra, James B. Carrell
- Fundamentals of Matrix Algebra, Gregory Hartman
- Introduction to Applied Linear Algebra, Stephen Boyd, Lieven Vandenberghe
- Introduction to Vectors and Tensors, Ray M. Bowen, C.-C. Wang
- Linear Algebra, Jim Hefferon
- Linear Algebra, David Cherney, Tom Denton, Rohit Thomas, Andrew Waldron
- Linear Algebra as an Introduction to Abstract Mathematics, Isaiah Lankham, Bruno Nachtergaele, Anne Schilling
- Linear Algebra Done Right, Sheldon Axler
- Linear Algebra Done Wrong, Sergei Treil
- Linear Algebra for Computer Science, Manoj Thulasidas
- Linear Algebra with Applications, W. Keith Nicholson
- Matrix Calculus for Machine Learning and Beyond, Paige Bright, Alan Edelman, Steven G. Johnson
Machine learning and artificial intelligence
- Algorithms for Decision Making, Mykel J. Kochenderfer, Tim A. Wheeler, Kyle H. Wray
- Artificial Intelligence: A Modern Approach, Stuart Russell, Peter Norvig
- Computing Neural Network Gradients, Kevin Clark
- Dive into Deep Learning, Aston Zhang, Zachary C. Lipton, Mu Li, Alexander J. Smola
- Foundations of Large Language Models, Tong Xiao, Jingbo Zhu
- Foundations of Machine Learning, Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar
- Information Theory, Inference, and Learning Algorithms, David J. C. MacKay
- An Introduction to Flow Matching and Diffusion Models, Peter Holderrieth, Ezra Erives
- The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer, Tianhua Chen
- Machine Learning Systems, Volume I: Foundations, Vijay Janapa Reddi
- Machine Learning Systems, Volume II: At Scale, Vijay Janapa Reddi
- Mathematical and Statistical Foundations of AI, Saman Siadati
- Mathematical Foundations of Deep Learning, Xiaojing Ye
- Mathematical Theory of Deep Learning, Philipp Petersen, Jakob Zech
- Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong
- Mathematics of Neural Networks, Bart M. N. Smets
- Pattern Recognition and Machine Learning, Christopher M. Bishop
- Patterns, Predictions, and Actions, Moritz Hardt, Benjamin Recht
- Transformers, Daniel Jurafsky, James H. Martin
- Understanding Deep Learning, Simon J. D. Prince
- Understanding Machine Learning: From Theory to Algorithms, Shai Shalev-Shwartz, Shai Ben-David
Mathematical physics
- Classical Mechanics, Joel A. Shapiro
- Lectures on Classical Dynamics, David Tong
- Mathematical Methods for Physics, Niels Walet
- Mathematics for Physics, Michael Stone, Paul Goldbart
Optimization
- Algorithms for Optimization, Mykel J. Kochenderfer, Tim A. Wheeler
- Branch-and-Price, Jacques Desrosiers, Marco Lübbecke, Guy Desaulniers, Jean Bertrand Gauthier
- Convex Optimization, Stephen Boyd, Lieven Vandenberghe
- Convex Optimization: Algorithms and Complexity, Sébastien Bubeck
- Convex Optimization: EE227BT Lecture Notes, Laurent El Ghaoui
- A First Course in Optimization, Charles L. Byrne
- Introduction to Online Convex Optimization, Elad Hazan
- Introduction to Optimization, Roland Herzog
- An Introduction to Optimization Algorithms, Thomas Weise
- Introduction to Stochastic Gradient Methods, Simon Weissmann
- Lecture Notes on Numerical Optimization, Miguel Á. Carreira-Perpiñán
- Lectures on Modern Convex Optimization, Aharon Ben-Tal, Arkadi Nemirovski
- A Modern Introduction to Online Learning, Francesco Orabona
- Optimization: Principles and Algorithms, Michel Bierlaire
Ordinary differential equations
- Differential Equations I, Paul Selick
- Elementary Differential Equations, William F. Trench
- Notes on Diffy Qs, Jiří Lebl
Probability and statistics
- The Elements of Statistical Learning, Trevor Hastie, Robert Tibshirani, Jerome Friedman
- High-Dimensional Probability: An Introduction with Applications in Data Science, Roman Vershynin
- Introduction to Probability, Charles M. Grinstead, J. Laurie Snell
- Introduction to Probability, Joseph K. Blitzstein, Jessica Hwang
- Introduction to Probability, Dimitri P. Bertsekas, John N. Tsitsiklis
- An Introduction to Statistical Learning, Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
- Lecture Notes on Probability, Statistics and Linear Algebra, C. H. Taubes
- Probability and Statistics: The Science of Uncertainty, Michael J. Evans, Jeffrey S. Rosenthal
- Probability on Trees and Networks, Russell Lyons, Yuval Peres
Topology
- Algebraic Topology, Allen Hatcher
- A Concise Course in Algebraic Topology, J. P. May
- Topology Without Tears, Sidney A. Morris