Re: Seeking Advice On Abstract Algebra Study Plan
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Mon, 3 Sep 2007 01:24:21 +0000 (UTC)
In article <1188769565.771078.266190@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<scaaahu@xxxxxxxxx> wrote:
First, please allow me to introduce myself.
I am an about-to-retire software engineer. I have a B.S. in Math. I am
currently doing research in automata theory as a hobby.
Once I retire from my job, I will devote myself full time in my
personal research project. So, I need prepare myself for the upcoming
challenge.
While I was in college, Herstein's Topics In Algebra was the book used
for the first year Algebra course, Lang's Algebra (first edition) was
the book used for the second year. These two books pretty much
illustrate my background and my algebra knowledge level. I was not an
A student in the class, though.
But do you know (or knew) the material in Herstein and in Lang's first
edition of Algebra?
My research project requires somewhat deep knowledge in algebra. I
believe I will also need to know quite a bit about Universal Algebra.
I am not sure how much I need to know about Topology and Analysis at
this moment. I doubt I need to know them very much. I do know that I
need to read two very specialized books, Word Processing In Groups by
Epstein and Cannon and Inverse Semigroups by Lawson, to some extent.
I am trying to draw my study plan before I start to read the two
specialized books. I have three choices,
i) Follow P. M. Cohn, i.e.
Classic Algebra, Basic Algebra, Introduction to Ring Theory, Further
Algebra, Universal Algebra and Free rings and their relations
(Classic, Basic and Further Algebra are revised editions of his
Algebra Vol. I, II and III)
ii) Dummit & Foote's Abstract Algebra, Burris's A course in Universal
Algebra and use the books in i) as references
iii) Go right ahead conduct my own research and use the books
mentioned above (including the two specialized books) as references
when necessary
I myself am more inclined to go for the last choice, conduct my own
research because I don't know how much longer I can live before I
publish my research results. On the other hand, I don't want to be a
crack pot. I don't want to see my research paper manuscript returned
by a research journal editor accompanied by a note saying that my
results were published by somebody else years ago.
Reading the books would give you knowledge of well-established
conventions, nomenclature, and notation, as well as the basic results
and the backbone of the subject. Reading well-established books will
not necessarily prevent you from rediscovering the wheel; that's an
occupational hazard even people actively working in a field run into.
P. M. Cohn's book series seem to be the most logical choice to me
because the approach he had taken in his books are close to the ideas
I have in automata theory. However, it'll be a long way to go.
D&F's Abstract Algebra is a very popular algebra book. Burris's book
is a standard text and has been referenced by many papers related to
Universal Algebra. However, in my humble opinion, P.M. Cohn's UA is
more beefy and again, close to my own research.
Then read the one closer to your research; Burris's book is more
recent, of course, but for the backbone of he subject you don't need
the latest. If you can already tell that Cohn is closer to your
research, then you should also be able to tell how much you need to
get started.
P.S. I cannot say exactly what topic in automata theory I am
researching in. I do have Lang's Algebra (revised third edition). I do
not plan to use it unless somebody can convince me it is a must read.
Lang is a very good reference, in fact almost invaluable as a
reference, but it is not necessarily the best book to learn material
from.
If you are already familiar with Herstein, then you might be better
served just re-reading it instead of trying to go through a new
book. It will give you the basics of Groups, Rings, and Fields, and
do so reasonable well. You can then pick and choose chapters or
sections from other books (D&F, or PM Cohn) for other topics such as
non-commutative rings, modules, etc. as needed.
There is of course no way to know, when doing research, just what part
of a particular subject will turn out to be useful in the end. One
cannot learn "all there is" about those subjects just in case: there
isn't enough time if you start at age 5, let alone when you
retire. You want enough to get you started, and enough so that you can
look around once you get stuck. Then you'll be able to formulate the
questions you need to answer in order to keep going. Being able to
formulate the question is really a very important, and often
overlooked, step in doing research.
So I would say to re-read Herstein to remind yourself of the basics,
read the two books you know will be needed, perhaps as much of Cohn's
UA as you feel is relevant, and then pick and choose topics as they
come up or as you feel you need them. Trying to read through six or
seven books on such sundry topics in order to get started seems like
overkill to me, but you'll know better what you think you need to do.
--
======================================================================
"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
.
- References:
- Seeking Advice On Abstract Algebra Study Plan
- From: scaaahu
- Seeking Advice On Abstract Algebra Study Plan
- Prev by Date: Re: polar equation to rectangular form
- Next by Date: Re: Mathematics: art or science?
- Previous by thread: Re: Seeking Advice On Abstract Algebra Study Plan
- Next by thread: Re: Repost of some math
- Index(es):
Relevant Pages
|
