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- Suggested Books by Subject

# Mathematics : Suggested Books by Subject

## About the Book Lists

The following are suggested readings in the main areas within mathematics. The books listed as **establishing texts** are meant to give readers new to a subject area a sense breadth of a subject and the fundamental results therein. The books listed as **further reading** are for those ready to really dive in and go deep on a topic. Any book marked with a ***** is suggested reading for the Mathematics Department's Qualifying Exams.

## Subjects

- Algebra
- Analysis
- Applied Mathematics
- Combinatorics
- Computational Mathematics
- Geometry & Topology
- Logic
- Number Theory

Establishing Texts:

Contemporary abstract algebra - Gallian

A survey of modern algebra - Birkhoff

Linear algebra and its applications - Strang

Linear algebra - Hoffman and Kunze*

Deeper Reading:

Abstract algebra - Dummit

Galois theory - Artin*

Algebra : a graduate course - Isaacs*

Algebra - Hungerford*

An introduction to the theory of groups - Rotman*

Establishing Texts:

Introduction to calculus and analysis - Courant

Complex variables and applications - Churchill

Mathematical analysis : an introduction - Browder

Mathematical analysis - Apostol

Invitation to complex analysis - Boas

Deeper Reading:

Complex analysis, an introduction to the theory of analytic functions of one complex variable - Ahlfors*

Real analysis : modern techniques and their applications - Folland*

Complex analysis - Gamelin*

Real analysis - Royden*

Principles of mathematical analysis - Rudin*

Real and complex analysis - Rudin*

Real analysis : measure theory, integration, and Hilbert spaces - Stein & Shakarchi*

Complex analysis - Stein & Shakarchi*

Establishing Texts:

Differential equations : a dynamical systems approach - Strang*

Basic partial differential equations - Bleecker

Boundary value problems - Gahkov

Further Reading:

Fourier series and boundary value problems - Churchill*

Calculus of variations - Gelfand & Fomin*

Partial differential equations : analytical solution techniques - Kevorkian*

Complex variables - Levinson & Redheffer*

Partial differential equations and boundary-value problems with applications - Pinsky*

Green’s functions and boundary value problems - Stakgold*

Partial differential equations of applied mathematics - Zauderer*

Establishing Texts:

Principles and techniques in combinatorics - Chen

Combinatorics and graph theory - Harris

Foundations of applied combinatorics - Bender

Graphs & digraphs - Chartrand

Graph theory : an introductory course - Bollobás

Further Reading:

Enumerative combinatorics. Volume 1 - Stanley

Graph theory - Tutte

Spectral graph theory - Chung

Random graphs - Bollobás

Ramsey theory - Graham, Rothschild, & Spencer

Handbook of combinatorics - Graham, Grötschel, & Lovász

Probabilistic methods in combinatorics - Erdös & Spencer

Establishing Texts:

Introduction to algorithms - Cormen, Leiserson, Rivest, & Stein

A friendly introduction to numerical analysis - Bradie*

Numerical analysis - Burden & Faires

Further Reading:

The art of computer programming - Knuth

Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems - LeVeque*

Finite difference schemes and partial differential equations - Strikwerda*

Spectral methods in MATLAB - Trefethen*

A practical guide to pseudospectral methods - Fornberg*

Finite volume methods for hyperbolic problems - LeVeque*

Computational differential equations - Eriksson, Estep, Hansbo, & C. Johnson*

Finite Element Methods and Their Applications - Chen*

Monte Carlo methods - Kalos & Whitlock*

Establishing Texts:

An invitation to algebraic geometry - Smith

Conics and cubics : a concrete introduction to algebraic curves - Bix

The shape of space : how to visualize surfaces and three-dimensional manifolds - Weeks

Basic topology - Armstrong

The four pillars of geometry - Stillwell

Topology - Munkres

Further Reading:

Topology and geometry - Bredon*

Differential topology - Guillemin and Pollack*

Algebraic topology - Hatcher*

Homology theory : an introduction to algebraic topology - Vick*

A comprehensive introduction to differential geometry. Volume 1 - Spivak*

Establishing Texts:

A mathematical introduction to logic - Enderton

Classic set theory : a guided independent study - Goldrei

Further Reading:

Categories for the working mathematician - Mac Lane

Mathematical logic - Ebbinghaus, Flum, & Thomas*

Mathematical logic - Shoenfield*

Set theory - Kunen*

Recursively enumerable sets and degrees : a study of computable functions and computably generated sets - Soare*

Theory of recursive functions and effective computability - Rogers*

Set theory - Kunen*

Set theory - Jech*

Model theory - Chang & Keisler*

Model theory : an introduction - Marker*

Establishing Texts:

The higher arithmetic : an introduction to the theory of numbers - Davenport

An introduction to the theory of numbers - Hardy & Wright

Higher mathematics from an elementary point of view - Rademacher

The beauty of doing mathematics : three public dialogues - Lang

Further Reading

Algebraic number theory - Lang

Elliptic curves - Knapp

Topics in analytic number theory - Rademacher

Chapter 1 From number theory to physics: An introduction to zeta functions - Cartier

Modular functions and Dirichlet series in number theory - Apostol

The theory of partitions - Andrews