92 Best Abstract Algebra Books of All Time (Updated for 2026)

1

A Book of Abstract Algebra

Charles C Pinter

5.0

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math te

2

Quantum Mechanics: The Theoretical Minimum

Leonard Susskind

4.8

From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum mechanics.

First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics.

In this follow-up to the New York Times best-selling The Theoretical M

Recommended by Eric Weinstein.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

3

Abstract Algebra

David S., Foote, et al.

4.8

Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way,

4

Algebra: Chapter 0

Paolo Aluffi

4.7

5

Contemporary Abstract Algebra

Joseph Gallian

4.6

Joseph Gallian is a well-known active researcher and award-winning teacher. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students.

6

Special Relativity and Classical Field Theory: The Theoretical Minimum

Leonard Susskind

4.6

A funny, insightful, and self-contained guide to Einstein's relativity theory and classical field theories--including electromagnetism

Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedm

7

A First Course in Abstract Algebra

John B. Fraleigh

4.6

Considered a classic by many, A First Course in Abstract Algebra, Seventh Edition is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations;

8

Abstract Algebra: Theory and Applications (2019)

Thomas W Judson

4.6

Abstract Algebra: Theory and Applications is an open-source textbook written by Tom Judson that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. The first half of the book presents group theory, through the Sy

9

Algebra - Part 2 (Quick Study) (Quickstudy: Academic)

S. B. Kizlik

4.5

Algebra 2 is the advanced QuickStudy guide specially designed for students who are already familiar with Algebra 1.

6-page laminated guide includes:

- real number lines

- graphing & lines

- types of functions

- sequences & series

- conic sections

- problems & solutions

- and much more

10

Algebra

Serge Lang

4.5

"Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." NOTICES OF THE AMS

"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bo

11

Matrix Analysis

Roger A Horn

4.5

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on

12

Topics in Algebra

I. N. Herstein

4.5

New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout.

13

Algebra (Graduate Texts in Mathematics) (v. 73)

Thomas W. Hungerford

4.5

14

Basic Algebra I: Their Sensory Evaluation

Nathan Jacobson

4.5

The second edition of a book designed to introduce mathematics students to abstract algebra.

Recommended by Eric Weinstein.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

15

Finite Group Theory

I. Martin Isaacs

4.5

16

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra

David A. Cox

4.5

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry the elimination theorem, t

17

Algebra

Michael Artin

4.5

18

Symmetry

Hermann Weyl

4.5

Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and cr

Recommended by Eric Weinstein.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

19

An Introduction to Homological Algebra

Joseph J. Rotman

4.4

Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman's book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included materi

20

Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability

Mattila

4.4

The focus of this book is geometric properties of general sets and measures in Euclidean spaces. Applications of this theory include fractal-type objects, such as strange attractors for dynamical systems, and those fractals used as models in the sciences. The author provides a firm and unified foundation for the subject and develops all the main tools used in its study, such as covering theorems,

21

An Introduction to the Theory of Groups

Joseph J. Rotman

4.4

Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions.

From the reviews:

"Rotman has given us a very readable and valuable text, an

22

Lie Algebras In Particle Physics: from Isospin To Unified Theories

Howard Georgi

4.4

Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions.

Recommended by Eric Weinstein.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

23

Algebra

Saunders Mac Lane, Garrett Birkhoff

4.4

This volume presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for group

24

Imaginary Numbers are Real

Stephen Welch

4.4

25

An Introduction to Mathematical Cryptography

Jeffrey Hoffstein, Jill Pipher, et al.

4.4

An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises.

It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may b

26

More Concise Algebraic Topology: Localization, Completion, and Model Categories

J. P. May

4.4

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, co

Cover unavailable

27

CLEP College Algebra with Online Practice Tests

Stu Schwartz

4.4

Earn College Credit with REA's Test Prep for CLEP* College Algebra

Everything you need to pass the exam and get the college credit you deserve.

CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs.

Our CL

28

An Introduction to K-Theory for C*-Algebras

M. R¿rdam

4.4

Over the past twenty-five years K-theory has become an integrated part of the study of C*-algebras. This book gives a very elementary introduction to this interesting and rapidly growing area of mathematics. The authors cover the basic properties of the functors K and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequ

29

Abstract Algebra

I. N. Herstein

4.4

Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results.

30

Field Theory (Graduate Texts in Mathematics)

Steven Roman

4.4

"Springer has just released the second edition of Steven Roman's Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own. All in all...a well-written expository account of a very exciting

31

Prandtl-Essentials of Fluid Mechanics

Herbert Oertel

4.4

Ludwig Prandtl, with his fundamental contributions to hydrodynamics, ae- dynamics, and gas dynamics, greatly in?uenced the development of ?uid - chanics as a whole, and it was his pioneering research in the ?rst half of the last century that founded modern ?uid mechanics. His book Fu]hrer durch die Str]omungslehre, which appeared in 1942, originated from previous pub- cations in 1913, Lehre von de

Cover unavailable

32

Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra

Steve Warner

4.4

Pure Mathematics for BeginnersPure Mathematics for Beginners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proofwriting skills that are essential for advanced study in mathemati

33

Linear Algebra

Georgi E. Shilov

4.4

In this volume in his exceptional series of translations of Russian mathematical texts, Richard Silverman has taken Shilov's course in linear algebra and has made it even more accessible and more useful for English language readers.
Georgi E. Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector

34

Elliptic Tales: Curves, Counting, and Number Theory

Avner Ash, Robert Gross

4.4

"Elliptic Tales" describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematic

35

Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates

Robert B. Ash

4.4

This survey of fundamental algebraic structures employs techniques applicable to mathematics, physics, engineering, and computer science. Topics include relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of number theory, geometry, and noncommutative and homological algebra. Solutions. 2006 edition.

36

Field and Galois Theory

Patrick Morandi

4.4

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sa

37

Category Theory

Steve Awodey

4.4

This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing

38

Naive Lie Theory

John Stillwell

4.4

This book aims to fill a gap in the literature by introducing Lie theory to junior and senior level undergraduates. In order to achieve this, the author focuses on the so-called "classical groups, '' viewed as matrix groups with real, complex, or quaternion entries. This allows them to be studied by elementary methods from calculus and linear algebra. Each chapter is enhanced with numerous exercis

Cover unavailable

39

A Concrete Approach to Abstract Algebra (Dover Books on Mathematics)

W. W. Sawyer

4.4

Brief, clear, and well written, this introduction to abstract algebra bridges the gap between the solid ground of traditional algebra and the abstract territory of modern algebra. The only prerequisite is high school–level algebra.
Author W. W. Sawyer begins with a very basic viewpoint of abstract algebra, using simple arithmetic and elementary algebra. He then proceeds to arithmetic and polynomial

40

Advanced Modern Algebra

Joseph J. Rotman

4.4

For two-term undergraduate level courses in Algebra. This text's organizing principle is the interplay between groups and rings, where rings includes the ideas of modules. It contains basic definitions, complete and clear theorems and gives attention to the topics of algebraic geometry, computers, homology and representations. More than merely a succession of definition theorem proofs, this text p

41

Schaum's Outline of Modern Algebra Abstract Algebra

Frank Ayres

4.3

42

Introduction to Lattices and Order

B. A. Davey

4.3

Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and all areas of discrete mathematics. This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and

43

Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics, #9)

James E. Humphreys

4.3

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first

44

Lie Groups, Lie Algebras, and Representations: An Elementary Introduction

Brian Hall

4.3

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.

In addition to its accessible treatment of

Cover unavailable

45

Algebra: 100 Fully Solved Equations To Explain Everything You Need To Know To Master Algebra! (Content Guide Included)

Math Wizo

4.3

46

Algebra II

B.L.van der Waerden

4.3

Das vorliegende, nunmehr zum neunten Male herausgebrachte Werk von B. L. VAN DER W AERDEN nimmt unter den mathematischen Lehrbiichem eine auBergewohnliche Stellung ein. Selten nur hat in der Vergangenheit ein Lehrbuch eine iihnlich groBe Wirkung auf das mathematische Leben ausgeiibt wie dieses. Seit seinem ersten Erscheinen im Sommer 1930, also vor nunmehr 63 Jahren, haben Generationen von Mathema

47

A Primer of Abstract Mathematics

Robert B. Ash

4.3

The purpose of this book is to prepare the reader for coping with abstract mathematics. The intended audience is both students taking a first course in abstract algebra who feel the need to strengthen their background, and those from a more applied background who need some experience in dealing with abstract ideas. Learning any area of abstract mathematics requires not only ability to write formal

48

Abstract Algebra

John A. Beachy, William D. Blair

4.3

49

Mach's Principle: From Newton's Bucket to Quantum Gravity

Julian B. Barbour

4.3

This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time, space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are

50

Introduction to the Theory of Abstract Algebras

Richard S Pierce

4.3

Intended for beginning graduate-level courses, this text introduces various aspects of the theory of abstract algebra. The book is also suitable as independent reading for interested students at that level as well as a primary source for a one-semester course that an instructor may supplement to expand to a full year. Author Richard S. Pierce, a Professor of Mathematics at Seattle's University of

51

Basic Abstract Algebra

P.B. Bhattacharya, S.K. Jain, S.R. Nagpaul

4.3

In addition to many new problems for practice and challenge, this edition of a self-contained graduate text on abstract algebra contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker-Noether theorem.

52

Symmetry: An Introduction to Group Theory and Its Applications

Roy McWeeny

4.3

This well-organized volume develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion. Designed to allow students to focus on any of the main fields of application, it is geared toward advanced undergraduate and graduate physics and chemistry students. 1963 edition. Appendices.

53

A Computational Introduction to Number Theory and Algebra

Victor Shoup

4.3

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal

54

Galois Theory for Beginners

Jorg Bewersdorff

4.3

Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are

55

Basic Algebra II

Nathan Jacobson

4.3

Volume II of a pair of classic texts — and standard references for a generation — this book comprises all of the subjects of first-year graduate algebra. In addition to the immediate introduction and constant use of categories and functors, it revisits many topics from Volume I with greater depth. 1989 edition.

56

Abstract Algebra with Applications: Volume 1: Vector Spaces and Groups

Karlheinz Spindler

4.3

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

57

Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry

Jürgen Richter-Gebert

4.3

This book provides a comprehensive introduction into the classical topic of projective geometry. It explains how metric concepts may be best understood in projective terms and explores the beauty of the interplay of geometry, algebra and combinatorics."

58

Exploring Abstract Algebra with Mathematica(r)

Allen C. Hibbard and Kenneth M. Levasseur

4.3

This upper-division laboratory supplement for courses in abstract algebra consists of several Mathematica packages programmed as a foundation for group and ring theory. Additionally, the "user's guide" illustrates the functionality of the underlying code, while the lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed a

59

A Course in Computational Algebraic Number Theory

Henri Cohen

4.3

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve

60

Higher Topos Theory (Am-170)

Jacob Lurie

4.3

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how e

61

Algebra (Classic Version)

Michael Artin

4.3

Appropriate for one- or two-semester algebra courses
This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics... for a complete list of titles.
Algebra, 2nd Edition, by Michael Artin, provides comprehensive coverage at the level of an honors-undergraduate or introductory-graduate

62

Rings, Fields and Groups: Introduction to Abstract Algebra

Reg Allenby

4.3

'Rings, Fields and Groups' gives a stimulating and unusual introduction to the results, methods and ideas now commonly studied on abstract algebra courses at undergraduate level. The author provides a mixture of informal and formal material which help to stimulate the enthusiasm of the student, whilst still providing the essential theoretical concepts necessary for serious study.

Retaining the high

63

A First Course in Noncommutative Rings

Tsi-Yuen Lam

4.3

Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

64

Abstract Algebra: A First Course

Dan Saracino

4.3

65

Student Solutions Manual for Gallian's Contemporary Abstract Algebra, 9th

Joseph A. Gallian

4.3

Contains worked-out solutions to odd-numbered problems.

66

Galois Theory

Steven Weintraub

4.3

Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin's classic text "Galois Theory," and this book is no exception. While Artin's book pioneered an approach to Galois theory that relies heavily on linear algebra, this book's author takes the linear algebra emphasis even further. This special approach to the su

67

Classical Mechanics with Maxima

Todd Keene Timberlake

4.3

This book guides undergraduate students in the use of Maxima--a computer algebra system--in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook.
When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly a

68

An Introduction to Hilbert Spaces

N. Young

4.3

This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for the solution of partial differential equations in mathematical physics and to the approximation of functions in compl

69

Algebra

Larry C. Grove

4.3

This graduate-level text is intended for initial courses in algebra that begin with first principles but proceed at a faster pace than undergraduate-level courses. It employs presentations and proofs that are accessible to students, and it provides numerous concrete examples.
Exercises appear throughout the text, clarifying concepts as they arise; additional exercises, varying widely in difficulty,

Cover unavailable

70

Weird Math: A Teenage Genius and His Teacher Reveal the Strange Connections Between Math and Everyday Life

David Darling

4.3

A teenage genius and his teacher take readers on a wild ride to the extremes of mathematics
Everyone has stared at the crumpled page of a math assignment and wondered, where on Earth will I ever use this? It turns out, Earth is precisely the place. As teen math prodigy Agnijo Banerjee and his teacher David Darling reveal, complex math surrounds us. If we think long enough about the universe, we'r

71

The Ultimate Hacking Guide: An In-Depth Guide Into The Essentials Of Hacking

The Code Academy

4.3

72

Finite Groups (AMS/Chelsea Publication)

Daniel Gorenstein

4.2

73

The Linear Algebra a Beginning Graduate Student Ought to Know

Jonathan S. Golan

4.2

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past d

74

Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics

David Hestenes

4.2

Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebm' suggested by Clifford himself. M

75

K-Theory: An Introduction

Max Karoubi

4.2

AT-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem (cf. Borel and Serre [2]). For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch [3] con sidered a topological analog defined for any compact space X, a group K(X) constructe

76

An Introduction to Abstract Algebra with Notes to the Future Teacher

Olympia Nicodemi, Melissa Sutherland, et al.

4.2

This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum a calculator such as the TI 89 with C. A. S. capabilities. KEY TOPICS: Includes "To the Teacher" sections that Draw connections from the number theory or abstract algebra under consideration t

77

Elements of Abstract Algebra

Allan Clark

4.2

Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. Includes 24 tables and figures. Reprint of the 1971 edition.

78

Boolean Algebra and Its Applications

J. Eldon Whitesitt

4.2

This introduction to Boolean algebra explores the subject on a level accessible even to those with a modest background in mathematics. The first chapter presents the algebra of sets from an intuitive point of view, followed by a formal presentation in chapter two of Boolean algebra as an abstract algebraic system, with no reference to applications.
Succeeding chapters offer concise accounts of app

79

Algebra: Volume I

B.L. van der Waerden, F. Blum, J.R. Schulenberg

4.2

This beautiful and eloquent text transformed the graduate teaching of algebra in Europe and the United States. It clearly and succinctly formulated the conceptual and structural insights which Noether had expressed so forcefully and combined it with the elegance and understanding with which Artin had lectured. This text is a reprinted version of the original English translation of the first volume

80

Semigroups of Linear Operators and Applications to Partial Differential Equations

Amnon Pazy

4.2

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applicati

81

A Survey of Modern Algebra (AKP Classics) (Akp Classics)

Garrett Birkhoff, Saunders Mac Lane

4.2

This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.

82

Group Theory: Birdtracks, Lie's, and Exceptional Groups

Predrag Cvitanović

4.2

If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic proj

83

Fundamental Concepts of Abstract Algebra

Gertrude Ehrlich

4.2

Designed to offer undergraduate mathematics majors insights into the main themes of abstract algebra, this text contains ample material for a two-semester course. Its extensive coverage includes set theory, groups, rings, modules, vector spaces, and fields. Loaded with examples, definitions, theorems, and proofs, it also features numerous practice exercises at the end of each section.
Beginning wit

84

A Radical Approach to Lebesque's Theory of Integration

David M. Bressoud

4.2

This lively introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author stresses the original purpose of the definitions and theorems, highlighting the difficulties mathematicians encountered as these ideas were refined. The story begins with Riemann's definition of the integral, and then follows the efforts of those who

85

Undergraduate Algebra

Serge Lang

4.2

The companion title, Linear Algebra, has sold over 8,000 copies

The writing style is very accessible

The material can be covered easily in a one-year or one-term course

Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem

New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

86

Algebra: A Very Short Introduction

Peter M. Higgins

4.2

Explains algebra clearly through theory and example
Renews the reader's aquaintance with school mathematics before taking them progressively further
Elucidates the laws governing algebra in order to reveal the elegance and power of equations and inequalities
Provides an accessible account of algebra for the general reader
Part of the bestselling Very Short Introductions series - over seven million sol

87

Combinatorics and Commutative Algebra

Richard P. Stanley

4.1

• Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra:

1) The theory of invariants of a torus acting linearly on a polynomial ring, and

2) The face ring of a simplicial complex

* In this new edition, the author further develops some interesting properties of face rings with application to combinatorics

88

Student Solutions Manual for Contemporary Abstract Algebra

Joseph Gallian

4.1

Contains complete worked solutions to all regular exercises and computer exercises in the text; additional test questions and their solutions; an online laboratory manual for the computer algebra system GAP, with exercises tied to the book and an instructor answer key; and links on the author's website to true/false questions, flash cards, essays, software downloads, and other abstract algebra-rel

89

From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory

Jean-Pierre Marquis

4.1

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein's Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane's work in the early 194

90

A Course in the Theory of Groups

Derek J.S. Robinson

4.1

A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with ot

91

Applied Abstract Algebra with Mapletm and Matlab(r)

Richard Klima

4.1

Applied Abstract Algebra with MapleTM and MATLAB(R) provides an in-depth introduction to real-world abstract algebraic problems. This popular textbook covers a variety of topics including block designs, coding theory, cryptography, and counting techniques, including Polya's and Burnside's theorems. The book also includes a concise review of all prerequisite advanced mathematics.

The use of sophisti

92

Foundations of Analysis: Book 1, Logic, Sets and Numbers

K. G. Binmore

4.1

In elementary introductions to mathematical analysis, the treatment of the logical and algebraic foundations of the subject is necessarily rather skeletal. This book attempts to flesh out the bones of such treatment by providing an informal but systematic account of the foundations of mathematical analysis written at an elementary level. This book is entirely self-contained but, as indicated above