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Michael Artin

30 of 35 people found the following review helpful:
Exactly how an undergrad abstract algebra book should be, May 7, 2000
By "mikeu3" (Cambridge, MA USA) - See all my reviews

Pretty much any introductory abstract algebra book on the market does a perfectly competent job of introducing
the basic definitions and proving the basic theorems that any math student has to know.
Artin's book is no exception, and I find his writing style to be very appropriate for this purpose.
What sets this book apart is its treatment of topics beyond the basics--things like
matrix groups and group representations.
I suppose many introductory books shy away from much of the material on matrix groups
in Artin's book because it involves a little analysis (and likewise for the section
on Riemann surfaces in the chapter on field theory). However, Artin correctly realizes
that a reasonably mathematically mature student--even one who doesn't know
much analysis--will be able to profit from and enjoy the relatively informal treatments
he gives these slightly more advanced topics. Of course these topics can also be found
in graduate-level texts, but I for one would much rather be introduced to them via
an example-based approach such as that in Artin than through the diagram-chasing obscurantism
in more advanced books. I happened upon this book a little late--in fact,
only after I'd taken a semester of graduate-level algebra and already felt like analysis
was the path I wanted to take--but I'm beginning to think
I would have been more keen on going into algebra if I'd first learned it from a book like this one.