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Sample:
Statement Of Purpose
Sample
SOP's
Math
The Mathematics Student admitted to UC
Berkeley, NYU
This
application is very important to me because completion of a PhD
degree in Mathematics will be the best chance for a unifying
career development with my labor of love - mathematics. I am
confident that when I become a serious and mature researcher my
desire to make a contribution to mathematics and to our
understanding of this world will remain my main driving force.
I
don't remember when I became keen on mathematics. At first it was
only entrainment as I found it exciting to solve intricate
problems. Later it became something more than a mere hobby. I
particularly enjoyed the ineffable feeling of triumph when you
realize that the problem is solved; that you have got the idea. I
think it is the profundity of this feeling that made mathematics
my chief enthusiasm. I have taken part in Olympiads and
Conferences. The most valuable contribution of these competitions
was a possibility to meet the same enthusiasts in mathematics. I
was particularly impressed when I was invited to participate in an
International Summer School and Conference in the ancient town of
Pereslavl-Zalessky. There I had an opportunity not only to work on
appealing research problems but also to interact closely with
working mathematicians such as X and Y. It is difficult to
describe the feelings that overwhelmed me but they did incite me
to further progress.
Being
a high school student I was doing a course on inequalities at Kiev
State University where I conducted my first research work. It was
essentially proof of Karamat inequality that utilized properties
of convex functions and Murhead inequality. It was unforgettable,
how the main idea of my central proof dawned upon me. That evening
I went to sleep the happiest boy in the world. Although,
relatively simple, I did something really innovative, something
that no one had ever done before with elementary methods. That was
my first moderate contribution to mathematics.
Later,
while being a freshman at the Moscow Institute of Physics and
Technology (MIPT), I refined the proof and presented it at the
52nd MIPT Scientific Conference where it was honored the first
prize.
In
my fourth year when students of our University get involved in
research activity, Professor X suggested to be my supervisor.
Under his guidance I wrote my thesis ”Integration of Multivalued
Mappings“ and defended it with Honors. Essentially it consisted
in a study of necessary and sufficient conditions under which
there exists Riemann integral of multivalued maps. My task was to
find some classes of sets of attainability and to investigate
relation between Lebesgue and Riemann integral for Multivalued
Maps. In this work I analyzed properties of spaces of compacts
with Housdorff metric and properties of support functions of
convex compacts and applied these theoretical findings to several
problems of theoretical mechanics. During this work I acquired a
broad range of research experience and background necessary for
further research in convex analysis.
My
current research work is devoted to differentiating of multivalued
mappings and differential inclusions. The main task is to become
familiar with ideas and approaches introduced in the Sci. D.
thesis of Professor X and to improve the results that are obtained
in it. One of the most challenging tasks in the project is to
obtain Pontryagin maximum principle in Hamiltonian form from
Lagrange form (in terms of tangent cones).
After
graduation I plan to continue my scientific career in mathematics.
Differential games, convex analysis and Optimization theory are of
particular interest to me. I have the strongest incentive to
advance as far as I can in this captivating science and feel
confident that application to the University of Chicago is the
best possible step to accomplish it. I would regard my admission
to your University not only as a great honor but also as a great
responsibility and an obligation to work hard.
Ivan
Ivanov
12/15/2002
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