Book recommendations: Abstract Algebra for self-study

In summary, Aluffi's Algebra: Chapter 0 might 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.
  • #1
Peter_Newman
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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.
 
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  • #3
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/
 
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  • #4
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.
 
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  • #5
Peter_Newman said:
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.
 
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  • #6
@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.
 
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  • #7
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!
 
  • #8
Peter_Newman said:
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.
Peter_Newman said:
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.
 
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  • #9
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.
 
  • #10
Dragon27 said:
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)
 
  • #11
Peter_Newman said:
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.
 
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  • #12
MidgetDwarf said:
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.
 
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  • #13
malawi_glenn said:
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.
 
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  • #14
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"
 
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  • #15
Peter_Newman said:
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.
 

1. What is abstract algebra and why is it important?

Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It is important because it provides a framework for understanding and solving complex mathematical problems, and has applications in various fields such as physics, computer science, and cryptography.

2. Is abstract algebra difficult to learn on your own?

Abstract algebra can be challenging to learn on your own, especially if you do not have a strong foundation in algebra and mathematical proofs. However, with dedication and a good study plan, it is possible to learn abstract algebra on your own.

3. What are some good books for self-studying abstract algebra?

Some highly recommended books for self-studying abstract algebra include "Abstract Algebra: Theory and Applications" by Thomas W. Judson, "A Book of Abstract Algebra" by Charles C. Pinter, and "Abstract Algebra" by David S. Dummit and Richard M. Foote.

4. How should I approach self-studying abstract algebra?

It is important to have a solid understanding of basic algebra and mathematical proofs before diving into abstract algebra. It is also helpful to have a study plan, to practice solving problems, and to seek out additional resources such as online lectures or study groups.

5. Are there any online resources for learning abstract algebra?

Yes, there are many online resources available for learning abstract algebra, such as video lectures, online courses, and interactive tutorials. Some recommended websites include Khan Academy, MIT OpenCourseWare, and Abstract Algebra Online.

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