Re: advice on how to study math in grad school
From: gowan (gowan4_at_hotmail.com)
Date: 08/30/04
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Date: 30 Aug 2004 12:32:43 -0700
mit12354@yahoo.com (Mike I. Thompson) wrote in message news:<6cb3c84c.0408290952.2d05a324@posting.google.com>...
> Hi,
>
> I was wondering how to approach studying math in graduate school. I'm
> starting my second year in math grad school, I'm in what is called the
> pure math program, and I've passed 2 of the 3 qualifying exams (the
> remaining exam is analysis, and i'll be taking it in a few weeks) but
> I feel there's a lot of basic math, especially analysis, that I don't
> know. I was wondering if a good approach to studying math is to set
> the goal of trying to learn all of "pure" mathematics. (Obviously,
> this is an impossible goal, but one can set impossible goals, and
> while they won't reach them, they would still get far.) So with this
> goal, I'd take time to thoroughly learn analysis (e.g. via various
> comprehensive texts in analysis), group theory, general topology,
> algebra, combinatorics, etc. all by working through various
> comprehensive texts on these subjects. I would eventually like to do
> research involving algebraic geometry, but I feel that maybe when I'm
> at that point, I'll come across a problem which I'll be able to solve
> only by knowing some trick I learned because I thoroughly studied some
> more basic math. Comments?
>
>
> Mike
Getting through your qualifying exams is of first importance. After
that you'll start looking for a research area and possibly a thesis
problem. Actually, every mathematician feels there is basic stuff
he/she doesn't know and would like to study. Once you begin your
research you will probably find such topics that are important to your
research. St that time you will find that you can pick up what you
need fairly fast because you have a context for it and a focussed
reason for studying it. If you still want to learn more you can get
ahold of advanced surveys of topics which will give you an overview
and references for learning the details. The MAA published a series
of books with survey articles on a wide variety of topics. They all
had titles such as "Studies in Analysis" and consisted of well-written
survey articles. They may be out of print now but your university
library will probably have them.
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