# 92 Best Abstract Algebra Books of All Time

We've researched and ranked the best abstract algebra books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more

An introductory chapter traces concepts of abstract algebra from their historical... more

**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 Minimum*, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic... more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

* The emphasis throughout has been to... more

**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 Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any... more

**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; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles,... more**

6-page laminated guide includes:

- real number lines

- graphing & lines

- types of functions

- sequences & series

- conic sections

- problems & solutions

- and much more less

"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS

This book is intended as a basic text for a one-year course in algebra at the... more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

*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 crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support.

*Symmetry*is a work of seminal... more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

From the reviews:

"Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS less

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

*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 be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background. less

*A Concise Course in Algebraic Topology*addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and... more

**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.

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

Our CLEP* test preps are perfect for adults returning to college (or attending for the first time), military service members, high-school graduates looking to... more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**Pure Mathematics for Beginners**

**Pure 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 mathematics are covered and reviewed extensively.Pure Mathematics for Beginners is perfect for

professors teaching an introductory college course in higher... more

Georgi E. Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and... more

The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet... more

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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 polynomials, slowly progressing to more complex matters: finite arithmetic, an analogy between integers and polynomials, an application of the analogy, extending fields, and linear dependence and...

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:

a treatment of the Baker Campbell Hausdorff formula and its use in place of... more

After a preliminary review of set theory, the treatment presents the basic... more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*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 existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*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.

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.

**, by Michael Artin, provides comprehensive coverage at the level of an honors-undergraduate or introductory-graduate course. The second edition of this classic text... more**

*Algebra*, 2nd EditionRetaining the highly readable style of its predecessor, this second edition has also been thoroughly revised to include a new chapter on Galois theory plus hints and solutions to many of the 800 exercises... more

*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 attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using... more

Exercises appear throughout the text, clarifying concepts as they arise; additional exercises, varying widely in difficulty, are included at the ends of the chapters. Subjects include groups, rings, fields and Galois theory, modules, and structure of rings and algebras. Further topics encompass infinite Abelian... more

**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're left not with material stuff, but a ghostly and beautiful set of equations. Packed with puzzles and paradoxes, mind-bending concepts, and surprising solutions,**

*Weird...*more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**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 to secondary mathematics. Provides historical context with "From the Past" sections in each chapter. Features "Worksheets" that outline the framework of a topic in most chapters. ... more

Succeeding chapters offer concise accounts of applications to symbolic logic, focusing on topics of logic common to elementary mathematics and discussing concepts of valid argument and indirect proofs. Additional topics include the algebra of... more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

The invariant tensors are presented in a somewhat unconventional, but in recent years... more

Beginning with sets, relations, and functions, the text proceeds to an examination of all types of groups, including cyclic groups, subgroups, permutation groups, normal subgroups, homomorphism, factor... more

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 less

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 sold worldwide

Algebra marked the beginning of modern mathematics, moving it beyond arithmetic, which involves calculations featuring given numbers, to problems where some... more

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 less

**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 other areas of algebra such as ring theory and homological algebra.

This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional... more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**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 sophisticated mathematical software packages such as MapleTM and MATLAB(R) allows students to work though realistic examples without having to struggle with extensive... more

**Don't have time to read the top Abstract Algebra books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.