Abstract algebra book recommendations for beginners.

Question

I am taking abstract algebra in this semester. I find that my lecturer didn't provide enough examples for understanding. So I would like to ask what are the recommended books which has lots of solved problems and exercises? The lecturer said in this semester, he will cover group theory, ring theory and a bit of field theory. Which book contains extensive information in these three fields?

Check these questions for some ideas: http://math.stackexchange.com/q/11626/4583, http://math.stackexchange.com/q/49253/4583, http://math.stackexchange.com/q/54839/4583, http://math.stackexchange.com/q/78286/4583. Herstein and Dummit&Foote are frequently recommended. — Ayman Hourieh, Mar 01 '13 at 15:12
but if you are studying it for the first time, then I must recommend Contemporary Abstract Algebra" by Joseph Gallain, the book is divided into 3 parts: groups, rings, fields. and each part is further broken down into 10 or so chapters, each containing about 50-60 problems, After studying from it though, you can follow whichever book you want. — Shreya, Mar 04 '16 at 12:21
Does this answer your question? Good abstract algebra books for self study — user1110341, Jul 21 '23 at 23:14

amWhy · Accepted Answer · 2013-03-02T02:27:17.333

10

For a one-semester course in abstract algebra: undergraduate/first-course-level, I'd highly recommend Fraleigh's A First Course in Abstract Algebra. It's very well written, very readable, and includes a LOT of examples in the text itself, as well as in the exercises.

Personally, I've found the most success using this text for first-course/semester-length classes.

Another possible aid, in addition to a supplementary text, is Beachy's Abstract Algebra Online Study Guide, where you'll find an extensive study guide and practice problems. It may help to supplement areas where you're feeling weakest. I'll include here, as well, a link for accessing Beachy's ~150 page pdf Abstract Algebra - Study Guide for Beginners available for downloading, freely distributed.

edited Mar 02 '13 at 02:27

answered Mar 01 '13 at 15:34

amWhy

210,739

I didn't know that you already read this book. I read it a lot before. Nice we are in an accord in that. – Mikasa Mar 01 '13 at 15:38
1

@Babak Yes, indeed - great book. + – amWhy Mar 01 '13 at 15:40
@Andrew: Take a look at the first few entries here. Many you can preview. The first few entries are all highly rated, but you can't go wrong with the price of the Dover book, listed first, which you could probably read concurrently to Fraleigh. I'll review my bibliography, as well. See also these recommendations from mathoverflow – amWhy Mar 01 '13 at 18:43
Are the suggestions helping at all, idonknow? What text are you currently using, if I may ask? – amWhy Mar 01 '13 at 18:47
currently i an using robert ash abstract algebra – Idonknow Apr 26 '13 at 05:47

score 4 · Answer 2 · answered Mar 01 '13 at 15:15

Dummit & Foote has lots.

But following up on the "Artin" recommendation which is excellent, you can watch these great videos that follow "Artin" and see many examples very nicely articulated. You can probably get a lot more out of these lectures by Benedict Gross at Harvard:

http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

score 3 · Answer 3 · answered Mar 01 '13 at 15:08

3

Michael Artin's book Algebra is very nice.

answered Mar 01 '13 at 15:08

Rasmus

18,946

+1 and comes as a $15 international edition... – gnometorule Mar 01 '13 at 15:59
I would suggest you get the 2nd edition - much improved. – Mar 01 '13 at 18:31

score 3 · Answer 4 · edited Mar 01 '13 at 16:15

3

I suggest you Algebra Through Practice collection by T. S. Blyth for first step and then Herstein or Fraleigh are good.

edited Mar 01 '13 at 16:15

answered Mar 01 '13 at 15:37

Mikasa

67,942

score 1 · Answer 5 · answered Mar 01 '13 at 15:48

This is a difficult level to write for. I suggest you pick up two or three books from your library and try to read chapters in each concurrently.

Fraleigh is the book I got my start on in abstract algebra. I didn't like the book at the time- its exposition is very unclear at certain points- but now looking back I think it's not too bad. I'm using Gallian right now in my group theory class, which is also not too bad.

Dummit & Foote is not a book I would recommend as the sole textbook for a beginner, but it is great to have as supplementary reading. In particular, you are looking for examples, and D&F is all about examples. I would say the same thing about Artin.

I dislike Hungeford and Herstein, but this is just personal preference.

I got a lot of points from Gallian's problems. Especially, when I could find some solutions at the end of the book. — Mikasa, Mar 01 '13 at 15:53

score 1 · Answer 6 · answered Mar 02 '13 at 02:44

I was happy with Contemporary Abstract Algebra by Gallian when I worked through it (I used the 5th edition, but it's up to at least the 6th). It covers all three areas you mention, and has tons of exercises (at least 30-some in most of the main chapters, if not 50- or 60-some, plus supplementary exercises every few chapters) with solutions or hints for the odd-numbered ones. It also is heavy on applications, and has computer exercises, if you like that sort of thing. He puts real emphasis on the "contemporary" in the title.

Abstract algebra book recommendations for beginners.

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