Re: advice on how to study math in grad school

From: Robert Vienneau (rvien_at_see.sig.com)
Date: 08/29/04 

Date: Sun, 29 Aug 2004 19:35:28 -0400

In article <6cb3c84c.0408290952.2d05a324@posting.google.com>,
mit12354@yahoo.com (Mike I. Thompson) wrote:

> 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?

A couple of months back I came across a book that purported to
summarize the (undergraduate?) math that one needed to do grad work
in math. It seemed to have stuff from a lot of different fields,
and lots seemed to me to be fairly advanced. Unfortunately, I forget
the title and author. 

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