advice on how to study math in grad school

From: Mike I. Thompson (mit12354_at_yahoo.com)
Date: 08/29/04 

Date: 29 Aug 2004 10:52:53 -0700

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

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