Best Abstract Algebra Books

Mathematics has always been fun for all ages of people. From younger to elder & from smarter to older, mathematics has always been there to rule us in a variety of modes. Some love it because of their high mental capabilities but some always tried to run away from it because of its long, tough calculations. But abstract algebra always fascinates the readers as it involves things that are in our minds.

Abstract algebra is the analysis of algebraic structures in algebra, which is a wide variety of mathematics. This field of research has been characterized by the word “abstract algebra” in the beginning of the 20th century. Abstract algebra is a collection of advanced algebraic themes that deal more than the regular number system of abstract algebraic structures Classes, rings, and fields are the most significant of these systems. The abstract algebra divisions, representation theory, and homological algebra are important switching algebra.

Listed below are the best abstract algebra books that can be used by the students of mid & senior level to learn the basics & in-depth algebra:

1: A Book of Abstract Algebra

A Book of Abstract Algebra

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  • Author: Charles C. Printer
  • Publisher: Dover Publications
  • Publication Date: January 14, 2010
  • Pages: 400

Book Description: This outstanding text is accessible but rigorous and contains all subjects covered by a traditional course in basic abstract algebra. Its easily readable treatment provides an intuitive approach with informal discussions and exercises arranged thematically. It also offers further exercises to enhance student knowledge of applications.

Book Author: The professor of mathematics at Bucknell University is Charles C. Pinter.

Our Opinion: Although some of the topics are familiar to me most of them are very new. It is well written and it is of great help to follow the logic of a complex subject, as the title suggests. In order to follow the logic of the subject, I think it is fair to say, that the reader should have a good head in Mathematics.

2: A Concrete Approach to Abstract Algebra

A Concrete Approach

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  • Author: Walter Warwick Sawyer
  • Publisher: Dover Publications
  • Publication Date: August 15, 2018
  • Pages: 240

Book Description: The arithmetic includes polynomials, which eventually move into more complicated issues: finite arithmetic, a study of the integers and polynomials, application of analogies, fields and linear dependency and vector areas. Algebraic calculations with vectors, field vectors and fields called vector spaces include other subjects.

Book Author: Starting at the universities in Dundee and Manchester, and later the universities of Ghana and Canterbury College in New Zealand, Walter Warwick Sawyer studied mathematics in St. John’s College, Cambridge, and taught worldwide.

Our Opinion: It’s a classic book with an outstanding approach to abstract algebra. Worth a look. However not recommended as a regular course.

3: Contemporary Abstract Algebra

Contemporary Abstract Algebra

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  • Author: Joseph Gallian
  • Publisher: Cengage Learning
  • Publication Date: January 1, 2016
  • Pages: 656

Book Description: The book text highlights how important it is to get a solid introduction to the traditional themes of abstract algebra, but it also presents it as a contemporary and highly active subject that work physicians, chemists and IT scientists are currently using.

Book Author: He got his PhD from Notre Dame from Joseph Gallian. He received numerous awards, first as the Second Vice-President, and then as President of the MAA, for his teaching and exhibition. More than 100 articles have been published and six books have been written.

Our Opinion: A great book of good ideas. An excellent book for those who would like to know more about abstract algebra.

4: Abstract Algebra

3rd Edition

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  • Authors: David S. Dummit & Richard M. Foote
  • Publisher: Wiley
  • Publication Date: July 14, 2003
  • Pages: 944

Book Description: The book sets out the theory of different algebraic structures carefully and uses numerous examples and exercises to help students understand it, ranging from basic definitions to some thorough results.

Book Author: David S. Dummit is the Professor at the University of Vermont in the College of engineering & mathematical sciences department.

Richard M. Foote possess the expertise in group theory and applications along with algebraic number theory.

Our Opinion: Possibly one of the best presentations of higher mathematics. The text provides an obvious framework for many ideas in the field and offers many good examples of more refined and rigorous proof. I’d advise you to go through your work even before you graduate.

5: Study Guide of Abstract Algebra

Study Guide

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  • Author: John A. Beachy
  • Publisher: Create Space Independent Publishing Platform
  • Publication Date: November 6, 2013
  • Pages: 268

Book Description: The concept declarations and theorems in the text are included. It contains over 600 problems for groups, rings and fields, and over 300 solutions are detailed. The exercises in the text are not solved by a manual since they contain completely new problems.

Book Author: John A. Beachy is the Professor Emeritus of Mathematical Sciences in the Northern Illinois University. He has written a number of research articles.

Our Opinion: It contains all the requisite theorems and demonstrations from an initial abstract algebraic course you would expect. The student has worked out a variety of options in full detail. It can also be used independent of a textbook for self-studies. One of the best purchases I made as a mathematics student frankly.

6: A Student-Friendly Approach: Abstract Algebra

Abstract Algebra

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  • Authors: Anthony J. Dos Reis & Laura L. Dos Reis
  • Publisher: Pearson Education
  • Publication Date: January 1, 2003
  • Pages: 364

Book Description: If you study abstract algebra independently or have problems with your professor’s comprehension, this is your book. It doesn’t just encourage studying abstract algebra, it lets you mathematically think and do mathematics when you read the book. In an introductory course it addresses all conventional subjects. High school algebra is the only precondition.

Book Author: Anthony J. Dos Reis is the Associate Professor of Computer Science at Department of Computer Science in the State University of New York at New Paltz.

Our Opinion: Excellent for the self-learner: simple and clear descriptions with several examples worked out. The typical way a mathematician does not complicate Dos Reis. If it’s not your math talent but rather your schoolbook that you are struggling with, then that’s what you need.


What is the use of abstract algebra?

Abstract algebra is used in many branches of mathematics and science due to the generality of algebra. For example, algebraic topology is used to study topology using algebraic objects.

Who is considered the father of algebra/abstract algebra?

Al-Khwarizmi is considered o be one of the prominent face & father of abstract algebra.

Define algebra.

Algebra is defined as the generalization of arithmetic in which numbers are combined according to arithmetic laws.

What are algebra’s four rules?

The Algebra Basic Laws are the laws of association, commutation, and distribution. They help clarify the link between numbers and promote or solve equations.

Does Physics use abstract algebra?

There is little question that the most significant mathematical method used as a physicist today is abstract algebra. The theory of groups, groups, co-representations, braid groups, lies algebra, etc.

What is meant by the theory of numbers?

The theory of numbers is the analysis of the entire set of positive statistics. 1,2,3,4,5,6,7… sometimes referred to as a natural number set.

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