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I read somewhere that Herstein would prepare me nicely (abstract algebra-wise) for grad studies. I don't remember where I read it and now that I was about to buy the book I found out that there two Hersteins:

Topics in Algebra (Amazon Link)

and

Abstract Algebra (Amazon Link)

I wanted to figure out whether one is more advanced than the other or whether one is sequel to the other.

So I looked at both TOCs on Amazon and saw that Topics in Algebra is about 100 pages longer. Then I tried to figure out which one is more advanced by comparing. But it's kind of confusing because for example in just the group theory part, in one book there is a chapter ''Factor groups'' whereas in the other book the chapter is called ''Normal subgroups and Quotient groups''.

Now I don't know much more. So my question is:

Is one of the two Hersteins a sequel to the other, that is, are they meant to be read in a particular order?

And:

Is one of them more advanced than the other?

And:

Is it a good idea to read both?

I cannot tell how much overlap there is.

a student
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3 Answers3

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Answers:

  1. Neither book is meant as a sequel, they are independent texts.
  2. The more advanced (and more generally well-accepted) book is Topics in Algebra.
  3. It's always a good idea to read more (especially in mathematics), but generally I would advise (a) to read more than one author and (b) to read something other than Herstein's Abstract Algebra.

Additional comments, respectively:

  1. No further comment.
  2. I don't know of any occasion where somebody has referred to an algebra book as "Herstein" and has been referring to Abstract Algebra - they always mean Topics in Algebra. To add to this point, Topics in Algebra is highly recommended on the Chicago undergraduate mathematics bibliography, while Abstract Algebra isn't mentioned.
  3. If you're looking towards graduate studies, you might want to check out Abstract Algebra by Dummit/Foote instead. If that's too heavy (also, perhaps too hard at this stage), an oft-recommended text is Fraleigh's A First Course in Abstract Algebra.
Will R
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  • Thank you very much. This answers my question very well. Would you recommend or not recommend to read both Hersteins? – a student Jun 14 '16 at 03:39
  • If you want to read Herstein, go for Topics in Algebra. If you want to read another abstract algebra textbook at the same time, I would recommend reading Herstein's Topics in Algebra and Fraleigh's A First Course in Abstract Algebra together. They have a lot of overlap of course, but the material is presented very differently by the authors. Good luck! – Will R Jun 14 '16 at 06:52
  • I used Fraleigh in a masters level course as an undergrad which greatly helped prepare for graduate school; I've always had Herstein (Topics) around as well. Fraleigh is excellent and surely there is a newer edition than mine, another good one I remember is Gallian. For first year graduate work maybe Hungerford not Lang! – AlgTop1854 Oct 27 '23 at 17:37
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Topic in Algebra by Herstein was published in $1964$ while Abstract Algebra was published in $1986$. Most widely Topics is considered as a classical book in abstract algebra. Topics is I think best for the subject. I don't know they are sequels or not as Topics is an advanced book. Very well written and exciting. I think everybody should read Topics. I will recommend you to start with Topics if you like to.

Kushal Bhuyan
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1

Topics in Algebra is a graduate level text, Abstract Algebra is more solidly an undergraduate textbook. Having said that, I found having Abstract Algebra around while I was a graduate student was super helpful as a study aid (we were using Dummit & Foote), and is a good preparation for a graduate level course -- but not a replacement for a graduate course or text at all. The writing in Abstract Algebra is very approachable and clear, and the problems range from the trivial to the quite challenging. Topics in Algebra is not a starter book for the topic.

SupposeNot
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