Textbook comments request (Hungerford's Algebra)
Arturo Magidin
course next Fall (the usual groups/rings/fields sequence).
The book I like the most, Herstein's "Topics", is way too expensive
and somewhat dated. The other book I've used in the past, Dummit and
Foote's, is also too expensive in my opinion. The only other book I
have experience with is Lang's "Algebra" (which was the textbook when
I took the graduate algebra sequence), but while I think it is an
excellent reference, I don't find it a very good textbook (and
probably too hard for the students here anyway). Rotman's book looked
good, but I'm not sure if I'm comfortable trying to teach a course in
which all functions are written on the right...
I am wondering if anyone in the newsgroup either learned from or has
taught from Hungerford's book, and if so what their feeling for the
book is. If you have other recommendations (I'm looking for something
that doesn't go too far above the range of the Springer GTM series,
which usually runs around US$60) I would also like to hear them.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
Bart Goddard
> I am wondering if anyone in the newsgroup either learned from or has
> taught from Hungerford's book, and if so what their feeling for the
> book is.
I took a graduate sequence out of Hungerford. At the time,
I hated it, but I've mellowed since then (and I've seen
what the competition is.) I think it's a very usable text
if one doesn't get bogged down in Chapter 1. It doesn't
do a lot with category theory (which is a good thing at
this level, I think.) It's kind of "dense" and encyclopedic,
so it makes for a good reference, (but first reading can
be heavy sledding for novices.) It's going to be a level
harder than Herstein's "Topics". It has tons of exercises.
(Way more than Lang or Herstein, IIRC.)
Bart
--
Fundamental Truth of the Universe: The dumber the louder.
gow...@hotmail.com
Herstein's book was first published when I was a graduate student and,
at the time, was considered an undergraduate level text though plenty
of graduate students used it to prepare for qualifying exams :)
Anyhow, how about Michael Artin's _Algebra_? Level seems right and
it's not too encyclopedic, lots of examples ...
Arturo Magidin
gow...@hotmail.com <gow...@hotmail.com> wrote:
>Herstein's book was first published when I was a graduate student and,
>at the time, was considered an undergraduate level text though plenty
>of graduate students used it to prepare for qualifying exams :)
I had Herstein as an undergraduate book for the algebra
sequence, though my undergraduate sequence was much stronger than most
I've seen in the U.S. (it was even marginally higher level than the
one at Berkeley when I was there).
>Anyhow, how about Michael Artin's _Algebra_? Level seems right and
>it's not too encyclopedic, lots of examples ...
Hmmm... As I hinted, price is an issue. I feel extremely uncomfortable
asking the students to shell out $100 or more on a textbook. I think
it is completely unreasonable for Herstein's book to be priced at
about $125, for example.
Alas, Artin's "Algebra", from Prentice Hall, is also listed at $125.
I think it is way too much; if I were willing to ask the students to
spend that much, I would go with either Herstein or Dummit/Foote.
Dave L. Renfro
> I am wondering if anyone in the newsgroup either
> learned from or has taught from Hungerford's book,
> and if so what their feeling for the book is.
It just so happens that, about two months ago, I wrote
some comments about Hungerford's book in a couple
of e-mails to a former student of mine who will be
starting graduate school this Fall.
-------------------
A book that used to be fairly standard is Hungerford's
"Algebra". He later wrote an undergraduate level algebra
text, which I don't have a copy of or know much about. Here,
I'm talking about his thick graduate level algebra text.
I've heard people say that it's a bit advanced, but these
comments are probably from those who have no experience
with other graduate level algebra texts (Jacobson's
"Basic Algebra II", Lang's "Algebra", and some others),
because it's actually quite straightforward compared to
some of these others. A good undergraduate algebra course
is almost overkill preparation for Hungerford, because
he pretty much starts at the beginning with every topic
and includes a lot of details that other graduate level
texts sometimes omit. Also, his exercises aren't especially
difficult -- probably easier than a third to a fourth of
the exercises in Herstein's undergraduate text "Topics
in Algebra". Finally, I like Hungerford because there
are virtually no typos or errors (which promotes a
feeling of trust in the text) and he carefully
cross-references things throughout the text. I would
also guess the fact that I've covered the entire text
in three different semesters of graduate algebra classes
(the most advanced being a commutative algebra course
that covered the last third of the text) may also have
something to do with my liking the book.
-------------------
The next comments are in response to his concern
on seeing some discussion of category theory in
Hungerford's book and thinking this could be a
problem, because he's not sure if he wants to
get all involved in that area, but if he later
decides to, he'll take a course in category theory.
-------------------
Hungerford makes very little use of category theory
until later in the book (primarily the last third of
the book). In particular, I think you'd lose almost
nothing by ignoring it in initial chapters on groups
and rings. Also, very few places offer courses in
category theory, and I'd imagine only those going
into a handful of areas specifically involving category
theory would even be taking such a course. (Exceptions
would be universities with a faculty member who is
really interested in the subject and who has done
a good job of eliciting interest in a general survey
course.) It's somewhat akin to taking a course in
mathematical logic. Most everyone picks up basic
logical issues involving quantifiers and such (the
negation of a statement preceded by (for all)(there
exists)(for all) is the negation of the statement
preceded by (there exists)(for all)(there exists),
for example) "on the fly" in upper level courses,
or sometimes (more often than not in the past 20-25
years, though) in various "transitions to advanced
mathematics" type courses. You don't have to take
a course in mathematical logic (and I'm not talking
about symbolic logic in a philosophy department) for
what you need, and the same is true for category theory.
[snip several paragraphs about functors in
algebraic topology, double duals of vector
spaces and natural transformations, etc.]
-------------------
Dave L. Renfro
Arturo Magidin
Dave L. Renfro <renf...@cmich.edu> wrote:
>Arturo Magidin wrote (in part):
>
>> I am wondering if anyone in the newsgroup either
>> learned from or has taught from Hungerford's book,
>> and if so what their feeling for the book is.
>
>It just so happens that, about two months ago, I wrote
>some comments about Hungerford's book in a couple
>of e-mails to a former student of mine who will be
>starting graduate school this Fall.
Thank you for your comments. I really appreciate them!
(Thanks to everyone else who has or will comment, as well; I've been
sending personal thanks, but the one to Dave bounced...)
quasi
(Arturo Magidin) wrote:
>I'm trying to decide on a textbook for a beginning graduate algebra
>course next Fall (the usual groups/rings/fields sequence).
>
>The book I like the most, Herstein's "Topics", is way too expensive
>and somewhat dated.
Great problems, but definitely dated. Also, on the whole, it's clearly
more of an undergraduate level text
>Dummit and Foote's, is also too expensive in my opinion. The only other book I
>have experience with is Lang's "Algebra" (which was the textbook when
>I took the graduate algebra sequence), but while I think it is an
>excellent reference, I don't find it a very good textbook (and
>probably too hard for the students here anyway).
Lang's Algebra is elegant but far too compact to serve as an
introductory text, even at the graduate level. More examples are
needed, more motivation. Students deserve to know why something is
being defined. What concept or problem motivates the definition? Very
few authors are able to do that well.
>Rotman's book looked good, but I'm not sure if I'm comfortable trying to teach a course in
>which all functions are written on the right...
Functions on the right -- ugh. Forget that book. Think about all the
time wasted making mental translations. The students would surely hate
such a book right from the outset.
>I am wondering if anyone in the newsgroup either learned from or has
>taught from Hungerford's book, and if so what their feeling for the
>book is.
The table of contents is fine, however, the book itself is dry to the
point of being not likeable, in my opinion.
>If you have other recommendations (I'm looking for something
>that doesn't go too far above the range of the Springer GTM series,
>which usually runs around US$60) I would also like to hear them.
There's an online book by Robert Ash titled
Abstract Algebra: The Basic Graduate Year
that looks very good and which is actually _free_.
Here's the link:
<http://www.math.uiuc.edu/~r-ash/Algebra.html>
Also, it can be downloaded as pdf files and thus can be read offline.
There is another book, also by Robert Ash, titled
Basic Abstract Algebra
for Graduate Students and Advanced Undergraduates
published as a Dover Paperback.
Perhaps it's essentially the same as the online text, I'm not sure. In
any case, it's inexpensive -- about $15.
Here's a link:
<http://www.amazon.com/Basic-Abstract-Algebra-Undergraduates-Mathematics/dp/0486453561>
quasi
franz_le...@freenet.de
> In article <1178114575.881745.258...@u30g2000hsc.googlegroups.com>,
> >Anyhow, how about Michael Artin's _Algebra_? Level seems right and
> >it's not too encyclopedic, lots of examples ...
>
> Hmmm... As I hinted, price is an issue. I feel extremely uncomfortable
> asking the students to shell out $100 or more on a textbook. I think
> it is completely unreasonable for Herstein's book to be priced at
> about $125, for example.
>
> Alas, Artin's "Algebra", from Prentice Hall, is also listed at $125.
Wow. The German edition from Birkhaeuser sells for EUR 38.
franz
Stephen J. Herschkorn
>I'm trying to decide on a textbook for a beginning graduate algebra
>course next Fall (the usual groups/rings/fields sequence).
>
>The book I like the most, Herstein's "Topics", is way too expensive
>and somewhat dated. [...]
>
I always thought of Herstein as an undergraduate text. If you are going
to go that level, how much is Jacobson going for these days?
--
Stephen J. Herschkorn sjher...@netscape.net
Math Tutor on the Internet and in Central New Jersey and Manhattan
Arturo Magidin
Stephen J. Herschkorn <sjher...@netscape.net> wrote:
>Arturo Magidin wrote:
>
>>I'm trying to decide on a textbook for a beginning graduate algebra
>>course next Fall (the usual groups/rings/fields sequence).
>>
>>The book I like the most, Herstein's "Topics", is way too expensive
>>and somewhat dated. [...]
>>
>
>I always thought of Herstein as an undergraduate text.
Herstein would seem to fit comfortably in between the locally expected
levels of the undergraduate and graduate courses.
>If you are going
>to go that level, how much is Jacobson going for these days?
I don't know if it is still in print. My two volumes are from Freeman,
one old and used, one newer one bought about 12 years ago, and I
cannot seem to find it in Amazon or elsewhere.
Arturo Magidin
quasi <qu...@null.set> wrote:
>>I am wondering if anyone in the newsgroup either learned from or has
>>taught from Hungerford's book, and if so what their feeling for the
>>book is.
>
>The table of contents is fine, however, the book itself is dry to the
>point of being not likeable, in my opinion.
>
>>If you have other recommendations (I'm looking for something
>>that doesn't go too far above the range of the Springer GTM series,
>>which usually runs around US$60) I would also like to hear them.
>
>There's an online book by Robert Ash titled
>
> Abstract Algebra: The Basic Graduate Year
>
>that looks very good and which is actually _free_.
I'll take a look. Thanks!
Bill Dubuque
>gow...@hotmail.com <gow...@hotmail.com> wrote:
>
>> Herstein's book was first published when I was a graduate student and,
>> at the time, was considered an undergraduate level text though plenty
>> of graduate students used it to prepare for qualifying exams :)
>
> I had Herstein as an undergraduate book for the algebra
> sequence, though my undergraduate sequence was much stronger than most
> I've seen in the U.S. (it was even marginally higher level than the
> one at Berkeley when I was there).
>
>> Anyhow, how about Michael Artin's _Algebra_? Level seems right and
>> it's not too encyclopedic, lots of examples ...
>
> Hmmm... As I hinted, price is an issue. I feel extremely uncomfortable
> asking the students to shell out $100 or more on a textbook. I think
> it is completely unreasonable for Herstein's book to be priced at
> about $125, for example.
>
> Alas, Artin's "Algebra", from Prentice Hall, is also listed at $125.
> I think it is way too much; if I were willing to ask the students to
> spend that much, I would go with either Herstein or Dummit/Foote.
Algebra: 3rd ed 1988, MacLane & Birkhoff, is $59 from AMS
http://www.ams.org/bookstore-getitem?item=CHEL-330-H
--Bill Dubuque
Arturo Magidin
Bill Dubuque <w...@nestle.csail.mit.edu> wrote:
>Algebra: 3rd ed 1988, MacLane & Birkhoff, is $59 from AMS
>http://www.ams.org/bookstore-getitem?item=CHEL-330-H
I didn't know it was still in print... Thanks.
Paul Sperry
<mag...@math.berkeley.edu> wrote:
> In article <y8zzm4n...@nestle.csail.mit.edu>,
> Bill Dubuque <w...@nestle.csail.mit.edu> wrote:
>
> >Algebra: 3rd ed 1988, MacLane & Birkhoff, is $59 from AMS
> >http://www.ams.org/bookstore-getitem?item=CHEL-330-H
>
> I didn't know it was still in print... Thanks.
Don't confuse Mac Lane and Birkhoff with the classic Birkhoff and
Mac Lane. I much prefer the later to the former.
In regard to Hungerford, it is very teachable and "semimodern". I
prefer it to any of the other texts mentioned with which I am familiar.
Be aware that solutions to the first few Chapters' exercises for
Hungerford are available on the internet.
--
Paul Sperry
Columbia, SC (USA)
William C Waterhouse
mag...@math.berkeley.edu (Arturo Magidin) writes:
> I'm trying to decide on a textbook for a beginning graduate algebra
> course next Fall (the usual groups/rings/fields sequence).
>
> good, but I'm not sure if I'm comfortable trying to teach a course in
> which all functions are written on the right...
Which book was this? Both _A First Course in Abstract Algebra_ and
_Advanced Modern Algebra_ write functions on the left of the variables.
(But again the price for either is high).
William C. Waterhouse
Penn State
porky_...@my-deja.com
>
> >Anyhow, how about Michael Artin's _Algebra_? Level seems right and
> >it's not too encyclopedic, lots of examples ...
>
> I think it is way too much; if I were willing to ask the students to
> spend that much, I would go with either Herstein or Dummit/Foote.
>
> Arturo Magidin
> magidin-at-member-ams-org
I've paid about $25.00 for my Artin, Chinese edition, softcover and
grayish paper but otherwise perfectly usable. Of course, you can't ask
your student to chase the textbook on eBay (this is where I got it) or
elsewhere. Which is a shame since Artin puts fun into the Abstract
Algebra, something many other textbooks fail to do.
Stephen J. Herschkorn
>I'm trying to decide on a textbook for a beginning graduate algebra
>course next Fall (the usual groups/rings/fields sequence).
>
Another textbook that is the favorite of many is Isaacs. I myself do
not know it well. I do know that it contains no references (i..e.,
footnotes or bibliography). This absence annoys me,
Arturo Magidin
>
>>I'm trying to decide on a textbook for a beginning graduate algebra
>>course next Fall (the usual groups/rings/fields sequence).
>>
>
>Another textbook that is the favorite of many is Isaacs. I myself do
>not know it well. I do know that it contains no references (i..e.,
>footnotes or bibliography). This absence annoys me,
Ah; I see why the confusion I caused elsewhere... I misidentified
Rotman as the book that has functions on the right. I got it confused
with Isaacs.
Arturo Magidin
William C Waterhouse <w...@math.psu.edu> wrote:
>In article <f1a3nk$2uhv$1...@agate.berkeley.edu>,
>mag...@math.berkeley.edu (Arturo Magidin) writes:
>> I'm trying to decide on a textbook for a beginning graduate algebra
>> course next Fall (the usual groups/rings/fields sequence).
>>
>>... Rotman's book looked
>> good, but I'm not sure if I'm comfortable trying to teach a course in
>> which all functions are written on the right...
>
>Which book was this? Both _A First Course in Abstract Algebra_ and
>_Advanced Modern Algebra_ write functions on the left of the variables.
You're right; turns out I got it confused in my head with Isaacs's
book ("Algebra: A Graduate Course"). While he sometimes does write the
function on the left, he often puts it on the right so that the
composition rule work out.
Michael Press
mag...@math.berkeley.edu (Arturo Magidin) wrote:
> In article <1178114575.8...@u30g2000hsc.googlegroups.com>,
> gow...@hotmail.com <gow...@hotmail.com> wrote:
>
> >Herstein's book was first published when I was a graduate student and,
> >at the time, was considered an undergraduate level text though plenty
> >of graduate students used it to prepare for qualifying exams :)
>
> I had Herstein as an undergraduate book for the algebra
> sequence, though my undergraduate sequence was much stronger than most
> I've seen in the U.S. (it was even marginally higher level than the
> one at Berkeley when I was there).
Has the expected level of competence at the undergraduate level
decreased? I was not a mathematics major, but took algebra out of
Herstein, and considered it par for the course, as did everyone
else.
By the way, it was one of the best elective classes I ever took
for the short and long term benefits conferred. As a programmer I
was always puzzled at the antipathy to mathematics manifested by
other programmers.
--
Michael Press
Rogério Brito
On 05/04/07 21:52, Michael Press wrote:
> Has the expected level of competence at the undergraduate level
> decreased? I was not a mathematics major, but took algebra out of
> Herstein, and considered it par for the course, as did everyone
> else.
I don't know if it has decreased or not, but one thing that was mentioned by a
friend of mine that has taught at the University of Ohio and University of
Tennessee is that while our (brazilian) undergraduate courses cover deeper
aspects than what is covered by undergraduate courses in the US, people usually
make graduate students sweat a lot to get their degree, basically nullifying the
difference in the degrees obtained at a Ph.D. level.
Oh, BTW, one cultural difference that I see is that a Master's degree in the US
is mostly taken as a "consolation prize" for those that can't get a Ph.D.
degree. Is that impression of mine correct?
Here, a Master's degree is almost *required* to enter a Doctorate level program
and going the Doctorate level is really not the norm here (quite a few
exceptions I'd add) and it can even touch quite a bit of research (at least,
mine did).
> By the way, it was one of the best elective classes I ever took
> for the short and long term benefits conferred.
Indeed, I'd say that Abstract Algebra is absolutely essential for developing the
formal, *mathematical thinking* that one should have for writing elegant programs.
> As a programmer I was always puzzled at the antipathy to mathematics
> manifested by other programmers.
You can't really imagine how many headaches I get when I try to give a stronger
mathematical bias when I'm teaching Analysis of Algorithms or Elementary Graph
Theory.
And that ruins all the beauty of intelligent, elegantly devised algorithms. :-(
Regards, Rogério Brito.
--
Rogério Brito : rbr...@ime.usp.br : http://www.ime.usp.br/~rbrito
Homepage of the algorithms package : http://algorithms.berlios.de
Homepage on freshmeat: http://freshmeat.net/projects/algorithms/