Textbook Recommendations

Mathematics

1. Mathematics: A Very Short Introduction by Timothy Gowers.
2. Fundamentals of Mathematics by Moses Richardson
3. Euler: Master of Us All by William Dunham
4. Journey through Genius: The Great Theorems of Mathematics by William Dunham
5. What Is Mathematics? An Elementary Approach to Ideas and Methods by Richard Courant and Herbert Robbins
6. Linear Algebra and Its Applications by Gilbert Strang
7. Riemann’s Zeta Function by Harold Edwards
8. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire
9. Nonlinear Dynamics and Chaos by Steven Strogatz
10. The Riemann Zeta-Function: Theory and Applications by Aleksandar Ivic
11. Complex Variables and Applications by James Brown and Ruel Churchill
12. Advanced Engineering Mathematics by Michael Greenberg
13. Real and Complex Analysis by Walter Rudin
14. Principles of Mathematical Analysis by Walter Rudin
15. The Princeton Companion to Mathematics by Timothy Gowers. An outstanding resource.
16. The Calculus Gallery by William Dunham
17. Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland
18. Partial Differential Equations: Methods and Applications by Robert McOwen
19. Complex Analysis by Lars Ahlfors
20. Partial Differential Equations by Lawrence C. Evans
21. Elliptic Partial Differential Equations by Qing Han and Fanghua Lin
22. Elliptic Partial Differential Equations of Second Order by David Gilbarg and Neil S. Trudinger
23. Functional Analysis by Peter D. Lax
24. Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis
25. Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory by Bender and Orszag
26. Ordinary Differential Equations and Dynamical Systems by Gerald Teschl
27. Differential Equations- A Dynamical Systems Approach by John H. Hubbard and Beverly H. West
28. Measure, Integration & Real Analysis by Sheldon Axler
29. Linear Alebra Done Right by Sheldon Axler
30. Applied Linear Algebra by Peter J. Olver and Chehrzad Shakiban

Computational Mathematics

1. An Introduction to Numerical Methods and Analysis by James Epperson
2. Finite Difference Methods for Ordinary and Partial Differential Equations by Randall LeVeque.
3. Numerical Methods for Conservation Laws by Randall LeVeque by Randall LeVeque.
4. Understanding And Implementing the Finite Element Method by Mark S. Gockenbach
5. Numerical Linear Algebra by Lloyd N. Trefethen
6. Approximation Theory and Approximation Practice by Lloyd N. Trefethen
7. Spectral Methods in MATLAB by Lloyd Trefethen
8. Introduction to High Performance Computing for Scientists and Engineers by Georg Hager and Gerhard Wellein
9. Scientific Parallel Computing by L. Ridgway Scott
10. Scientific Computing: An Introductory Survey by Michael T. Heath
11. A Computational Introduction to Number Theory and Algebra by Victor Shoup
12. Introduction to the Theory of Computation by Michael Sipser
13. Computational Complexity: A Modern Approach by Sanjeev Arora and Boaz Barak
14. Computational Science and Engineering by Gilbert Strang

Astronomy and Physics

1. Introduction to Electrodynamics by David J. Griffiths
2. Introduction to Quantum Mechanics by David J. Griffiths
3. Classical Mechanics by John R. Taylor
4. Introduction to Classical Mechanics by David Morin
5. Modern Quantum Mechanics by J.J. Sakurai
6. Numerical Methods for Physics by Alejandro Garcia
7. Optics by Eugene Hecht
8. Statistical Physics of Particles by Mehran Kardar
9. Thermal Physics by Daniel V. Schroeder
10. Cosmic Queries: StarTalk’s Guide to Who We Are, How We Got Here, and Where We’re Going by Neil Degrasse Tyson
11. Smithsonian Handbook: Stars and Planets by Ian Ridpath
12. Universe: The Definitive Visual Guide by Smithsonian

Statistics

1. Statistical Inference by George Casella and Roger L. Berger
2. Mathematical Statistics by Bickel and Berger
3. Statistical Models: Theory and Practice by David A. Freedman
4. An Introduction to Stochastic Differential Equations by Lawrence C. Evans
5. Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li
6. Time Series Analysis and Its Applications by Shumway and Stoffer
7. Computational Statistics by Givens and Hoeting

Fluid Mechanics

1. Elementary Fluid Dynamics by D. J. Acheson
2. Wave Motion by J. Billingham and A. C. King
3. Mathematical Theory of Compressible Fluid Flow by Richard von Mises
4. Introduction to Mathematical Fluid Dynamics by R.E. Meyer.
5. A Mathematical Introduction to Fluid Mechanics by A.J. Chorin and J.E. Marsden
6. Turbulent Flows by Stephen B. Pope
7. Elements of Gasdynamics by Liepmann and Roshko
8. Transport Phenomena by Bird, Stewart, and Lightfoot

Data Science and Machine Learning

1. Data Science from Scratch by Joel Grus
2. Deep Learning with Python by François Chollet
3. Understanding Machine Learning: From Theory to Algorithms by Shai Shalev-Shwartz and Shai Ben-David
4. Hands-On Machine Learning with Scikit-Learn, Keras and TensorFlow by Aurélien Géron
5. Pattern Recognition and Machine Learning by Bishop
6. High-Dimensional Probability: An Introduction with Applications in Data Science by Roman Vershynin
7. Artificial Intelligence: A Modern Approach by Stuart Russell and Peter Norvig
8. The Craft of Research by Booth, Colomb, and Williams
9. Mining of Massive Datasets by Leskovec, Rajaraman, and Ullman
10. The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Hastie, Tibshirani, and Friedman

Related Subjects

1. The Cuckoo’s Egg: Tracking a Spy Through the Maze of Computer Espionage by Cliff Stoll
2. Ender’s Game Saga by Orson Scott Card
3. The Hobbit and Lord of the Rings by J.R.R. Tolkien
4. Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R Hofstadter

Authors Whose Textbooks I Like

1. Lloyd N. Trefethen
2. Gilbert Strang
3. Lawrence C. Evans
4. Randall J. LeVeque
5. Sheldon Axler
6. The Math Sorceror