Top books of Abstract Algebra: If you are looking for the best abstract algebra books, then you are right place. As I have over 16 years of experience in Abstract Algebra, it helps me to identify the best reference books on abstract algebra. This can make you decide to buy the top abstract algebra books even if you are a beginner on this area. The list contains the following books on abstract algebra:
1. Abstract Algebra by Dummit and Foote
| Author: David S. Dummit and Richard M. Foote |
Abstract Algebra by Dummit and Foote is one of the best books and most widely accepted abstract algebra books.
This is a substantial and comprehensive textbook that covers all the main topics in abstract algebra, including group theory, ring theory, field theory, module theory, and Galois theory. It also covers representation theory and homological algebra. So it can be a good choice for both undergraduate and graduate students.
The book is highly recommended for its clear explanations and numerous examples and exercises.
Product Details:
- Publisher : Wiley; 3rd edition (July 14, 2003)
- Language : English
- Hardcover : 944 pages
- ISBN-13 : 978-0471433347
- Item Weight : 3.6 pounds
- Dimensions : 7.8 x 1.6 x 9.5 inches
- Customer Reviews: 4.6 out of 5 stars (210 ratings)
2. Contemporary Abstract Algebra by Gallian
| Author: Joseph Gallian |
Contemporary Abstract Algebra by Gallian is known for its clear and precise explanations. It explains the concepts very clearly and provides a lot of exercises to practice for readers. A few highlights of Gallian’s abstract algebra are as follows.
- Clear and concise explanations with numerous examples
- Hints and solutions for exercises
- Cover the major topics in abstract algebra: Groups, Rings, and Fields, and the Theory of Numbers
Overall, Gallian’s abstract algebra is an excellent text for studying abstract algebra. The book can help you to crack a Ph.D. interview as it has many important materials that are asked in an interview. It is highly recommended to students motivated in abstract algebra.
Product Details:
- Publisher : CENGAGE INDIA; 9th edition (January 1, 2017)
- Language : English
- ISBN-13 : 978-9353502522
- Item Weight : 0.071 ounces
- Dimensions : 7.99 x 10 x 1.85 inches
- Customer Reviews: 4.5 out of 5 stars (505 ratings)
3. A Book of Abstract Algebra (Dover Books on Mathematics)
| Author: Charles C. Pinter |
A Book of Abstract Algebra by Pinter is accessible to all readers of this area, but enriched with concepts, examples, and exercises. It has the materials that are covered by a typical course in elementary abstract algebra. The author provides elementary background wherever it is needed and discusses major topics of abstract algebra in their usual order.
Although it is written for undergraduate students, it is also suitable for graduate students and math teachers. The 2nd edition of this book is having additional exercises to improve student familiarity with applications.
Product Details:
- Publisher : Dover Publications; Second edition (January 14, 2010)
- Language : English
- Paperback : 400 pages
- ISBN-13 : 978-0486474175
- Item Weight : 14.4 ounces
- Dimensions : 5.4 x 0.8 x 8.4 inches
- Best Sellers Rank: #6 in Abstract Algebra (Books)
- Customer Reviews: 4.5 out of 5 stars (502 ratings)
4. A First Course in Abstract Algebra
| Author: John Fraleigh |
A First Course in Abstract Algebra by John Fraleigh is considered a classic by many abstract algebra lovers. This book is focused on groups, rings, and fields with an in-depth introduction to this area of algebra. By finishing this book, one can get a firm foundation understanding of the nature of algebraic structures.
It contains a bunch of problems that may help to crack many competitive exams. The book can be followed together with the textbooks by Dummit-Foote or Gallian at the same time to get a better understanding.
Product Details:
- Publisher : Pearson; 7th edition (November 6, 2002)
- Language : English
- Hardcover : 544 pages
- ISBN-13 : 978-0201763904
- Item Weight : 2.23 pounds
- Dimensions : 9.3 x 7.7 x 0.9 inches
- Best Sellers Rank: #2 in Abstract Algebra (Books)
- Customer Reviews: 4.2 out of 5 stars (245 ratings)
5. Topics in Algebra by I.N. Herstein
| Author: I.N. Herstein |
Herstein’s Topics in Algebra remains the ultimate introduction to modern abstract algebra to the previous generation of algebraists. It is the clearest, most naturally motivated exposition of abstract algebra that covers key topics like group theory, rings, etc.
This abstract algebra textbook is often considered an excellent choice as it includes extensive revisions of the material on finite groups and Galois Theory.
Product Details:
- ASIN : 0471010901
- Publisher : John Wiley & Sons; 2nd edition (January 16, 1991)
- Language : English
- Paperback : 388 pages
- ISBN-13 : 978-0471010906
- Item Weight : 1.44 pounds
- Dimensions : 6.26 x 0.97 x 9.37 inches
- Customer Reviews: 4.4 out of 5 stars (191 ratings)
6. Algebra by Serge Lang
| Author: Serge Lang |
Algebra by Serge Lang is one of the best graduate-level texts on abstract algebra that covers all of the basic concepts of algebra. It can be considered as a useful reference for mathematicians and professionals who use higher-level algebra. The author has added exercises and made numerous corrections to the text in the new edition.
AMS (American Mathematical Society) MathSciNet’s review of the first edition: “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.”
Product Details:
- Publisher : Springer; 3rd edition (January 8, 2002)
- Language : English
- Hardcover : 933 pages
- ISBN-13 : 978-0387953854
- Item Weight : 3.46 pounds
- Dimensions : 6.14 x 1.94 x 9.21 inches
- Customer Reviews: 4.6 out of 5 stars (127 ratings)
7. Algebra: Chapter 0 by Paolo Aluffi
| Author: Paolo Aluffi |
Algebra: Chapter 0 by Paolo Aluffi is a self-contained textbook of algebra suitable for both undergraduate and graduate students. It has approximately 1,000 exercises which are sufficient for adequate practice to gather knowledge of algebra that helps to explore many other topics, including applications to number theory and algebraic geometry.
Product Details:
- Publisher : American Mathematical Society (August 29, 2009)
- Language : English
- Paperback : 713 pages
- ISBN-13 : 978-1470465711
- Item Weight : 2.86 pounds
- Dimensions : 7 x 1.5 x 10 inches
- Customer Reviews: 4.7 out of 5 stars (68 ratings)
8. First Course in Abstract Algebra with Applications
| Author: Joseph J. Rotman |
A First Course in Abstract Algebra with Applications by Joseph J. Rotman introduces the rich concepts of algebraic topics on groups and rings. These topics are covered with a comprehensive discussion of theory as well as a significant number of applications for each.
Product Details:
- Publisher : Pearson; 3rd edition (September 28, 2005)
- Language : English
- Paperback : 640 pages
- ISBN-13 : 978-0131862678
- Item Weight : 2.38 pounds
- Dimensions : 7 x 1.5 x 9.2 inches
- Customer Reviews: 4.2 out of 5 stars (17 ratings)
9. Basic Algebra I by Nathan Jacobson
| Author: Nathan Jacobson |
Basic Algebra I by Nathan Jacobson is a classic text and standard reference for a generation. This volume is the work of an expert algebraist who taught at Yale for two decades. Volume I explores all of the major topics in algebra:
set theory, group theory, rings, modules, Galois theory, linear algebra, and associative algebra. It also covers rigorous topics such as Lie and Jordan algebras and Boolean algebras.
This Algebra text by Jacobson is recommended as a classroom text; in addition, it can serve as a valuable reference.
Product Details:
- ASIN : 0486471896
- Publisher : Dover Publications; Second edition (June 22, 2009)
- Language : English
- Paperback : 528 pages
- ISBN-13 : 978-0486471891
- Item Weight : 1.48 pounds
- Dimensions : 6.3 x 1.18 x 9.06 inches
- Customer Reviews: 4.6 out of 5 stars (127 ratings)
10. Algebra: A Course in Modern Algebra by Hungerford
| Author: Thomas W. Hungerford |
Algebra: A Course in Modern Algebra by Hungerford is a self-contained, one-volume, graduate-level algebra textbook that is suitable for the average graduate student as well as the wide variety of instructors and course contents
It is one of the most comprehensive coverages of all basic together with some advanced topics of a graduate-level algebra course. It also contains an extraordinarily large number of illustrative exercises. So it’s a great buy overall.
Product Details:
- Publisher : Springer; 8th edition (December 3, 1980)
- Language : English
- Hardcover : 528 pages
- ISBN-13 : 978-0387905181
- Item Weight : 2.24 pounds
- Dimensions : 6.14 x 1.13 x 9.21 inches
- Customer Reviews: 4.5 out of 5 stars (70 ratings)
11. Abstract Algebra: Theory and Applications by Beachy and Blair
| Author: Beachy and Blair |
Abstract Algebra: Theory and Applications by Beachy and Blair is well-known for its sequencing of topics and extensive set of exercises. The authors Beachy and Blair have presented the concepts very clearly with a lot of important examples that help inexperienced students who stumble over problem-solving.
The new edition introduces more chapters in group theory: nilpotent groups, semidirect products, the classification of groups of small order, and an application of groups to the geometry of the plane.
Product Details:
- Publisher : Waveland Pr Inc; 4th edition (February 18, 2019)
- Language : English
- Hardcover : 541 pages
- ISBN-13 : 978-1478638698
- Item Weight : 2.32 pounds
- Dimensions : 7.5 x 1.5 x 10 inches
- Customer Reviews: 3.9 out of 5 stars (16 ratings)
FAQs on Best Abstract Algebra Books
Q: What are the best abstract algebra books?
Answer: The list of best abstract algebra books is given as follows:
1. Abstract Algebra by Dummit and Foote
2. Contemporary Abstract Algebra by Gallian
3. A Book of Abstract Algebra (Dover Books on Mathematics) by Charles C. Pinter
4. A first course in abstract algebra by J. B. Fraleigh
5. Topics in Algebra by I.N. Herstein
6. Algebra by Serge Lang
7. Algebra: Chapter 0 by Paolo Aluffi
8. A First Course in Abstract Algebra with Applications by Joseph J. Rotman
9. Basic Algebra I by Nathan Jacobson
10. Algebra: A Course in Modern Algebra by Hungerford
11. Abstract Algebra: Theory and Applications by Beachy and Blair
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