Bearing in mind my academic background, interests and capabilities, I desire to pursue graduate study in Computer Science leading to a doctoral degree at Pennsylvania State University (University Park). I am a final year student of Computer Science at a premier engineering school – Birla Institute of Technology and Science (BITS), Pilani, India.
Research interests: The mathematically rigorous curriculum at BITS, coupled with my interests, provides an ideal setting for me to pursue research in Theoretical Computer Science. My research interests include – randomized and approximation algorithms, combinatorial optimization, complexity, parallel algorithms, graph theory, number theory, and allied areas of cryptography and quantum computation.
Career goals: I aspire to build a career in academia by joining as a faculty member in a reputed university. My assistance in coursework design (for Theory of Computation and Pattern Recognition) and as a TA(for Data Structures & Algorithms, and Operating Systems) have provided me with the requisite experience in this arena. The task of designing assignment problems and preparing expository notes was a revelation, as it enabled me to view the same subjects from a different perspective. Based on the knowledge gained through the teaching assistantship for Operating Systems, I partially implemented an OS (thread synchronization, memory management) on the lines of the Minix and Nachos systems.
Project experience: My projects in Theoretical Computer Science and other areas have provided me with a sound knowledge of theoretical as well as practical aspects of Computer Science.
In graph theory, I worked on an algebraic, randomized algorithm for maximum matching of non-bipartite graphs (relying on the works of Mucha-Sankowski and Harvey). Further, I studied on matroid intersection and the bipartite matroid matching problem and gained a sound understanding of combinatorial optimization and randomization techniques. I also worked on computing undirected single-source shortest path in the comparison-addition model and studied the component hierarchy tech nique of Thorup. (Study was based on Pettie-Ramachandran algorithm for undirected shortest paths.) Prior to this, I worked on a deterministic, comparison-based minimum spanning tree algorithm. I am interested in parallelization of sequential algorithms for MSF.
My interest in number theory since my high school days has motivated me to direct my efforts towards a comprehensive understanding of recent developments in this field. I have authored a technical report on AKS primality test and my paper on patterns of sums of digits of powers of natural numbers was among top two papers at a National student conference in Chennai, 2008. I also implemented an application for the RSA encryption and decryption system on a Java platform.
My study on number theory and cryptography inspired me towards quantum computation, where I researched quantum algorithms, including Shor’s and Grover’s algorithms, and algorithms for solving Pell’s equation. I am studying Professor Adam Smith’s thesis on Multi-party quantum computation.
I have also worked in other areas of CS. I presented a paper on tournament design at the BITS Tech Fest. Additionally, I have successfully completed course projects in architecture (pipelined MIPS processor), compiler construction (in phases: scanner, parser, abstract syntax tree, optimization etc.), and microprocessor programming (water-level controller) among others. My project on image processing at the premier Central Electronics Engineering Research Institute, Chennai acquainted me with work in a research organization. [Please refer to my “Resume/Curriculum Vitae” for details about project work.]
Academic achievements: I have maintained an excellent academic record throughout my student life. I was awarded the Central Board of Secondary Education (CBSE) merit certificates for finishing among the top 0.1% of around 600,000 students in the All India Secondary School Examination in 2003 and for being among the top 0.1% of 400,000 students in the All India Senior School Certificate Examination in 2005. I obtained All India Rank 5 in the National Science Talent Search Examination (NSTSE) in 2001 and All India Rank 18 in NSTSE, 2000. I also obtained rank 9 in the Senior Mathematics Olympiad, Delhi in 2002 and qualified the National Standard Exam in Physics in 2004.
Personal background: Coming from an Indian middle class family, I have been taught the importance of hard work and sincerity from an early age. Constant encouragement from my parents inspired me to develop a passion for Mathematics. Also, the training for Math and Science competitions introduced me to relatively advanced topics in these subjects at a young age. Teaching underprivileged children as a volunteer for My India and the National Service Scheme (2005-08) was an unforgettable experience and opened my eyes to the joys of teaching.
The financial constraints associated with middle class families in India make me seek graduate assistantship from Pennsylvania State University to the maximum extent possible.
Coursework and Thesis: I am one of only 4 bachelors’ degree students of my CS batch at BITS-Pilani to have opted for the semester-long thesis option, for which I would continue my work on number theory and cryptography (in spring 2009). I have performed commendably in the Mathematics courses at BITS, being among the top 5 students in three of them. My passion for Mathematics has inspired me to take courses on Real Analysis, Graph theory and Algebra this semester. I am also auditing a course on Advanced Algorithms and Complexity.
Match of interest with Pennsylvania State University: I have perused in great detail the web site of the CS department, especially the Algorithms and Complexity group and am enthused by the frontline research work carried out in approximation algorithms, graph algorithms, complexity, quantum computing and cryptography among others. I have partly studied Professor Martin Furer’s paper on faster integer multiplication. My study on classical and quantum algorithms for Pell’s equation led me to Professor Sean Hallgren’s works on the subject.
I have studied the paper on Pell’s equation and principal ideal problem and partly read the paper on computing unit group and class group of a number field. I plan to continue my study of Professor Adam Smith’s multi-party quantum computation thesis into the next semester. I am also interested in the work on the graph isomorphism problem. I am excited at the possibility of increasing my knowledge of all aspects of Theoretical Computer Science through seminars such as the Theory seminar and in specific areas through the High Performance Computing Lab and others. The presence of experienced faculty and support infrastructure gives me the confidence of having a fruitful relationship with Pennsylvania State University
Equipped with a sound knowledge of Theoretical Computer Science and a strong academic and research background, I believe that I can contribute positively to research endeavors at Pennsylvania State University. I hope that the honorable admissions committee provides me an opportunity to realize my dreams and career goals by pursuing a Ph.D. at your esteemed institution.
Courtney from Study Moose
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