Curated resources for mathematics, physics, computer science. See tree, misc, suggested/math, suggested/cs, ramanujan.

📚 Learning

• Learning How to Learn — Alistair McConville, Barbara Oakley, Terrence Sejnowski
• How to Study Math — Paul Dawkins — site
• How to Solve It — George Pólya
• Art of Doing Science and Engineering — Richard Hamming, Bret Victor

🧮 Mathematics

Foundations

• The Joy Of X — Steven Strogatz
• A Mathematician's Lament — Paul Lockhart
• Letters to a Young Mathematician — Ian Stewart
• Project Mathematics — Tom M. Apostol
• Gateways to Mathematics — Herbert I. Gross — site
• Introduction to Mathematical Thinking — Keith Devlin
• How to Think Like a Mathematician — Kevin Houston
• Precalculus — Israel Gelfand — book video
• Measurement — Paul Lockhart
• Elements of Mathematics: From Euclid to Gödel — John Stillwell
• Mathematics and its History — John Stillwell

Proofs

• Book of Proof — Richard Hammack
• Proofs from THE BOOK — Martin Aigner, Günter M. Ziegler

Calculus

• What Is Calculus About? — Walter Sawyer
• Calculus Made Easy — Martin Gardner, Silvanus P. Thompson
• Infinite Powers — Steven Strogatz
• The Essence of Calculus — Grant Sanderson
• Calculus: An Intuitive and Physical Approach — Morris Kline
• Calculus Revisited — Herbert Gross
• MIT Highlights of Calculus — Gilbert Strang
• Calculus with Analytic Geometry — George F. Simmons — video
• Differential and Integral Calculus — Richard Courant
• Calculus — Michael Spivak

Linear Algebra

• The Essence of Linear Algebra — Grant Sanderson
• Linear Algebra: Step by Step — Kuldeep Singh
• Introduction to Applied Linear Algebra — Stephen Boyd, Lieven Vandenberghe
• Lectures on Linear Algebra — Israel Gelfand
• Linear Algebra Done Right — Sheldon Axler
• Linear Algebra Problem Book — Paul Halmos
• Finite-Dimensional Vector Spaces — Paul Halmos

Differential Equations

• Ordinary Differential Equations — Harry Pollard, Morris Tenenbaum
• Ordinary Differential Equations — Vladimir Arnold

Discrete Math & Combinatorics

• Discrete Mathematics and Its Applications — Kenneth H. Rosen — video
• Principles and Techniques in Combinatorics — Chen Chuan-Chong, Koh Khee-Meng
• Concrete Mathematics — Ronald Graham, Donald Knuth, Oren Patashnik
• Generatingfunctionology — Herbert Wilf

Probability & Statistics

• Introduction to Probability — Joseph K. Blitzstein, Jessica Hwang — video

Real Analysis

• Understanding Analysis — Stephen Abbott
• Principles of Mathematical Analysis — Walter Rudin
• Real Mathematical Analysis — Charles C. Pugh
• Princeton Lectures in Analysis (4 vols) — Elias M. Stein, Rami Shakarchi

Complex Analysis

• Visual Complex Analysis — Tristan Needham
• Complex Variables and Applications — James Ward Brown, Ruel V. Churchill

Functional Analysis

• Introductory Functional Analysis with Applications — Erwin Kreyszig

Abstract Algebra

• Algebra — Michael Artin
• Abstract Algebra — David S. Dummit, Richard M. Foote
• Algebra: Chapter 0 — Paolo Aluffi

Number Theory

• The Higher Arithmetic — Harold Davenport
• An Introduction to the Theory of Numbers — G.H. Hardy, E.M. Wright
• Introduction to Analytic Number Theory — Tom Apostol
• An Introduction to the Circle Method — M. Ram Murty
• Number Theory in the Spirit of Ramanujan — Bruce Berndt
• Hilbert's Tenth Problem — M. Ram Murty, Brandon Fodden

Topology

• Topology Illustrated — Peter Saveliev
• Topology — James Munkres

Differential Geometry

• Visual Differential Geometry and Forms — Tristan Needham

Problem Solving

• Mathematical Circles: Russian Experience — Dmitri Fomin, Sergey Genkin, Ilia Itenberg
• The Art and Craft of Problem Solving — Paul Zeitz

General

• The Princeton Companion to Mathematics — Timothy Gowers
• The Princeton Companion to Applied Mathematics — Nicholas J. Higham
• Mathematics: Its Content, Methods and Meaning — Andrey N. Kolmogorov
• What Is Mathematics? — Richard Courant
• Vector Calculus, Linear Algebra, and Differential Forms — Barbara Burke Hubbard, John H. Hubbard
• An Infinitely Large Napkin — Evan Chen — book
• The Art of Insight in Science and Engineering — Sanjoy Mahajan
• Euler's Pioneering Equation — Robin Wilson

History

• Mathematical Thought from Ancient to Modern Times — Morris Kline
• Prime Obsession — John Derbyshire
• The Story of Proof — John Stillwell
• The Crest of the Peacock — George Joseph
• An Imaginary Tale: The Story of √−1 — Paul Nahin
• Non-Euclidean Geometry — Roberto Bonola

🍎 Physics

Foundations

• Why Is It So? — Julius Sumner Miller
• Conceptual Physics — Paul G. Hewitt
• For the Love of Physics — Walter Lewin
• Understanding Physics — Isaac Asimov
• Six Easy Pieces — Richard Feynman
• The Character of Physical Laws — Richard Feynman
• The Mechanical Universe — David Goodstein
• Mathematics and the Physical World — Morris Kline
• Teach Yourself Physics — Jakob Schwichtenberg
• Fundamentals of Physics — Ramamurti Shankar

Intermediate

• Six Not-So-Easy Pieces — Richard Feynman
• An Introduction to Mechanics — Daniel Kleppner, Robert Kolenkow
• Introduction to Electrodynamics — David J. Griffiths
• Introduction to Quantum Mechanics — David J. Griffiths
• An Introduction to Thermal Physics — Daniel V. Schroeder
• Classical Mechanics — IIT Madras
• Quantum Mechanics — IIT Madras

Advanced

• Theoretical Minimum — Leonard Susskind — site
• The Feynman Lectures on Physics — Richard Feynman, Robert B. Leighton, Matthew Sands
• The Variational Principles of Mechanics — Cornelius Lanczos
• Course of Theoretical Physics — Vladimir Berestetskii, Lev Landau, Evgeny Lifshitz, Lev Pitaevskii
• The Road to Reality — Roger Penrose
• The Emperor's New Mind — Roger Penrose
• Truth and Beauty — Subrahmanyan Chandrasekhar
• The Relation Between Mathematics and Physics — Paul Dirac
• The Principia — Isaac Newton

🖥️ Computer Science

Foundations

• Code — Charles Petzold
• Computer Science: An Interdisciplinary Approach — Robert Sedgewick, Kevin Wayne
• The Elements of Computing Systems — Noam Nisan, Shimon Schocken
• Structure and Interpretation of Computer Programs — Harold Abelson, Gerald Jay Sussman — video

Computer Architecture

• Computer Organization and Design — David A. Patterson, John L. Hennessy
• Computer Architecture: A Quantitative Approach — John L. Hennessy, David A. Patterson

Algorithms & Data Structures

• Algorithms and Data Structures — Niklaus Wirth
• Introduction to Algorithms — Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein — video
• The Art of Computer Programming — Donald Knuth

Theory of Computation

• Gödel, Escher, Bach — Douglas Hofstadter
• Feynman Lectures on Computation — Richard P. Feynman
• Introduction to Theoretical Computer Science — Boaz Barak
• Introduction to the Theory of Computation — Michael Sipser — video
• Computation: Finite and Infinite Machines — Marvin Minsky
• The Nature of Computation — Cristopher Moore, Stephan Mertens

Information Theory

• Information Theory: A Tutorial Introduction — James Stone
• Information Theory, Inference, and Learning Algorithms — David J.C. MacKay

Cryptography

• Understanding Cryptography — Christof Paar
• Introduction to Modern Cryptography — Jonathan Katz, Yehuda Lindell

Programming Languages

• The Little Schemer — Daniel P. Friedman, Matthias Felleisen
• Programming Language Pragmatics — Michael L. Scott — video
• Concepts, Techniques, and Models of Computer Programming — Peter Van Roy, Seif Haridi
• Types and Programming Languages — Benjamin C. Pierce

Compilers

• Crafting Interpreters — Robert Nystrom — book
• Compilers: Principles, Techniques, and Tools — Alfred V. Aho, Monica S. Lam, Ravi Sethi, Jeffrey D. Ullman — video

Systems

• The Unix Programming Environment — Brian W. Kernighan, Rob Pike
• Computer Systems: A Programmer's Perspective — Randal E. Bryant, David R. O'Hallaron — video
• Operating Systems: Three Easy Pieces — Andrea C. Arpaci-Dusseau, Remzi H. Arpaci-Dusseau — video
• Advanced Programming in the Unix Environment — W. Richard Stevens
• The Design of the Unix Operating System — Maurice J. Bach
• Computer Networks: A Systems Approach — Bruce S. Davie, Larry L. Peterson — video
• Project Oberon — Niklaus Wirth
• Plan 9
• Suckless

Concurrency

• The Art of Multiprocessor Programming — Maurice Herlihy, Nir Shavit

Databases

• Database System Concepts — Henry F. Korth, Abraham Silberschatz, S. Sudarshan — video
• Readings in Database Systems — Michael Stonebraker

Distributed Systems

• Designing Data-Intensive Applications — Martin Kleppmann
• Distributed Systems — Andrew S. Tanenbaum, Maarten Van Steen

AI & Machine Learning

• Artificial Intelligence: A Guide for Thinking Humans — Melanie Mitchell
• Neural Networks — Grant Sanderson
• Machine Learning — Andrew Ng
• Understanding Deep Learning — Simon J.D. Prince — book
• Artificial Intelligence: A Modern Approach — Peter Norvig, Stuart Russell
• Pattern Recognition and Machine Learning — Christopher Bishop
• Deep Learning — Yoshua Bengio, Aaron Courville, Ian Goodfellow

Graphics

• Fundamentals of Computer Graphics — Steve Marschner, Peter Shirley

Software Engineering

• The Mythical Man-Month — Frederick P. Brooks Jr.
• The Pragmatic Programmer — Andrew Hunt, David Thomas
• The Practice of Programming — Brian W. Kernighan, Rob Pike
• Programming Pearls — Jon Bentley
• A Philosophy of Software Design — John Ousterhout
• Systematic Programming — Niklaus Wirth
• A Discipline of Programming — Edsger W. Dijkstra
• The PhD Grind — Philip Guo

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Many titles are published by:

• AMS Student Mathematical Library
• Cambridge University Press
• Dover Publications
• MIT Press
• Princeton University Press

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