| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
I am very interested in Algebraic Topology, and I had taken a graduate
level Algebraic Topology in U of I. However, even though I got
an A in that course, I felt that the whole subject was was rushed during
the course work and I had barely skimmed the surface of the subject
(even at the introductory level). So Now I am thinking of reading about
the subject. The text book used for the course was the infamous
_Algebraic Topology_ by Spanier :-) (impossible to read).
My college professor recommended
a book by C. R. F. Maunder also titled Algebraic Topology, but I
still think it is not a good text book. Since then I have looked
at many other books on the subject, but none of them suits my need.
Would someone on the net recommend a good introductory Al. Top.
book for me (At 1.5 - 2 year of graduate level)?
I am also interested in Manifold theory even though I never had
a course on the subject. So would someone also recommend a book
please?
Finally, I will eventually learn some lie group and lie algibra.
Would someone tell me what kind of prerequisit I need in order to
get into that subject? My algebra background is at the Hungerford
level. Well that is a mouthfull. Thanks in advance
Eugene
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 878.1 | a few (somewhat biased) references | CTCADM::ROTH | If you plant ice you'll harvest wind | Mon May 23 1988 12:03 | 41 |
I'm an engineer, not a math person, so my perspective may or may not
be useful. In particular, I don't like the unmotivated "abstract
nonsense" that seems fashionable in a lot of the pure math books.
Still, I've been curious about some of these things, and have read
up on them - from a physics and engineering point of view.
- Gravitation
Misner, Thorne, and Wheeler
Excellent chapters on differential geometry with great visual
insight. A neat book (about the size of the Manhattan phone book)
- Geometric Methods of Mathematical Physics
Schutz (I think) - in paperback form
Very clear and intuitive introduction to differential geometry
for physics.
- Mathematical Methods of Classical Mechanics
V. Arnold (probably Springer Verlag)
Has theory of differential geometry in one of the contexts it
came from - configuration spaces of mechanical systems. Also
symplectic geometry.
- Theory of Continuous Groups
C. Loewner, MIT Press
I bought this at a book sale on impulse - it doesn't seem well known
but is a very nice intro to Lie groups.
Another good way to learn topology is to read about Riemann Surfaces;
this is where topology really came from in the first place. The
geometric theory of complex variables is really beautiful - and actually
useful to engineers, in the form of conformal maps, feedback theory,
filter synthesis.
If you want trendy looking commutative diagrams and lots of thin-air
abstract algebra, the above books may not be for you.
- Jim
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| 878.2 | Rather personalized book | MJG::GRIER | In search of a real name... | Tue May 24 1988 10:25 | 12 |
Over the summer, I'm doing some readings with one of my professors
in Algebraic Topology. In asking him what books he recommends, he
didn't really have any. He normally ends up writing his own
mimeographed books by the end of a semester which cover the topic
usually pretty well (just finished Complex Analysis with him.) If
you're interested, drop me a line...
(Professor is A. Robb Jacoby from the University of New Hampshire.)
-mjg
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