Book recommendations: Abstract Algebra for self-study

[Peter_Newman]

Hello,

I am looking for one or more books in combination for self-study of abstract algebra. Desirable would be a good structure of the book with good examples of sentences and definitions. Of course, exercise problems should not be missing.

I am now almost tending to buy the Algebra 0 book by Aluffi, but I am not completely sure whether the book is well suited for a first study of algebra. If anyone has any experience here, please feel free to let me know, it would help me in my literature search.

I look forward to receiving good book suggestions from you guys.

 

[fresh_42]

I think you can't do much better than Serge Lang, Algebra, GTM 211
https://www.amazon.com/dp/038795385X/?tag=pfamazon01-20
when it comes to structure and completeness. Maybe a bit dry.

 

[malawi_glenn]

Gallian.
Get an older edition used copy in good condition. Very cheap and good.
There is also student solutions guides, also very cheap for older editions.
Some say it is not good to have solution guides, but I think when it is in a separate book you are less tempted to look at the solution right away.

I posted a handful of 100% legally free PDF "books" on abstract algebra here https://www.physicsforums.com/threa...-online-math-books-and-lecture-notes.1044710/

 

[The Bill]

In order of cost and ease of finding, starting with free:

Tom Judson has a nice PDF textbook on introductory abstract algebra called Abstract Algebra: Theory and Applications:
http://abstract.ups.edu/

There is a nice introductory Dover book by Pinter called A Book of Abstract Algebra.

Abstract Algebra: A First Course by Dan Saracino is highly regarded, but I haven't used it myself. Also, unless you hunt pretty hard for a used copy, it'll cost more than $70. That's not bad all things considered, but I thought I should mention it.

All three of these cover the basics on groups, rings, fields, and polynomial rings. I don't think Saracino covers Galois theory, but Judson and Pinter both do. Pinter's book has a conversational but relatively traditional style. Judson is conversational and sometimes veers into very gentle hand-holding territory when developing motivation. The YouTube channel The Math Sorcerer has a review of Saracino's book here:

I wouldn't recommend using only Aluffi's Algebra: Chapter 0 or Lang's Algebra as a first introduction, but both are excellent as part of the core of an algebra study plan and reading list. Aluffi leans hard into categorical language and reasoning, which I think is good. Lang is more categorical than most textbooks of that age, also.

If you can get a cheap copy of Dummit & Foote, it makes a pretty good companion text for in-depth study. It has a more traditional graduate level approach with about as wide a coverage as Aluffi. Aluffi, Lang, and Dummit & Foote each cover or put special emphasis on topics the others don't, though.

Based on your post, I'd recommend downloading a copy of Judson's book(linked above), reading the first two chapters, and working a few exercises in chapter 2 to see if you like the style of that text.

 

[MidgetDwarf]

Hello,

I am looking for one or more books in combination for self-study of abstract algebra. Desirable would be a good structure of the book with good examples of sentences and definitions. Of course, exercise problems should not be missing.

I am now almost tending to buy the Algebra 0 book by Aluffi, but I am not completely sure whether the book is well suited for a first study of algebra. If anyone has any experience here, please feel free to let me know, it would help me in my literature search.

I look forward to receiving good book suggestions from you guys.

Aluffi's book, which I have read parts of, would be too advanced for an introduction for the average students.

The suggestion of Gallian was a good one. A similar book to Gallian, would be the one by Fraleigh. Overall, I found Gallian to be the superior book, however I like the layout of Fraleigh better. Ie., definitions, lemmas, theorems, corollary, are easily spotted. In Gallian, only lemmas, theorems, and corollary are boxed in. The language of Fraileigh is more mathematically precise. However, Gallian has interesting examples, he motives the study of algebra clearly, and introduces some good group examples. Ie., places importance on the centralizer, introduces GL group with entries that are not necessarily real or complex, something most authors keep at real for introductory text. Also introduces students to when integers modulo n are a group under multiplication very early, instead of waiting for rings and fields like many authors do. This allows for easier examples/counterexamples to problems.

The exercises are more interesting. Exercises in Fraileigh are a bit trivial, except for maybe 3-5 in each section. I would go with Gallian, if you find it too hard, then try Fraileigh.

A good book to reference, is the book by by Michael Artin (Algebra). More advanced then either of the two, but it is a well written book. I prefer it to Dummit and Foote, although DF covers more topics. I found DF to be to encyclopedic and offers no insights. I know one poster here, does not like the Artin book.

 

[MidgetDwarf]

@OP. Send me a pm, I cannot send you one, due to your account settings. I know of a way to get the newest edition of Gallian a bit cheaper.

 

[Peter_Newman]

Thank you for your suggestions!

So the Lang book I have also looked at, it is considered the bible of algebra, but I'm not sure if the book is really suitable for self-study, maybe more as a reference?

I almost figured that Aluffi's book is more for second reading, what is nice though is that solutions are available for each problem.

Saracino's book seems good too! At least in the video it is said that you can understand the text directly while reading, not every book manages that either. Also the tasks seem to be fair!

The book by Gallian also looks very promising to me!

I myself have then found "Abstract Algebra" by Gregory Lee, here there are also solutions at the end of the book!

 

[malawi_glenn]

So the Lang book I have also looked at, it is considered the bible of algebra, but I'm not sure if the book is really suitable for self-study, maybe more as a reference?

Yes, I do not think it is a good first book.

I myself have then found "Abstract Algebra" by Gregory Lee, here there are also solutions at the end of the book!

It is probably a good book, but it does not cover as much material as, say, Gallian.

 

[Dragon27]

What can you say about "Abstract Algebra: An Integrated Approach" by Joseph H. Silverman? It is interesting in its approach of alternating between the subjects of groups, rings and fields.
From the review by Michele Intermont, Kalamazoo College

The author explicitly writes in his introduction that he was not aiming to produce a reference book, but rather a book to be read as one enters the subject. I do think my students will find this very accessible. Indeed, Silverman won the American Mathematical Society’s Leroy Steele prize for mathematical exposition in 1998 for his graduate texts on elliptic curves; here he confirms his expositional skills.

Silverman’s dedication says “This one is for the next generation”. Indeed, this is a wonderful resource for training the next generation of mathematicians.

 

[malawi_glenn]

What can you say about "Abstract Algebra: An Integrated Approach" by Joseph H. Silverman? It is interesting in its approach of alternating between the subjects of groups, rings and fields.
From the review by Michele Intermont, Kalamazoo College

Pretty new isn't it? It looks good, I like the structure of it. I have his number theory book which is very good (have not worked it through yet though)

 

[MidgetDwarf]

Thank you for your suggestions!

So the Lang book I have also looked at, it is considered the bible of algebra, but I'm not sure if the book is really suitable for self-study, maybe more as a reference?

I almost figured that Aluffi's book is more for second reading, what is nice though is that solutions are available for each problem.

Saracino's book seems good too! At least in the video it is said that you can understand the text directly while reading, not every book manages that either. Also the tasks seem to be fair!

The book by Gallian also looks very promising to me!

I myself have then found "Abstract Algebra" by Gregory Lee, here there are also solutions at the end of the book!

If you need solutions, you are not ready for Algebra.

 

[malawi_glenn]

If you need solutions, you are not ready for Algebra.

That is not a fair statement. Since if you are in a class at a university, there will always be tutors, solutions on the course homepage, etc.

 

[MidgetDwarf]

That is not a fair statement. Since if you are in a class at a university, there will always be tutors, solutions on the course homepage, etc.

I say this, because the average student (even when taking a class), searches the solution asap when getting stuck. Instead, of trying the problem out failing, trying it from a "different" angle, failing, rereading and working out examples again . This is when the real learning occurs. We see examples of students looking at solutions all the times on this forum, or even in actual lectures. Not to mention people who graduate, with no understanding of basic material.

So yes, I believe solutions manuals do more hard than good, and should be avoided at all cost. Moreover, this website offers excellent hw help. Since the poster posted here, I am sure they are well aware of this.

 

[malawi_glenn]

Yes, solutions guides should be use with care and self-awerness.
Same as asking questions. I tell my students that I will not answer questions if they start with "I know nothing" or "I have no idea"

 

[jbergman]

Hello,

I am looking for one or more books in combination for self-study of abstract algebra. Desirable would be a good structure of the book with good examples of sentences and definitions. Of course, exercise problems should not be missing.

I am now almost tending to buy the Algebra 0 book by Aluffi, but I am not completely sure whether the book is well suited for a first study of algebra. If anyone has any experience here, please feel free to let me know, it would help me in my literature search.

I look forward to receiving good book suggestions from you guys.

Aluffi has a new book out designed for undergrads.