Is Fraleigh a good first exposure to Algebra

[glb_lub]

Hello ,
I wish to study Analysis and Algebra 1-2 years down the line when I take up graduate level courses on the subject.I wish to strengthen my foundations during the year in my free time , before I join the courses.

As a prerequisite for Analysis I aim to do a study of Apostol - Calculus Volume 1 and use Spivak as a reference. I hope to gain some knowledge that is necessary before beginning analysis. I estimate that I may need anywhere between 6 months to 1 year to learn something substantial from Apostol.

My question is , as Apostol is a prerequisite before studying analysis , is there something similar in Abstract Algebra.

How is the book on Abstract Algebra by Fraleigh ? https://www.amazon.com/dp/0201763907/?tag=pfamazon01-20
I read parts of Herstein(https://www.amazon.com/dp/0471010901/?tag=pfamazon01-20) and Artin (https://www.amazon.com/dp/0130047635/?tag=pfamazon01-20) and found them a bit tough.

Will a year spent with Fraleigh prepare me for these books ?
And do I have to finish Apostol(not the problems of course those may take much longer, at least the theory part) before I can begin Fraleigh or can I do them side by side ?

 

[micromass]

Fraleigh is a good first book for algebra. It's not as hard as books like Artin, which may be daunting for first timers.

You don't need to finish Apostol at all to be able to start algebra. You can do them side-be-side if you want to.

 

[qspeechc]

If you work through Apostol I would say you are mathematically mature enough to go on to Herstein, but you have to workon some problems in each chapter, very important. Herstein is written at a higher level than Fraleigh. I have no experience with Artin so I won't comment on it, but from what I hear it's tougher than Herstein. Both Herstein and Artin do not have any algebra prerequisites, so theoretically at least they are suitable for an absolute beginner. For what it's worth, I read Herstein with no previous knowledge of algebra.

So my advice would be so finish Apostol (but you must work on some problems) then move on to Herstein (or Artin). If you do Fraleigh before Herstein/Artin you may find Fraleigh has taken out some of the joy of discovering algebra from one of those books, since Fraleigh does a lot of the work for you (I have a copy of Fraleigh).

I do not recommend you read Fraleigh because I believe that it is not challenging enough for a maths major, but some people will disagree with me. Furthermore, I don't see why you should split your study of undergraduate algebra in a simple and a standard level course, taking twice as long as normal. If you read Herstein you may want to supplement the linear algebra chapters, for example with a book like Axler. Many people say Artin is better than Herstein, so that's another book to consider.

 

[20Tauri]

I got a copy of Fraleigh to study on my own and I had some trouble with it. I bought the book with the understanding that Calc III and Linear Algebra were its prerequisites, but it seemed to require either substantially more proof experience than I have or a professor to guide you. I haven't taken a formal proofs class yet--I assumed that wouldn't matter, but when I picked up the book I found I was wrong--so if your situation is similar to mine that might be something to consider.

 

[glb_lub]

Thanks for the help people.
Thanks to PF I discovered books like Apostol and Spivak both of which I am highly enjoying , even though I am on first 1-2 chapters. People spoke highly of Apostol's and Spivak's books in other threads and hence I bought those books.

I was browsing through the chapter on integration in Apostol and I found his approach to it amazing. And he doesn't even use the word infinity or infinitesimal in it , which was a first for someone like me who has learned only formula substitution before this.

By the way how is Gallian - http://books.google.co.in/books?id=...2&dq=algebra artin&pg=PP1#v=onepage&q&f=false ?

 

[qspeechc]

By the way how is Gallian - http://books.google.co.in/books?id=...2&dq=algebra artin&pg=PP1#v=onepage&q&f=false ?

Again, I have not read Gallian myself, but judging from the reviews:
https://www.amazon.com/gp/product/0547165099/?tag=pfamazon01-20
it seems like a bad book. It sounds very watered down to me, from reading the reviews, and it is very unusual for students to say a book is not advanced enough. Also the book is hideously expensive, and on that basis alone I probably would not recommend it, even if it was a good book.

Look, you don't need a "algebra for dummies" book to get started in algebra. After Apostol you should be well enough prepared to do Herstein or Artin. Those two books are the standard textbooks for undergrad algebra, you can't go wrong with them (chose one or the other). Another common undergrad book is Dummit and Foote, but again I haven't read that one. Chose one book (or two if you want) from Herstein, Artin, Dummit & Foote, whichever you can find for the cheapest price, and work through it , working on the problems as well, and you'll be more than fine.

 

[Elwin.Martin]

Thanks for the help people.
Thanks to PF I discovered books like Apostol and Spivak both of which I am highly enjoying , even though I am on first 1-2 chapters. People spoke highly of Apostol's and Spivak's books in other threads and hence I bought those books.

I was browsing through the chapter on integration in Apostol and I found his approach to it amazing. And he doesn't even use the word infinity or infinitesimal in it , which was a first for someone like me who has learned only formula substitution before this.

By the way how is Gallian - http://books.google.co.in/books?id=...2&dq=algebra artin&pg=PP1#v=onepage&q&f=false ?

I have a strong preference for Gallian over Fraleigh, having looked at both, but I recommend you try to read some of each.

 

[A. Bahat]

For what it's worth, I think Artin's book is excellent. It's at about the same level as Herstein and Dummit/Foote, but I find that Artin conveys the most insight. Another great book written by a famous algebraist is Jacobson's Basic Algebra I (a Dover, so it's cheap too). However, Jacobson is a bit dense and may be too hard for a first exposure to algebra. I would definitely look at both though and see which one you prefer.

 

[glb_lub]

Thanks for all the suggestions . They have been helpful.

 

[Sankaku]

...I have not read Gallian myself, but judging from the reviews...
it seems like a bad book.

As a rule of thumb, do not rely on Amazon reviews for books used in standard 1st or 2nd year University courses. There are far too many unprepared students taking them, and they skew the results badly. That said, Gallian is a decent book, but not my favourite. Buy an older copy for much less money - they do not change much between editions.

If you have access to a library, go and read through a few different books and get a feel for the style. Different people like different approaches - there is no one best book for everyone. However, here are my thoughts:

My personal favourite intro text is Pinter's A Book of Abstract Algebra (another inexpensive Dover). It is rigorous and a pleasure to read.

Jacobson's BA1 is a classic book but I would not recommend it for any first course.

Herstein's Abstract Algebra is pretty good, as mentioned above, but fairly short and far too expensive.

I am not keen on Artin's approach myself, but many people like it a lot.

Dummit & Foote is a great text, but probably too advanced for a first book if you don't have a good professor to go along with it.

Carter's Visual Group Theory is a very interesting book that starts at a very very basic level, but introduces concepts in a unique way. Probably best used as a supplement to another book.

 

[Barre]

Hello, I do not want to make a new topic as my question is kind of similar.

I will have a holiday from school in a couple weeks and I want to expand my knowledge in algebra during this time. I have last year went through this book;
https://www.amazon.com/dp/0030105595/?tag=pfamazon01-20

It have not been reviewed especially well, but I was fine with it and I consider myself mastering all the material covered in the book by now. Before christmas break I bought following book, by the same author, as my next goal:
https://www.amazon.com/dp/0387905189/?tag=pfamazon01-20

Many sections I've managed to work through (group actions, sylow theorems, nilpotent and solvable groups, factorization in rings etc) but I feel some stuff simply takes too much time to get through (free groups, chain series, jordan-hölder theorem, modules, galois theory). I have no intuition for the new topics covered. On top of that, he introduces category theory early on and uses it later on, which I feel is beyond my scope for the moment. I do not feel the book is bad in any way, but simply too many sections are above my level in sophistication.

So I'm thinking about getting another book, and therefore my question here. First of all, are there even books out there more 'accessible' for an avarage joe than Hungerford's Algebra, yet on similar level of covered material? What would you guys recommend?

Here is a list of topics that I am currently interested in learning about and would like the next book of choice to introduce in a 'friendly' :) manner:
*Free groups/free abelian groups and fundamental theorem of finitely generated abelian groups
*Group presentations, relations.
*some theory on nilpotent/solvable groups
*modules
*serious but elementary treatment of galois theory.
*perhaps and introduction to more advanced ring theory (noetherian/artinian rings etc)

 

[A. Bahat]

For a book similar Hungerford but perhaps easier, try Dummit and Foote. Category theory is relegated to an appendix, but the book is very complete and rife with examples. It sounds like what you are looking for.

 

[Sankaku]

Many sections I've managed to work through (group actions, sylow theorems, nilpotent and solvable groups, factorization in rings etc) but I feel some stuff simply takes too much time to get through (free groups, chain series, jordan-hölder theorem, modules, galois theory). I have no intuition for the new topics covered. On top of that, he introduces category theory early on and uses it later on, which I feel is beyond my scope for the moment. I do not feel the book is bad in any way, but simply too many sections are above my level in sophistication.

I am not familiar with his undergraduate book, but Hungerford's Algebra is a very serious graduate-level book.

Personally, I find it is a great reference but, as you say, it provides absolutely no intuition for the material it is covering. If I can get the intuition somewhere else, coming back to Hungerford makes me appreciate it more. Really, it needs a good professor to teach the context.

Unfortunately there is no one perfect upper-level algebra textbook. I have found Jacobson's BA1 & BA2 and Dummit & Foote are good places to look for alternative explanations of material in Hungerford. However, each takes its own unique approach and the order of coverage is often different.

Jacobson:
https://www.amazon.com/dp/0486471896/?tag=pfamazon01-20

Another very good upper-level algebra book is by Robert Ash. It is well-written and available free from his website:
http://www.math.uiuc.edu/~r-ash/Algebra.html

Paper version:
https://www.amazon.com/dp/0486453561/?tag=pfamazon01-20

You will be mostly familiar with the first half of the book and it doesn't go as far in most areas as Hungerford, but it is a great place to get a start in the upper-level topics.

 

[glb_lub]

My personal favourite intro text is Pinter's A Book of Abstract Algebra (another inexpensive Dover). It is rigorous and a pleasure to read.

I'm interested in this one. But I read on Amazon that this reads like a novel. "Like a novel" and "rigorous" how did the author pull it off ?
Could you tell me more about it. Is it advisable to start off with Pinter's book instead of Fraleigh?
Thanks.

See , my aim is to lay groundwork before starting off with Herstein/Artin , because I did find it a bit tough.Artin can't be studied till I gain some more maturity in mathematics I think. I am enjoying Apostol's Calculus at the moment and hope that it would help me with books such as Rudin's POMA. I am looking for some similar precursor for Artin/Herstein. .So that I don't have to wait till I finish Apostol .

 

[qspeechc]

As a rule of thumb, do not rely on Amazon reviews for books used in standard 1st or 2nd year University courses. There are far too many unprepared students taking them, and they skew the results badly.

Well, you conveniently left out the important part of what I said:

It sounds very watered down to me, from reading the reviews, and it is very unusual for students to say a book is not advanced enough.

If the rating was low because students were saying the book was too difficult, then I would agree with you, but they all say it is too simple, which is highly unusual.

 

[Sankaku]

I'm interested in this one. But I read on Amazon that this reads like a novel. "Like a novel" and "rigorous" how did the author pull it off ?
Could you tell me more about it. Is it advisable to start off with Pinter's book instead of Fraleigh?

Well, it is just a well-written book. Yes, I know that sounds strange in the world of math textbooks. I am not familiar with Fraleigh, so I can't compare. However, Pinter only costs about $12, so it is hardly a big risk. You can always use more than one book - start with whatever makes the most sense to you.

If the rating was low because students were saying the book was too difficult, then I would agree with you, but they all say it is too simple, which is highly unusual.

Except the people who bash Stewart (and books like it) for being too basic? Yes, you are correct - that is a different set of students that the ones who are unprepared. However, I think those kinds of reviews are also often skewed for other reasons.

In the end, six reviews on Amazon does not make a good statistical sample. Like I said, Gallian may not be the best book, but it isn't bad. I have actually read it. Have you?

 

[qspeechc]

Except the people who bash Stewart (and books like it) for being too basic? Yes, you are correct - that is a different set of students that the ones who are unprepared. However, I think those kinds of reviews are also often skewed for other reasons.

In the end, six reviews on Amazon does not make a good statistical sample. Like I said, Gallian may not be the best book, but it isn't bad. I have actually read it. Have you?

Well I don't want to de-rail this thread so I hope we can make this our last posts on this topic. Judging by these reviews (there are of course many Stewart calculus books, but this one seems the most recent so I chose this one), of all the bad reviews, that is 1, 2, or 3 starts, of those that are relevant (not about the condition of the book etc.), most of them say the book is too difficult, not too simple.

What other reasons are the reviews skewed for? You only have to read the reviews to see how lowly both students and instructors think of the book. And 6 reviews is not exactly a great sample, but it is much better than no evidence to the contrary. And none of the big universities, as far as I know, use Gallian for their undergrad maths students.

And to repeat myself, if you have worked through Apostol then there is no reason to read a 'baby algebra' book, as one reviewer described it. After Apostol you should be sufficiently prepared for a proper, challenging algebra book, like Artin or Herstein, the ones I recommended. Fraleigh, I am sure, and Gallian, I suspect (with some evidence to back me up), will not be challenging or stimulating enough for someone who has gone through Apostol.

I have nothing further to add.

 

[A. Bahat]

I'm with qspeechc on this one. If you've used Apostol, you are sufficiently mathematically mature to read the harder algebra books e.g. Artin.

 

[Barre]

I am not familiar with his undergraduate book, but Hungerford's Algebra is a very serious graduate-level book.

Personally, I find it is a great reference but, as you say, it provides absolutely no intuition for the material it is covering. If I can get the intuition somewhere else, coming back to Hungerford makes me appreciate it more. Really, it needs a good professor to teach the context.

Unfortunately there is no one perfect upper-level algebra textbook. I have found Jacobson's BA1 & BA2 and Dummit & Foote are good places to look for alternative explanations of material in Hungerford. However, each takes its own unique approach and the order of coverage is often different.

Jacobson:
https://www.amazon.com/dp/0486471896/?tag=pfamazon01-20

Another very good upper-level algebra book is by Robert Ash. It is well-written and available free from his website:
http://www.math.uiuc.edu/~r-ash/Algebra.html

Paper version:
https://www.amazon.com/dp/0486453561/?tag=pfamazon01-20

You will be mostly familiar with the first half of the book and it doesn't go as far in most areas as Hungerford, but it is a great place to get a start in the upper-level topics.

Thanks for your reply. I've decided to order the paper version of Ashs book after checking through it's contents. The preface sold me, where he was discussing the upsides of an intuitive introduction. The price was reasonable as well, and he actually includes a solution manual which is (for me) unheard of on this level.

 

[glb_lub]

I'm using Charles Pinter's book and I am enjoying it. Thanks. It was just what I was looking for.