Best Algebra Book, like Rudin & Halmos
Douglas Squirrel
development of linear algebra, with bountiful references to topics the student
will find in later courses.
Replacing Halmos with Rudin, FDVS with *Principles of Mathematical Analysis*,
and linear algebra with analysis yields a true statement.
If I want a similar classic rigorous treatment of the topics usually covered
in an Intro to Abstract Algebra course, what book should I buy? An additional
condition, which Halmos and Rudin also satisfy, is that one finds the book
useful for many years after taking the course. (I wish I hadn't sold my
copies of Halmos and Rudin!)
Thanks!
Douglas Squirrel
The winner by several votes is Herstein's *Topics in Algebra*. Jacobsen's
*Basic Algebra I* also got several mentions, but several people warned me that
his proofs are unclear and the writing is too.
Getting positive mention as well were Serre, Steinberger, Hungerford, and
Clark. Artin got two yesses and a passionate no.
Two people warned me against Lang's book.
I'm going to buy the Herstein. Thanks, everybody!
Mike Ruxton (CHS)
>If I want a similar classic rigorous treatment of the topics usually covered
>in an Intro to Abstract Algebra course, what book should I buy? An additional
>condition, which Halmos and Rudin also satisfy, is that one finds the book
>useful for many years after taking the course. (I wish I hadn't sold my
>copies of Halmos and Rudin!)
>Thanks!
>--dsqu...@reed.edu
Herstein, Nathanson, Artin, van der Waerden, ...
--
rux...@agcrr.bio.ns.ca
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Nothing will ever be attempted if all possible objections
must first be overcome. --- Samuel Johnson
Benjamin P. Carter
--
Ben Carter internet address: b...@netcom.com
Chow Chak On
: dsqu...@reed.edu (Douglas Squirrel) writes:
****** stuffs deleted *****
: Herstein, Nathanson, Artin, van der Waerden, ...
: --
: rux...@agcrr.bio.ns.ca
: _-=-_-=-_-=-_-=-_-=-_-=-_-=-_-=-_-=-_-=-_-=-_-=-_-=-_-=-_
: Nothing will ever be attempted if all possible objections
: must first be overcome. --- Samuel Johnson
Actually, for classic rigorous treatment of topics covered in introductory
abstract algebra course, I would like to say:
I.N. Herstein, Topics in Algebra -- a classic in abstract algebra, some
proofs of groups are hard to understand, i.e. those concerning the Sylow
theory. However, the treatments there are rigorous enough.
Nathan Jacobson, Basic Algebra -- a book for graduates, materials
covered in volume I are useful to students at undergraduate level. Though
not all are helpful.
M. Artin, Algebra -- a book covering many aspects of algebra. You can find
many ideas not found in the above but the proofs are not elegant
enough. (When compared with the proofs found in others, I have the feeling
that the proofs by Artin can hardly be called a proof!)
In addition to the above, I would like to recommend two more books:
Thomas W. Hungerford, Algebra -- despite this is one for graduates, the
coverage of topics in groups, rings and fields at undergraduate level is
straightforward enough that an average undergraduate can understand.
John B. Fraleigh, A First Course in Abstract Algebra -- a good substitute
of the book by Artin.
For the best way to learn abstract algebra, since many contemporary textbooks
use concrete algebraic objects in visualizing the picture, especially the
advanced topics, i.e. Sylow theory and finitely generated abelian groups,
For the elementary topics, I would like to suggest you to read the books
by Herstein or Fraleigh first.
For the advanced topics, read that by Fraleigh first and make sure you
understand those proofs using concrete objects, then read that by Herstein
and try to use the ideas you get from Fraleigh to understand the proofs by
Herstein.
Hope my ideas here help.
C.Chow
Hugh LaMaster
is the best junior-senior level algebra book, but it is also, to
my mind, unconscionably expensive (currently $85 U.S.).
So, my question would be, is there an inexpensive (e.g. Dover)
introductory abstract algebra book which is "almost as good"?
--
Hugh LaMaster, M/S 233-9, UUCP: ames!lamaster
NASA Ames Research Center Internet: lama...@ames.arc.nasa.gov
Moffett Field, CA 94035-1000 Or: lama...@george.arc.nasa.gov
Phone: 415/604-1056 #include <std_disclaimer.h>
Andrew Tucker
: I agree with the other posters that Herstein's "Topics in Algebra"
: is the best junior-senior level algebra book, but it is also, to
: my mind, unconscionably expensive (currently $85 U.S.).
: So, my question would be, is there an inexpensive (e.g. Dover)
: introductory abstract algebra book which is "almost as good"?
I don't know how these measure up to Herstein, but these are the abstract
algebra books listed in the latest Dover catalog:
Elements of Abstract Algebra by Allan Clark,$7.95
Abstract Algebra and Solution by Radicals by John and Margaret Maxfield,$7.95
An Introduction to Algebraic Structures by Joseph Landin, $7.95
A Concrete Approach to Abstract Algebra by W.W. Sawyer, $6.95
----
/* Andrew */
a_tu...@paul.spu.edu
Gerald Edgar
>
Not much out of line with other upper-division college textbooks in
technical subjects.
--
Gerald A. Edgar Internet: ed...@math.ohio-state.edu
Department of Mathematics Bitnet: EDGAR@OHSTPY
The Ohio State University telephone: 614-292-0395 (Office)
Columbus, OH 43210 -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Jerry Kuch
>I agree with the other posters that Herstein's "Topics in Algebra"
>is the best junior-senior level algebra book, but it is also, to
>my mind, unconscionably expensive (currently $85 U.S.).
Michael Artin's "Algebra" which was also mentioned in this thread is
similiar priced... around $76 US. I also don't like it much (it's not
awful I just don't think it's worth $76 or the $96 Cdn that I paid for
it). Hungerford is considerably cheaper. I think that I paid about $50
Canadian for it.
>So, my question would be, is there an inexpensive (e.g. Dover)
>introductory abstract algebra book which is "almost as good"?
Dover has Clark's "Abstract Algebra" which my former roommate read quite
heavily and liked a lot. I think it's in the $10 range.
--
o | Jerry Kuch je...@cecm.sfu.ca |
_ |-----------------------------------------------------------------|
= | "Be careful with your skiing... people get killed you know." |
o o | -- David Ford |
Hugh LaMaster
je...@reno.cecm.sfu.ca (Jerry Kuch) writes:
|> In article <328ksf$e...@onramp.arc.nasa.gov>
lama...@puma.arc.nasa.gov (Hugh LaMaster) writes:
|> >I agree with the other posters that Herstein's "Topics in Algebra"
|> >is the best junior-senior level algebra book, but it is also, to
|> >my mind, unconscionably expensive (currently $85 U.S.).
|> Dover has Clark's "Abstract Algebra" which my former roommate read quite
|> heavily and liked a lot. I think it's in the $10 range.
For $7.95, I will have to look at it:
Clark, Allan, 1935-
Elements of abstract algebra / Allan Clark. New York :
Dover Publications, 1984. xvii, 205 p. : ill. ; 22 cm.
LC CALL NUMBER: QA162 .C57 1984
SUBJECTS:
Algebra, Abstract.
DEWEY DEC: 512/.02 dc19
NOTES:
"Corrected republication".
Originally published: Belmont, Calif. : Wadsworth, c1971.
ISBN: 0486647250 (pbk.) : $7.95
LCCN: 84-6118 r86
****
a_tu...@paul.spu.edu (Andrew Tucker) writes:
|> I don't know how these measure up to Herstein, but these are the abstract
|> algebra books listed in the latest Dover catalog:
|> Elements of Abstract Algebra by Allan Clark,$7.95
|> Abstract Algebra and Solution by Radicals by John and Margaret Maxfield,$7.95
|> An Introduction to Algebraic Structures by Joseph Landin, $7.95
|> A Concrete Approach to Abstract Algebra by W.W. Sawyer, $6.95
And I will add another one:
Modern Algebra by Seth Warner, $17.95
The only ones I know about are the Maxfield book, and the book
by Seth Warner. The Maxfield book is a watered-down book
intended for future math teachers. It is in no way comparable
to Herstein, etc. The Warner book looks OK. It is a little
long-winded, yet seems to cover less overall, than Herstein.
I haven't looked at Clark yet, or Landin, or Sawyer (though
Sawyer sounds like Maxfield).
****
ed...@math.ohio-state.edu (Gerald Edgar) writes:
|> In article <328ksf$e...@onramp.arc.nasa.gov>
lama...@puma.arc.nasa.gov (Hugh LaMaster) writes:
|> >my mind, unconscionably expensive (currently $85 U.S.).
|> >
|> Not much out of line with other upper-division college textbooks in
|> technical subjects.
Well, yes and no. It certainly follows a trend. But, it is a trend
for which I find precious little justification. At $0.30/page, it
isn't the most absurdly priced book I have seen - probably Halmos
Naive Set Theory gets that honor, at $0.33/page, for what is rather
an old hat book with no special printing requirements. On the other
hand, Donald Knuth's "Concrete Mathematics" is a quality hardback
printing/binding job, and a new book, and it costs $0.08/page. This
is a price which is comparable to what books used to cost. When
you consider the cost reductions that have taken place in the
typesetting world in the last twenty years (I know about this:
One of my inlaws was a typesetter in a print shop before the
company shut down), isn't it kind of surprising that books
seem to cost about twice as much in real dollars as they did
twenty years ago?
But, we discussed this about three months ago, didn't we?
The conclusion then was that textbook companies perceive
that their prices are very inelastic, because textbook selection
is made by professors on grounds other than price, and that the
price could be arbitrarily set by the publisher.
When this was previously discussed, it was pointed out that if
authors would like to keep the price of their books down, the
time to specify this is when the contract is signed. I suggest
to those authors or potential authors who might be reading this
that you probably could get "Concrete Mathematics" pricing for
your book, if you ask for it -- less than 8 cents/page in 1994.
Douglas Squirrel
deal. Certainly better than a Dover book, dollar for dollar. The occasional
underline or margin note is more entertaining than bothersome.
Ruchira Datta
examples and problems. It seemed a little long-winded to me, but I only
saw it after I had already learned the material. I don't know what someone
learning from it would think.
Ruchira Datta
da...@math.berkeley.edu
Matthew P Wiener
For what it's worth, I got Herstein (2nd edition) *new* for about $25.
Of course, I had the foresight to buy it nearly 20 years.
I also picked up a copy of the first edition, used, for about $5.
--
-Matthew P Wiener (wee...@sagi.wistar.upenn.edu)