Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, however, the self written syllabus was not self study friendly (good syllabus overall though).

The course was split up into 3 parts, group theory, ring theory and field theory. As a computer science major we only had to study the first 2.

Now that I passed the exam for this course I want to study the field theory part ( which covers Galois theory, etc).

So, now I want to ask whether any of you know any good books on abstract algebra, which lift off at basic ring theory and continue to more advanced ring theory and to finite fields, Galois theory, ...

Please keep in mind that I am not a math major, and that I would like books which are suited for self study (thus a lot of examples and intuition).

Thanks in advance!

share|improve this question
2  
I have converted the question to community wiki, as it's asking for a list of suggestions and there is no single right answer. –  Zev Chonoles Aug 1 '11 at 0:39
4  
I think Topics in Algebra by I.N. Herstein is an excellent algebra text. –  Amitesh Datta Aug 1 '11 at 1:39
2  
@Amitesh I first learned algebra from the outstanding Herstein and it's awesome exercises, so it'll always have a special place in my heart despite it's old-fashioned approach. –  Mathemagician1234 Nov 25 '11 at 7:49

6 Answers 6

up vote 11 down vote accepted

There's always the classic Abstract Algebra by Dummit and Foote. Section II of the text gives a nice treatment of ring theory, certainly providing plenty of review for what you have already covered while introducing more advanced concepts of ring theory. Section III will cover the field and Galois theory you're interested in. Some of the exercises can be difficult at times, especially for self-study, but the authors tend to give a number of examples and always provide the motivation for why they are doing what they are doing.

share|improve this answer
    
As it contains no answers to the exercises, do you think it is still suitable for self study? –  sxd Aug 1 '11 at 0:53
1  
From my experience, most of the exercises are not so difficult that you would need solutions. Those examples that further the development of the theory often either have very good hints or are broken down into smaller, more managable problems (often with hints too!). However, there are solutions (or at least sketches) available on the internet for most of the exercises anyway. It may not be the easiest text available, but I think it is one of the best for a first course. –  Michael Banaszek Aug 1 '11 at 0:59
    
Thanks for your response in the first place. Are there plenty of examples in the book present? This is something where my syllabus clearly lacks! –  sxd Aug 1 '11 at 1:10
    
When I was reading through it, I very rarely found myself wanting an example of a topic or technique and not being able to find one. In general, any time they mention anything they give at least one example of it, though more often than not they'll give three or four. They also constantly provide motivation as to why you are learning any given topic, so very rarely will you ever finish a section wondering why you had to study it. –  Michael Banaszek Aug 1 '11 at 2:42
    
If you miss solutions to a particular problem, I can recommend using IRC. Both Freenode and EFNet have excellent #math channels with plenty of people happy to help with details. –  Tobias Kildetoft Aug 1 '11 at 9:25

I learned abstract algebra from Rotman's "First Course in Abstract Algebra". His expository style is easy to follow and the exercises he gives are helpful.

share|improve this answer
1  
+1 for Rotman. ANYTHING by Rotman claiming to be a textbook is outstanding in my experience! –  Mathemagician1234 Nov 25 '11 at 7:53

Fraleigh's "A First Course in Abstract Algebra, 7th Edition" is a good book for self study. It is easy and good for the beginners, and it has a complete solution manual written by the author.

share|improve this answer

Try Contemporary Abstract Algebra. This one, I think, has lots of nice examples. The following is from Googlebooks:

"Contemporary Abstract Algebra 7/e provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students."

Also, I would like to suggest you read this article in wikipedia. You may find the references valuable.

share|improve this answer

Note: This answer is copied over from an answer I gave on a previous very-similar question, because it still applies here.

This is likely not going to be a popular suggestion, since it's relatively unknown, but I think the perfect book for you is Allan Clark's Elements of Abstract Algebra.

It's a unique book that covers the basics of group theory, ring theory, and even a tiny bit of Galois Theory, but it does it almost entirely through problems. Every chapter begins with a short section defining some terms and giving a few basic proofs, and then it leads the reader through the rest of the exposition in a series of problems, some difficult, some not. The end result is that if you actually do all the problems, you've written the book yourself. It's impossible not to be comfortable with basic abstract algebra if you take this book seriously.

It's also probably the cheapest book on this entire list :)

share|improve this answer

My suggestions are 1) Fraleigh 2) Gallian 3) Herstein and 4) Rotman,

share|improve this answer
1  
Maybe you could add more information as the poster is asking for a reference request. –  Ryan Sullivant Jul 2 '13 at 7:34
1  
I've corrected Rotoman to Rotman - I suppose it was a typo. (I do not know about a book on algebra by Rotoman, neither does Google.) –  Martin Sleziak Jul 2 '13 at 8:40

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.