- University of Michigan Library
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- Mathematics
- Suggested Readings by Subject

Resources in mathematics.

**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