I am applying to Stanford University for admission to the Ph.D. program in Computer Science. I am interested in Theoretical Computer Science, particularly in the Design
and Analysis of Approximation Algorithms, Combinatory and Complexity Theory.

My interest in Mathematics goes back to the time I was at school. This interest has only grown through my years in school and high school, as I have learnt more and more about the subject. Having represented India at the International Mathematical Olympiads on two occasions, I have been exposed to elements of Discrete Mathematics, particularly Combinatory and Graph Theory, outside the regular school curriculum at an early stage. The intensive training programs we were put through for the Olympiads have given me a lot of confidence in dealing with abstract mathematical problems.

My exposure to Computer Science began after I entered the Indian Institute of Technology (IIT), Bombay. The excellent facilities, courses and faculty have given me a firm background of the fundamentals in Computer Science. Having been exposed to the various facets of Computer Science in the course of my undergraduate studies, I have found Theoretical Computer Science most intellectually satisfying and stimulating. Courses like `Discrete Structures', `Data Structures and Algorithms’, Theory of Computation' and Algorithms and Complexity' have been my firm favorites. I find the problems in Theoretical Computer Science particularly appealing because of the flavor of abstract mathematics that I love so much. At the same time, the problems in this field
have a concrete basis, originating from practical problems in Computer Science. This adds to their appeal.

Recently, a lot of exciting developments have taken place in the field of approximation algorithms. The Markov chain approach and the primal/dual approach have emerged as powerful techniques for the development of approximation algorithms. More recently, semi-definite programming has...