Skip to Main Content

Mathematics : Preparing for Quals

About the Book Lists

On this page are suggested readings in the main areas within mathematics.

Establishing texts are meant to give readers new to a subject area a sense breadth of a subject and the fundamental results therein.

Further reading are for those ready to really dive in and go deep on a topic.

Suggested reading for the Mathematics Department's Qualifying Exams are exactly that.

Guide for Topics for Math Qualifying Exams
Describes the format and scope of the qualifying exams for the Department of Mathematics, plus references and suggested reading lists.
Mathematics Course & Qualifying Exams
Course and qualifying exams selected by the department for wider distribution. Solutions are typically not available.

Algebra

Suggested Reading for Qualifying Exams

Introduction to Commutative Algebra by Michael Atiyah
Call Number: QA251 A8
Abstract Algebra by David S. Dummit; Richard M. Foote
Call Number: QA162 D85 2004

Establishing Texts

Contemporary Abstract Algebra by Joseph Gallian
Call Number: QA162 G34 2013
A Survey of Modern Algebra by Garrett D. Birkhoff
Call Number: QA162 B57 1977
Linear Algebra and Its Applications by Gilbert Strang
Call Number: QA184 S8 1988
Linear Algebra by Kenneth Hoffman; Ray Kunze
Call Number: QA251 H67 1971

Deeper Reading

Galois Theory by Emil Artin
Call Number: QA214 A77 1998
Algebra by Thomas W. Hungerford
Call Number: QA155 H83 1974
Algebra: A Graduate Course by I. Martin Isaacs
Call Number: LH 7G72 S92 v.100
An Introduction to the Theory of Groups by Joseph J. Rotman
Call Number: QA171 R67 1995

Analysis

Suggested Reading for Qualifying Exams

Functions of One Complex Variable I by John B. Conway
Call Number: QA331 C659 1978
Functions of One Complex Variable II by John B. Conway
Call Number: QA331 C659 1995
Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland
Call Number: QA300 F67 1999

Also available online.
Complex Analysis by Theodore Gamelin
Call Number: QA300 G25 2001

Also available online.
Function Theory of One Complex Variable by Robert E. Greene; Steven G. Krantz
Call Number: LH 7G72 S92 v.40 2006
Functional Analysis by Walter Rudin
Call Number: QA320 R83 1991
Real and Complex Analysis by Walter Rudin
Call Number: QA300 R82 1987
Complex Analysis by Elias M. Stein; Rami Shakarchi
Call Number: QA331 S74 2003

Also available online.
Functional Analysis by Elias M. Stein; Rami Shakarchi
Call Number: QA320 S839 2011

Also available online.
Real Analysis by Elias M. Stein; Rami Shakarchi
Call Number: QA320 S74 2005

Also available online.

Establishing Texts

Introduction to Calculus and Analysis by Richard Courant
Call Number: QA303 C85
Complex Variables and Applications by Ruel V. Churchill
Call Number: QA331 C524 1974
Mathematical Analysis by Andrew Browder
Call Number: QA300 B727 1996
Mathematical Analysis by Tom Apostol
Call Number: QA300 A6 1974
Invitation to Complex Analysis by Ralph P. Boas
Call Number: QA331 B644 2010

Also available online.

Applied Mathematics

Suggested Reading for Qualifying Exams

Advanced Mathematical Methods for Scientists and Engineers by Carl M. Bender; Steven A. Orszag
Call Number: QA371 B43
Fourier Series and Boundary Value Problems by James Ward Brown; Ruel V. Churchill
Call Number: QA404 B76 2008
Calculus of variations by I. M. Gelfand; S. V. Fomin
Call Number: QA315 G417
Partial Differential Equations by J. Kevorkian
Call Number: QA377 K48 2000
Complex Variables by Norman Levinson; Raymond M. Redheffer
Call Number: QA331 L47 1970
Partial Differential Equations and Boundary Value Problems with Applications by Mark A. Pinsky
Call Number: QA374 P55 1991
Green's Functions and Boundary Value Problems by Ivar Stakgold; Michael J. Holst
Use "Request a Copy" to borrow.
Introduction to Applied Mathematics by Gilbert Strang
Call Number: QA37.2 S87 1986
Partial Differential Equations of Applied Mathematics by Erich Zauderer
Call Number: QA377 Z38 2006

Establishing Texts

Differential Equations by Beverly H. West; John H. Hubbard
Call Number: QA371 H77 1991
Basic Partial Differential Equations by D. D. Bleecker; G. Csordas
Call Number: QA374 B64 1996
Boundary Value Problems by F. D. Gakhov; Ian N. Sneddon
Call Number: QA431 .G2813

Also available online.

Combinatorics

Establishing Texts

Principles and Techniques in Combinatorics by C. C. Chen; K. M. Koh
Call Number: QA164 C54 1992
Combinatorics and Graph Theory by John M. Harris; Jeffry L. Hirst; Michael J. Mossinghoff
Call Number: QA165 H37 2000
Foundations of Applied Combinatorics by Edward A. Bender; S. Gill Williamson
Call Number: QA164 B46 1991
Graphs and Digraphs by Gary Chartrand
Call Number: QA166 C4525 2005
Graph Theory by Bela Bollobas
Call Number: QA166 B662

Further Reading

Enumerative Combinatorics: Volume 1 by Richard P. Stanley
Call Number: QA164.8 S73 2012
Graph Theory by W. T. Tutte
Call Number: QA166 T815 1984
Spectral Graph Theory by Fan R. K. Chung
Call Number: LH 7R26 C76 no.92
Random Graphs by Béla Bollobás
Call Number: QA166.17 B66 2001
Ramsey Theory by Ronald L. Graham; Bruce L. Rothschild; Joel H. Spencer
Call Number: QA166 G68 1990
Handbook of Combinatorics by R. L. Graham
Call Number: QA164 H33 1995
Probabilistic Methods in Combinatories by Paul Erdős; Joel Spencer
Call Number: QA164 E7

Computational Mathematics

Suggested Reading for Qualifying Exams

An Introduction to Numerical Analysis by Endre Süli; David F. Mayers
Call Number: QA297 E52 2003
Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque
Call Number: QA431 L548 2007
Spectral Methods in MATLAB by Lloyd N. Trefethen
Call Number: QA377 T65 2000
Numerical Analysis of Spectral Methods by David Gottlieb; Steven A. Orszag
Call Number: LH 7R26 C74 no.26
Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson
Call Number: TA347 F5 J62 1987
The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson; Fredrik Bengzon
Use "Request a Copy" to borrow.
Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque
Call Number: QA377 L41566 2002
Monte Carlo Methods by Malvin H. Kalos; Paula A. Whitlock
Call Number: QA298 K35 1986

Establishing Texts

Introduction to Algorithms by Thomas H. Cormen; Charles E. Leiserson; Ronald L. Rivest; Clifford Stein
Call Number: QA76.6 C662 2009
A Friendly Introduction to Numerical Analysis by Brian Bradie
Call Number: QA297 B72 2006
Numerical Analysis by Richard L. Burden; J. Douglas Faires
Call Number: QA297 B84 1993

Geometry & Topology

Suggested Reading for Qualifying Exams

Algebraic Topology by Allen Hatcher
Call Number: QA612 H42 2002
Introduction to Smooth Manifolds by John M. Lee
Call Number: QA613 L44 2013
Foundations of Differentiable Manifolds and Lie Groups by Frank W. Warner
Call Number: QA614.3 W37 1983
A Comprehensive Introduction to Differential Geometry by Michael Spivak
Call Number: QA641 S6 1979

Establishing Texts

An Invitation to Algebraic Geometry by Karen E. Smith; Lauri Kahanpää; William Traves; Pekka Kekäläinen
Call Number: QA564 .I62 2004
Conics and Cubics by Robert Bix
Call Number: QA567 B59 1998
The Shape of Space by Jeffrey Weeks
Call Number: QA612.2 W44 1985
Basic Topology by Mark A. Armstrong
Call Number: QA611 A68
The Four Pillars of Geometry by John Stillwell
Call Number: QA445 S77 2005
Topology by James R. Munkres
Call Number: A611 M82 2000

Further Reading

Topology and Geometry by G.E. Bredon
Call Number: QA612 .B74 1993
Differential Topology by Victor Guillemin; Alan Pollack
Call Number: QA613.6 G84
Homology Theory by James W. Vick
Call Number: QA612.3 V5 1994

Logic

Suggested Reading for Qualifying Exams

Mathematical Logic by Heinz-Dieter Ebbinghaus; Jörg Flum; Wolfgang Thomas
Call Number: QA9 .E2213 2021
The Foundations of Mathematics by Kenneth Kunen
Call Number: QA9 K796 2009
Set Theory by Kenneth Kunen
Call Number: QA248 K75
Recursively Enumerable Sets and Degrees by R. I. Soare
Call Number: QA9.615 S63 1987
Computable Structures and the Hyperarithmetical Hierarchy by C. J. Ash; J. Knight
Call Number: QA9.59 A84 2000
A Shorter Model Theory by Wilfrid Hodges
Call Number: QA9.7 H65 1997
Model Theory by David Marker
Call Number: QA9.7 M367 2002
A Course in Model Theory by Katrin Tent; Martin Ziegler
Call Number: QA9.7 T45 2012

Establishing Texts

A Mathematical Introduction to Logic by Herbert B. Enderton
Call Number: QA9 E54 2001
Classic Set Theory by D. C. Goldrei
Call Number: QA248 G65 1996

Number Theory

Establishing Texts

The Higher Arithmetic by H. Davenport
Call Number: QA241 D2 2008
Introduction to the Theory of Numbers by Godfrey H. Hardy; E. M. Wright
Call Number: QA241 H28 1979
Higher Mathematics from an Elementary Point of View by H. Rademacher
Call Number: QA241 R214 1983
The Beauty of Doing Mathematics by Serge A. Lang
Call Number: QA7 L28 1985

Further Reading

Algebraic Number Theory by S. Lang
Call Number: QA247 L29 1994
Elliptic Curves by Anthony W. Knapp
Call Number: LH 7M43 N8463 v.40
Topics in Analytic Number Theory by H. Rademacher
Call Number: LB 8G92 Bd.169
From Number Theory to Physics by M. Waldschmidt; P. Cartier
Call Number: QA241 F76 1992
Modular Functions and Dirichlet Series in Number Theory by Tom M. Apostol
Call Number: QA241 A62
Number Theory by George E. Andrews
Call Number: QA165 A58

Last Updated: Aug 13, 2025 2:26 PM
URL: https://researchguides.library.wisc.edu/mathematics
Print Page

Subjects: Mathematics / Statistics