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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.

Math

Basic Algebra

Algebra -- Gelfand and Shen

Geometry

Planiometry -- Kiselev

Linear Algebra

Finite Dimensional Vector Spaces -- Halmos

Calculus

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

Combinatorics

 

Algebraic Topology

 

Algebraic Geometry

Algebraic Geometry -- Hartshorne

RepresentationTheory

Representations of Finite Groups -- Serre

Manifolds

An Introduction to Manifolds -- Tu

Probability Theory

A First Course in Probability Theory -- Ross

Numerical Methods

 

Partial Differential Equations

Partial Differential Equations -- Evans

Topoi

Topoi: The Categorical Analysis of Logic -- Goldblatt

Category Theory

Categories for the Working Mathematician -- Mac Lane

Physics

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

Relativity

Spacetime Physics -- Taylor and Wheeler

Particle Physics

Introduction to Elementary Particles -- Griffiths

Condensed Matter

Solid State Physics -- Ashcroft & Mermin

Optics

Optics -- Hecht

Atomic

 

Statistics

Introduction to Statistics

 

Methods

 

Mathematical Statistics

Mathematical Statistics with Applications -- Wackerly

Regression

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

Causation -- Pearl

Computer Science

Introduction to Computer Science

 

Functional Programming

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

Algorithms

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

Computer Architecture

Structured Computer Organization -- Tannenbaum

Networks

Computer Networks -- Tanenbaum and Wetherall

Databases

An Introduction to Database Systems -- Date

Automata and Languages

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

Compilers

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

Computability

Introduction to the Theory of Computation -- Sipser

Distributed Systems

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

Graphics

Fundamentals of Computer Graphics -- Shirley and Marschner

Information Theory

Information Theory -- Cover and Thomas

Cryptography

Cryptography Engineering -- Schneier

Lambda Calculus

Lambda Calculi: A Guide for Computer Scientists -- Hankin

Logic

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

Computability

Introduction to the Theory of Computation -- Sipser

 

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