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Differences between Artin's Algebra editions?

  • Algebra
  • Thread starter MidgetDwarf
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  • #1
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Main Question or Discussion Point

Will be taking my first abstract algebra course in the fall. I am going through Pinter's:A Book On Abstract Algebra. Pinter is very simple, but the ideas are lucid and gives great motivation.

I am familiar with proof writing. I can read books such as Axler LA, Shilov Analysis, and Courant Differential and Integral Calculus.

For the abstract algebra course in the Fall, there is no required textbook. The teacher teaches from his own written notes.

I have seen Artin recommended on these forums. I have found the first edition for less than $20, and the second edition for $80.
Is their any significant difference between the two editions? Ie., numerous typos in the first?explanations made clearer in the 2nd? etc?

Also, how does this book compare to say Harsthorne or Dummit and Foote?
 

Answers and Replies

  • #2
mathwonk
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get the first edition. always get the first edition. in all cases, it is the first edition that makes the reputation of the book. if the first edition is not excellent the book does not become recommended. i can think of maybe one counterexample to this principle: lang's book on differential manifolds, where the first edition was very short and terse and later ones incorporated much more material. maybe also lang's book on abelian functions which also went from a short pamphlet to an actual book. In over 50 years experience with hundreds and hundreds of books, those are almost the only counterexamples i know of.

dummit and foote is a book that can be used for undergraduate and graduate courses, hence is much more comprehensive than artin. but artin is perhaps a higher level master than are dummit and foote, so his book is written with more depth of insight, at least in my personal opinion. so do you want the book that is written to read easier by the average student, or the one that is going to offer more insight to the serious student? Artin's book was written as the text for talented undergrads at MIT, and Dummit and Foote is aimed at a larger audience. Which one are you? So take a look at them and decide which speaks to you. I think D&F is probably easier to read, but I prefer artin. I own both and use both from time to time. When I first read artin I had to go more slowly than I expected.

I am not familiar with an algebra book by hartshorne, but he writes very carefully and well, and is an expert. his algebraic geometry book is a standard and his "geometry-euclid and beyond" book is simply great.

but all those authors are fine, you cannot go wrong. you should really look at them and decide.


edit: there does not seem to exist any algebra book by hartshorne, and for you i do not recommend his AG book, as it is quite abstract and advanced.
 
  • #3
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Thanks a lot for the detailed response. I confused Harsthrone with Herstein, my apologize. I prefer books that explain fewer things and offer more insights into the material presented. Ie., Axler has less material than say Friedberg/Insel/Spence Linear Algebra, but I never truly understood what a linear transformation , eigen values, and Jordan Canonical forms really meant until Axler. Granted, Friedberg is a great book, but I felt that Axler carefully wrote his explanations after many revisions. At least, that is what I got.

I was looking for prices for Dummit and Foote, and they are quite expensive.
I am leaning towards Martin. Have you viewed Herstein?
 
  • #4
mathwonk
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i read herstein 50 years ago, it is very slick and to me not so insightful. i always felt the explanations went in one ear and out the other, but some people like it. there are a lot of good exercises, but i never really got much out of it. artin is infinitely better in my estimation. the high price of dummit and foote reflects its popularity as a general text, whatever sells, goes up in price, and tends to be less than the top level work in terms of being challenging.

oh you meant artin, not martin. i agree.

here is a used copy for $32.50 + shpg:

https://www.abebooks.com/servlet/BookDetailsPL?bi=22799211269&searchurl=sortby=19&an=dummit%2C+foote&cm_sp=snippet-_-srp1-_-title1


you get what you pay for usually, but if you want a free book, here is my webpage with free algebra notes for math 843-4-5:

http://alpha.math.uga.edu/~roy/
 
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  • #5
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Thanks. I ordered both books. If I get stuck in Artin, I can look at Dummit and Foote. I had a look at your website. I really liked the explanation of the well ordering principle. Our instructor skipped it, because he said he only used it twice in graduate school, so it was not important according to him. I think he is an Analysist?
I think the definition of the well ordering principle is somewhat similar to the definition of minimal element of a well ordered set? Except, that well ordering principle applies to only subsets of a non empty set of natural numbers and it ensures the existence of a "minimal element"?

I will be printing the algebra notes. Im sure they are just as clear. Greatly appreciate your help and recommendations.
 
  • #6
mathwonk
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the well ordering principle applies to any well ordered set, such as the natural numbers. but in fact the axiom of choice implies that every set can be well ordered, a rather amazing statement, if you try to imagine a well ordering say of the real numbers. so the well ordering principle is quite useful in dealing with the natural numbers, i.e. in number theory, and it has another equivalent version, called zorn's lemma, that is also quite useful in many areas. zorns lemma asserts that in any ordered collection where strictly ordered chains always have an upper bound, then there exists a maximal element. This situation occurs much more often in nature than do well ordered sets, e.g. the collection of all independent sets of vectors in a given vector space satisfies the hypothesis, and this guarantees the existence of maximal sets of independent elements, i.e. bases of infinite dimensional vector spaces.
 
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  • #7
Demystifier
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get the first edition. always get the first edition. in all cases, it is the first edition that makes the reputation of the book. if the first edition is not excellent the book does not become recommended.
Interesting theory!
 

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