Here are my thoughts on this. The most important mathematical
requirements are calculus, real analysis, and linear algebra.
You need to to know these topics thoroughly. Whatever
textbooks are used for undergraduate math majors wherever you
are are probably fine. You also need to know non-measure
theoretic probability at the level of a book like Pitman's
Probability.
Despite Herman Rubin's admonitions against weak courses, I think
it is very useful to know some "basic" statistics at the level
of Rice's "Mathematical Statistics and Data Analysis" or DeGroot's
"Probability and Statistics." A very concise overview of statisical
theory is Silvey's book, which I think may be called "Statistics."
If you don't have exposure to statistics at least at this level,
you may have trouble understanding the motivation for many things
you do in first year courses. I had this problem myself.
During your first year, I think you will find Serfling's
Approximation Theorems of Mathematical Statistics is a
useful reference.
Good luck.
Mike
In sci.math Cengiz <[EMAIL PROTECTED]> wrote:
: First of all thank you for all replying to my original question. Out
: of curiousity, at what textbook level should one's understanding of
: analysis, linear algebra, statistics, probability, etc be upon
: entering a a typical PhD program. I am trying to gauge which gaps in
: my background I need to fill in before I enter such a program and
: truly appreciate your help.
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