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I am applying to Stanford 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 ****. 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 been used to obtain approximation algorithms for Optimization problems. An interesting connection with results in Interactive Proof Systems has yielded lower bounds on the approximability of various problems. I believe that these methods have a lot of potential. Members of the faculty at Stanford have done a lot of the pioneering work in these areas. Prof.YYY has been involved in the work on Interactive Proof Systems and semi-definite programming. I have read about these results in the course of my seminar (Junior Thesis), my summer training at the Tata Institute of Fundamental Research (TIFR), Bombay, and my B.Tech. Project (Senior Thesis). I find them very fascinating and intend to work with problems of a similar flavor.

I am convinced that I should pursue a career in research and teaching. For me, problem solving is an exhilarating experience, unequaled by anything else. It would be immensely gratifying for me to be able to contribute something to the understanding of a subject that has given me so much pleasure and joy. It would also be wonderful to have the opportunity to share with others that feeling of pleasure and joy, through teaching. My few experiences with teaching, as a tutor for an undergraduate course and as a lecturer in student workshops, have evoked favorable responses and have been thoroughly enjoyable. I believe that I have the capacity to make the commitment and accept the challenges that a career in research involves. I am confident that I have the requisite aptitude, exposure and motivation to make a meaningful contribution to my chosen field.

My summer training at TIFR has given me the experience of working in an organization oriented towards research. In the course of the two months I spent there, my interaction with the Theoretical Computer Science group has taught me a lot of things and also whets my appetite for more knowledge. I realize how important it is, as a researcher, to interact with other people working in the same field, and at the same time, am able to work individually.

A good research career can only be built above the firm foundation of a good education. With my long-term goal in mind, my immediate objective is to work towards a Ph.D. in Computer Science. Having done my undergraduate studies at undoubtedly one of the best undergraduate institutions in India, I would consider it my privilege to be able to pursue my doctoral studies at Stanford and avail of the excellent infrastructure facilities and research opportunities it has to offer. I am sure that the stimulating academic environment and interaction with the distinguished faculty at Stanford will prove immensely fruitful and facilitate my development as an individual Researcher in my field. I feel that Stanford has a lot to offer me, and at the same time, I am confident that I would be able to make a positive contribution to on going research work at Stanford University.

Having decided that I will engage in the pursuit of a career in research, I am fully aware of the implications. I am aware of the kind of dedication, resilience and resolve that it calls for. I feel that I am adequately prepared, both in having the technical qualifications, and in having the right mind-set for doctoral level Research work. I look forward to a long and mutually beneficial relationship with Stanford University.

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