Sample Statement of Purpose for Mathematics
Statement by MIPT Alumnus (01/2003)
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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