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The classics

Here are books that I (and others) deem to be "classics" for their respective fields.  If I'm missing one, please let me know!  I'm trying to keep the lists somewhat sparse, and I'm shooting from the hip when it comes to deciding which classics get on the list--it's some murky combination of popularity among professionals, personal enjoyment, rigor, the extent to which a "style" or "approach" is commonplace, and probably other stuff that I can't even identify in my psyche.  Also, I generally have in mind introductory undergraduate courses.


Basic Algebra

Algebra -- Gelfand and Shen


Planiometry -- Kiselev

Linear Algebra

Finite Dimensional Vector Spaces -- Halmos


Calculus -- Spivak

Differential Equations

Elementary Differential Equations -- Boyce and DiPrima

discrete mathematics

Discrete Mathematics with Applications -- Epp

symbolic logic

Introduction to Logic -- Suppes

Real analysis

Principles of Mathematical Analysis -- Rudin

Abstract Algebra

Topics in Algebra -- Herstein

General topology

Topology -- Munkres

Set Theory

Elements of Set Theory -- Enderton

Mathematical Logic

Mathematical Logic -- Mendelson

Graph Theory

Introduction to Graph Theory -- West

Complex Analysis

Complex Analysis -- Stein and Sakarichi

Riemannian Geometry

An Introduction to Riemannian Geometry -- do Carmo

Number Theory

A Classical Introduction to Modern Number Theory -- Ireland and Rosen

Mathematical Statistics

All of Statistics -- Wasserman

Math for Physics

Mathematical Methods in the Physical Sciences -- Boas



Algebraic Topology


Algebraic Geometry

Algebraic Geometry -- Hartshorne


Representations of Finite Groups -- Serre


An Introduction to Manifolds -- Tu

Probability Theory

A First Course in Probability Theory -- Ross

Numerical Methods


Partial Differential Equations

Partial Differential Equations -- Evans


Topoi: The Categorical Analysis of Logic -- Goldblatt

Category Theory

Categories for the Working Mathematician -- Mac Lane


Introductory physics

The Fundamentals of Physics -- Halliday and Resnick

Classical mechanics

Classical Mechanics -- Goldstein

Electricity and magnetism

Introduction to Electrodynamics -- Griffiths

Quantum Mechanics

Introduction to Quantum Mechanics -- Griffiths

Statistical Mechanics and Thermal Physics

An Introduction to Thermal Physics -- Schroeder


Spacetime Physics -- Taylor and Wheeler

Particle Physics

Introduction to Elementary Particles -- Griffiths

Condensed Matter

Solid State Physics -- Ashcroft & Mermin


Optics -- Hecht




Introduction to Statistics




Mathematical Statistics

Mathematical Statistics with Applications -- Wackerly


Applied Linear and Statistical Models -- Kutner, NachtSheim, Neter, Li

Stochastic Processes

Statistical Models Based on Counting Processes -- Andersen, Borgan, Gill, Keiding

Computing with Data


Survey and Experiment Design


Time Series

Time Series Analysis: Forecasting and Control -- Box and Jenkins

Probability Theory

A First Course in Probability Theory -- Ross

Bayesian Statistics

Doing Bayesian Data Analysis -- Kruschke

Nonparametric Statistics

Practical Nonparametric Statistics -- Conover


Causation -- Pearl

Computer Science

Introduction to Computer Science


Functional Programming

Structure and Interpretation of Computer Programs -- Abelson, Sussman, Sussman


Introduction to Algorithms -- Cormen, Leiserson, Rivest, Stein

Computer Architecture

Structured Computer Organization -- Tannenbaum


Computer Networks -- Tanenbaum and Wetherall


An Introduction to Database Systems -- Date

Automata and Languages

Introduction to Automata Theory, Languages, and Computation -- Hopcroft, Motwani, Ullman


Compilers: Principles, Techniques, and Tools -- Aho, Lam, Sethi, Ullman

Operating Systems

Operating System Design and Implementation -- Tanenbaum

Machine Learning

The Elements of Statistical Learning: Data Mining, Inference, and Prediction -- Hastie, Tibshriani, Friedman


Introduction to the Theory of Computation -- Sipser

Distributed Systems

Distributed Systems: Concepts and Design -- Dollimore, Coulouris, Kindberg, Blair


Fundamentals of Computer Graphics -- Shirley and Marschner

Information Theory

Information Theory -- Cover and Thomas


Cryptography Engineering -- Schneier

Lambda Calculus

Lambda Calculi: A Guide for Computer Scientists -- Hankin


Introduction to Symbolic Logic

Introduction to Logic -- Suppes

Non-Classical Logic

Introduction to Non-classical Logic -- Priest

Mathematical Logic

A Mathematical Introduction to Logic -- Enderton

Modal Logic

First-order Modal Logic -- Mendelson

Proof Theory

Model Theory

Model Theory: An Introduction -- Marker

Recursion Theory


Introduction to the Theory of Computation -- Sipser


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