The following lists of books are suggested readings from the primary areas of mathematics. The books listed as foundational texts will provide readers new to an area a sense of a subject and its fundamental results. The books listed as deeper reading are for readers who are ready to dig deeper into a topic. Books with an * have been suggested as readings for the Mathematics Department's Qualifying Review Exams or for the Applied & Interdisciplinary Mathematics Qualifying Review Exams.
Foundational Texts:
Contemporary abstract algebra - Gallian
A survey of modern algebra - Birkhoff
Basic Algebra - Jacobson*
Linear algebra and its applications - Strang*
Linear algebra - Hoffman and Kunze
Deeper Reading:
Abstract Algebra - Dummit and Foote*
Algebra - Lang*
Rings, Modules & Linear Algebra - Hartley and Hawkes*
Algebra - Hungerford*
Commutative Algebra - Zariski and Samuel*
Lectures in Abstract Algebra, Vol. III - Jacobson*
The Theory of Groups - Rotman*
Foundational Texts:
Multivariable Calculus - Stewart*
Elementary Analysis: The Theory of Calculus - Ross*
Introduction to calculus and analysis Volume I and Volume II- Courant & John
Mathematical analysis: an introduction - Browder
Invitation to complex analysis - Boas
Deeper Reading:
Complex analysis, an introduction to the theory of analytic functions of one complex variable - Ahlfors*
Real analysis - Royden*
Principles of mathematical analysis - Rudin
Real and complex analysis - Rudin
Theory of Functions of a Real Variable - Natanson*
Fourier Series - Dym & McKean*
Foundational Texts:
Differential equations: a dynamical systems approach - Hubbard & West
Elementary Differential Equations - Boyce and DiPrima*
Boundary value problems - Gahkov
Mathematics for Physics - Stone & Goldbart*
Deeper Reading:
Applied Analysis - Hunter & Nachtergaele*
Partial differential equations: theory and completely solved problems - Hillen, Leonard, Roessel*
Applied Partial Differential Equations with Fourier Series and Boundary-Value Problems - Haberman*
Numerical Methods for Ordinary Differential Systems - Lambert*
Functional Analysis - Reed and Simon*
Functional Analysis - Lax*
Calculus of variations - Gelfand & Fomin
Numerical Solution of Partial Differential Equations - Morton & Myers*
Complex Variables and Applications - Churchill & Brown*
Numerical Initial Value Problems for Ordinary Differential Equations - Gear*
Numerical Partial Differential Equations - Thomas*
Foundational Texts:
Introductory Combinatorics - Brualdi*
Combinatorics and graph theory - Mossinghoff, Hirst, & Harris
Foundations of applied combinatorics - Bender
Graphs & digraphs - Chartrand
Graph theory: an introductory course - Bollobás
A First Course in Probability - Ross*
Deeper 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
Probability - Shiryayev
Probability and Measure - Billingsley
Foundational Texts:
Introduction to algorithms - Cormen, Leiserson, Rivest, & Stein
A friendly introduction to numerical analysis - Bradie
Numerical analysis - Burden & Faires
Introduction to Numerical Linear Algebra and Optimization - Ciarlet*
Deeper Reading:
Algorithm Design - Kleinberg & Tardos*
The art of computer programming - Knuth
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
Finite Element Methods and Their Applications - Chen
Monte Carlo methods - Kalos & Whitlock
Foundational Texts:
An invitation to algebraic geometry - Smith
Conics and cubics : a concrete introduction to algebraic curves - Bix
Basic topology - Armstrong
The four pillars of geometry - Stillwell
Topology: a first course - Munkres
Deeper Reading:
The shape of space : how to visualize surfaces and three-dimensional manifolds - Weeks
Elements of Algebraic Topology - Munkres
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
Foundational Texts:
A mathematical introduction to logic - Enderton
Introduction to Set theory - Hrbacek & Jech
Mathematical logic - Shoenfield
Model theory: an introduction - Marker
Deeper Reading:
Categories for the working mathematician - Mac Lane
Theory of recursive functions and effective computability - Rogers
Model theory - Chang & Keisler
Foundational 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
Deeper Reading
Algebraic number theory - Lang
Elliptic curves - Knapp
Topics in analytic number theory - Rademacher
Chapter 1 of 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