Abstract algebra learning recommendations: Difference between revisions
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It is worth keeping in mind that for higher mathematics in general and for abstract algebra in particular, books and other written media facilitate a far more complete learning experience than videos do. While videos can help you learn a few subtopics and give you a ''feel'' for the subjects, you will still probably need to do the majority of your learning from books or other written material. | |||
* Math Doctor Bob has some videos on abstract algebra including group theory: See [http://mathdoctorbob.org/Algebra.html here]. | * Math Doctor Bob has some videos on abstract algebra including group theory: See [http://mathdoctorbob.org/Algebra.html here]. | ||
* Vipul Naik made videos on some introductory topics in group theory to supplement his [http://groupprops.subwiki.org/wiki/Tour:Getting_started_%28beginners%29 guided tour to group theory] (the videos can be viewed along with the material in the tour). | * Vipul Naik made videos on some introductory topics in group theory to supplement his [http://groupprops.subwiki.org/wiki/Tour:Getting_started_%28beginners%29 guided tour to group theory] (the videos can be viewed along with the material in the tour). | ||
Revision as of 22:40, 31 January 2014
This page provides subject-specific learning recommendations for the subject abstract algebra. See all our learning recommendations pages |
Abstract algebra is an important component of undergraduate mathematics that includes group theory, ring theory, field theory, and some advanced aspects of linear algebra (such as the Jordan canonical form and rational canonical form) that rely on some knowledge of ring theory and field theory.
Usefulness
- Abstract algebra is largely useful only for people who intend to major in mathematics and do further work in a mathematics-intensive area (such as physics, some parts of computer science, and some parts of chemistry).
- Abstract algebra provides a deeper conceptual foundation for linear algebra, which is quite useful.
- The modes of thinking introduced in abstract algebra, particularly the ideas of isomorphism and homomorphism, can be useful for understanding logic, philosophy, and various cognitive science-based subjects. However, the specifics of algebraic structures are not relevant.
Recommended books
Our top general recommendations are recommendations that we would give people if we had to name just a few top books. Our niche recommendations are recommendations that suit learners with specific learning styles or goals. For learners who fit one of the niches, the niche recommendation would be better.
Top general recommendations
| Book | Author | ISBN and purchase links | Why we're recommending it and who we're recommending it for |
|---|---|---|---|
| A Book of Abstract Algebra (Second Edition, Dover) | Charles Pinter | ISBN 978-0486474175, Amazon | We recommend this book for people who are relatively new to higher mathematics and want a book focused on mastery of basic ideas and formalisms. It does not include too much information that sets a foundation for graduate work in mathematics. The book is also sufficiently cheap that you can buy it, use it, and then move on to more advanced books after extracting value from it. |
| Abstract Algebra (3rd Edition) | David S. Dummit and Richard M. Foote | ISBN 978-0471433347, Amazon | We recommend this book for people who are quite comfortable with mathematical abstraction and want to learn the subject in considerable depth, sufficient to be prepared for graduate study in mathematics. A number of universities have moved to using Dummit and Foote for their (honors) undergraduate algebra sequences, moving away from books by Artin, Lang, and Herstein. The comments on a Less Wrong thread about book recommendations made the case for the book over the books by Lang and Hungerford, see here. |
Niche recommendations
| Book | Author | ISBN and purchase links | Why we're recommending it and who we're recommending it for |
|---|---|---|---|
| Algebra (2nd Edition) (Featured Titles for Abstract Algebra) [Hardcover] | Michael Artin | ISBN 978-0132413770, Amazon hardcover | Artin's book has a fair amount of coverage of the geometric intuition behind algebraic constructions, such as the role of groups in symmetry. However, it seems to be harder for people to do self-study from this book and obtain a comrephensive picture of the subject. We would advise this book to people who are reading with the help of a mentor who is willing to use the book, or people who have already studied the basic material and are now looking to delve deeper into the material from the perspective that Artin uses. |
Video recommendations
It is worth keeping in mind that for higher mathematics in general and for abstract algebra in particular, books and other written media facilitate a far more complete learning experience than videos do. While videos can help you learn a few subtopics and give you a feel for the subjects, you will still probably need to do the majority of your learning from books or other written material.
- Math Doctor Bob has some videos on abstract algebra including group theory: See here.
- Vipul Naik made videos on some introductory topics in group theory to supplement his guided tour to group theory (the videos can be viewed along with the material in the tour).