**GOALS**

I am applying to Princeton University for admission to the Ph.D. program in (Computer Science}. My research interests lie in the field of Theoretical Computer Science. More specifically, I am interested in the Design and Analysis of Algebraic, Combinatorial and Number Theoretic Algorithms as well as their applications. Other areas that interest me are Theory of Computation, Complexity Theory and Geometric Algorithms.

My long-term goal is to be actively involved with research and teaching in an area that I love. I look forward to such an involvement as a faculty member at a reputed university. A Ph.D. in one of the aforementioned areas would be the crucial first step towards this goal.

**PERSONAL-BACKGROUND**

Both my parents have done their Ph.D.’s in Mathematics and my father is an active researcher in Applied Mathematics. This had inculcated in me a love for Mathematics right from my school days. On the other hand, I entered school in the same year in which the “personal computer revolution” began in India; therefore I have, in some sense, “grown up with computers”. My interest in Theoretical Computer Science is the combined result of these two influences.

**MATHS-BACKGROUND**

While in high school, I was involved with the Mathematical Olympiad program and this culminated in my being awarded a silver medal at the 34th International Mathematical Olympiad. As a result of this involvement, I was exposed to basic Combinatory, Graph Theory and Number Theory at an early age. Moreover, the intensive training-cum-selection program I underwent has honed my skills and bolstered my confidence in problem solving. It has also whetted my appetite for problem solving and made me a regular reader of the Problem sections of periodicals like American Mathematical Monthly and Mathematics Magazine.

I was chosen, by the National Board of Higher Mathematics, as one of 18 undergraduates all over India to participate in their nurture program, in parallel with my formal undergraduate training. The resulting three-year-long interaction with the School of Mathematics of the prestigious Tata Institute of Fundamental Research (TIFR), has given me a substantial background in advanced mathematics (including Group, Ring and Field Theory, Linear Algebra, Real and Complex Analysis, Measure Theory and Topology). As part of this year’s program, I am studying Commutative Algebra, Algebraic Number Theory and Functional Analysis.

I hope to put my mathematical background to good use in my research work.

**CS-BACKGROUND**

I am currently a senior undergraduate student of the **** majoring in Computer Science and Engineering. I had chosen this department for its academically stimulating atmosphere, excellent faculty and broad spectrum of courses, many of which have a strong mathematical flavor.

Now, having acquired a firm foundation in the various areas of Computer Science, I am sure that my forte is Theoretical Computer Science. I find that my motivation, as well as my aptitude, is the strongest in this field: I have secured the highest possible grade (AA) in all the five theory courses that I have taken at **** namely, Discrete Structures, Data Structures and Algorithms, Design and Analysis of Algorithms, Theory of Computation} and Operations Research.

I have further enhanced my Theory background by opting for theoretical topics in my

{Seminar} (junior thesis) and my {B.Tech.\Project} (senior thesis). The former involved studies in Commutative Algebra and Computational Algebra, while the latter has involved Combinatorial Algorithms, Graph Theory and Randomized Algorithms and will soon involve Approximation Algorithms and applications of graph partitioning to VLSI design.

**RESEARCH-PLANS**

I find Algorithms and Complexity theory the most appealing areas of Computer Science because of their many beautiful results together with their numerous applications to real-life problems in Databases, Operating Systems, Graphics, Compilers and so on. I am fascinated with the enormous potential for research in these areas which has been revealed to me in my {Seminar} and {B.Tech\project} and that is what I envisage myself doing a decade from now.

Since problem solving is the most enjoyable and rewarding experience I have ever known, and since it is an integral part of a career in research and teaching in Theoretical Computer Science, I am convinced that such a career is the right choice for me. I am eager to contribute something to a subject that has given me so much joy. I am also enthusiastic about being involved in its teaching, as teaching a subject enhances one’s own understanding of it.

**WHY-THIS-UNIV**

Princeton University has one of the world’s very best Theoretical Computer Science groups. An opportunity to interact with this group would be a golden one for any budding theoretician.

From a careful study of the department’s brochures and the advice of the faculty at ****, I have realized that Princeton can provide me with a perfect environment for directing my mental resources towards independent research. I am confident of meeting the high standards of Princeton; my active involvement and enthusiasm in my undergraduate studies, which is amply reflected in my being ranked {first in the institute}, should serve as proof of my possessing the necessary qualities.

**CONCLUDING**

Keeping in mind my long-term goals, my immediate objective is to work towards a Ph.D. in Computer Science. I am aware of the kind of dedication, perseverance and resolve I need to have for a fruitful career in research and teaching. I believe my background has not only qualified me technically but also given me the right mind-set for such a career.

I look forward to joining as a graduate student in your department and having a long and mutually profitable association with Princeton University.