Re: advice needed on what classes to take

In article <[EMAIL PROTECTED]>,
Keder Ipkess <[EMAIL PROTECTED]> wrote:
>I am an undergrad but plan to enter grad school to study statistics(PhD
>programme in financial mathematics). Besides classes from statistics
>department(probability theory, linear regression e.t.c.) ,i need advice,
>what pure math classes i should take to prepare myself. I have taken
>calculus(up to multivariable calculus and vector calculus), linear algebra
>and discrete mathematics.

>Should i also take classes like complex analysis, real analysis ? 

A STRONG real analysis, which is really what calculus is
about and more, is essential for anything in statistics.  It
is your statistics courses, other than probability, if that
is a good course, which are likely to be of little value.
Linear algebra is much used, but a cookbook course may not
be sufficiently strong.  Learning how to calculate is not of
that much importance without understanding what it means.

A good complex analysis course will help greatly.  Fourier
transforms are heavily used.

What you need is strong abstract mathematics.  The type of
stochastic processes and their treatment used in financial
mathematics uses measure theory and measure-theoretic
probability; these are rarely at the undergraduate level,
but the real variables background is needed for them.

        Do these
>classes have any(non vague) connection with statistics ?

Not only now, they had when I started doing statistics
almost 60 years ago.  It was my knowledge of mathematics
which was important, and not just the immediately relevant
mathematics, but the abstract concepts.

What was of little importance then, and less now, in
understanding statistics is a catalog of statistical
methods.  A strong undergraduate mathematical statistics
course can replace a graduate course, but a weak one must
be repeated.

                What about function
>analysis , fourier analysis ?

Fourier SERIES are of some, but not much, importance.
Fourier analysis is heavily used in probability, and
not enough in statistics.  Some of functional analysis
is of considerable use.

>Thanks in advance.




-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
[EMAIL PROTECTED]         Phone: (765)494-6054   FAX: (765)494-0558