Sample Statement of Purpose - Mathematics

Mathematics has always been my passion and obsession since my childhood. It always occupied most of

my time and I never had any ambition in my life other than being a research mathematician.

I was introduced to mathematics at an age as early as two years through basic arithmetic operations.

When I grew older to enter primary school I was haunted by the questions like what is addition and what

is subtraction etc. I was not at all happy with the basic school level idea of computing the sum for two

given numbers. I started asking the question to myself, what is a number. The non-rigorous nature of

school level mathematics always pained me and I tried to have my own way of defining mathematical

concepts for myself, which I came to know to be true later. When I was introduced to Euclidean

Geometry, the book told me the conditions when two triangles are congruent. But it never told when two

figures in a plane are called congruent. So I defined congruence for myself, and in the process I

conceived the notions of isometry and equivalence relations. This way I always tried to rigorize the

elementary mathematics. While leaving school I had developed my keen interest on number theory also.

In the penultimate year in my high school, I took part in Regional Mathematical Olympiad-about ten

thousand students took that test-and got selected for participation in Indian National Mathematical

Olympiad. I also took part in several mathematics talent search examination that is widely taken by almost

all school kids nowadays. And I never achieved anything except the top grade. I also took part in several

national level quiz competitions and represented my state. I also received the top grade in Australian

Mathematics Competition, in which students from all the countries participated.

After completing fourteen years of schooling I joined the Indian Statistical Institute (I.S.I) as an

undergraduate student in 1997 and completed Bachelor of Statistics (Honors), a three years

undergraduate course. After passing Bachelor of Statistics (Honors) with First Division in 2000, I joined

the Master of Statistics - a two years Masters program. I am presently in my final year of Master of

Statistics doing advanced courses in Mathematics. I.S.I is an Institute of National Importance in India and

reputed for its high quality teaching and research in Mathematics, Statistics and Probability. Entry to I.S.I

is a highly competitive business. Selection is done through a nation wide examination on mathematics

followed by an interview by the I.S.I faculty. This selection carries substantial financial support apart from

the tuition waiver all through the undergraduate years and the two years of masters. Besides the stipend

we are provided with other facilities like contingency grant etc. I.S.I. is the only institute in the country that

provides financial support for the undergraduates and hence the competition involved at the entry point is

very keen.

In I.S.I., I got interested in Probability Theory and Analysis. I received a very strong and rigorous training

in both analysis and probability theory. My advanced courses in analysis include courses on functional

analysis, Fourier analysis on locally compact abelian groups and Brown-Douglas-Fillmore Theory. And as

for probability I have been exposed to training in Brownian motion, Martingale Theory, Markov Processes,

Diffusion Theory and Stochastic Calculus. I got interested in Differential Geometry when I was trying to

understand the structure of Mbius Strip, whose non-orientability drew my attention. Then I visited our

Bangalore Center to start my study on Differential Geometry under Prof. V. Pati. Then subsequently I

visited the School of Mathematics of Tata Institute of Fundamental Research (T.I.F.R) (the national center

of the Government of India for Mathematics and nuclear Science) twice to take part in Visiting Students

Research Program (V.S.R.P.) where I worked with Dr. Pablo A. Gastesi on Differentiable Manifolds and

Lie Groups. During my next visit to T.I.F.R. I worked with Prof. T. N. Venkataramana on Analytic Number

Theory. I also attended acourse on Set Theory meant for the Doctoral students. While continuing my

study on Differential Geometry I felt that I should have some knowledge of Algebraic Geometry also. So I

started to learn Commutative Algebra and subsequently Algebraic Geometry also. This year I took part in

International Conference on Algebra and Geometry held during 7th to 12th December 2001 at University

of Hyderabad. I was the only student invitee in that conference. I am also attending the Workshop on

Operator Theory and Operator Algebra in Indian Statistical Institute, Bangalore.

Presently I am working on deriving some known properties of Riemann zeta function using some

probabilistic techniques, and metrizing certain class of figures in the plane and looking at the convergence

of shapes. And also I am reading some materials about Brownian motion on smooth manifolds.

Throughout my student life I had also given a lot effort to extra-curricular activities also. I have been

playing violin for quite a few years from now. I have always been interested in poetry also and have been

publishing them from time to time. I have also borne the responsibility of editing a few magazines on

literature and science awareness. I have been also acting in several stage performances of plays and

audio-dramas from my childhood.

I have also put great effort in order to teach mathematics at elementary level in a rigorous fashion. I have

been the in-charge of the mathematics cell of an organization that is involved in science awareness. Thus

teaching has always been of great pleasure to me. I carried out several training camps in mathematics

and many of my students performed excellently in Regional and National Mathematical Olympiads. And

my background in acting has always enhanced my skill of presentation. I have also given several student

seminars in my institute, which were widely appreciated. The topics of my seminar include Differential

Geometry, Analytic Number Theory, Measure Theory and many more. But learning mathematics for

myself has always remained at the center of my attention.

Apart from having the requisite background, I am confident that my dedication, hard work and strong will

to achieve success will help me create a niche for myself in the areas of my interest. I am also confident

that I will be able to meet the demands and requirements of the graduate courses and research work in

your department. I hope to pursue a career in research in mathematics, and eventually contribute

significantly to this branch of knowledge.Thank you very much for considering my application.