SOP(s) from 2000

Another subject which has attracted me right from my school days is combinatorics.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 Olympiad,through which I qualified for the preparatory camp for International Mathematical Olympiad which was attended by about fifty students.In that camp I was introduced to some nice combinatorial problems (like seven-bridge problem,four-color and five-color theorems;some applications of pigeon-hole principle etc.) that I found much more interesting than what I was doing in my high school. My keen interest in that subject still remains unabated and has given rise to my love for graph theory and design of experiments.Whereas I studied the former all by myself till now,I have had two full-semester formal courses in the later one during my B. Stat (Hons.) and M. Stat years.

After passing out from high school,I joined the Indian Statistical Institute, one of the the most prestigious academic institutions of India,whose standard of training in mathematics and statistics has received accolades from all over the world,by qualifying through a nationwide admission test. Quite naturally it was a matter of pride to get a chance to study here.

I joined the B.Stat(hons.) course in the Indian Statistical Institute which offered a number of intriguing courses in analysis and algebra.While enjoying these courses thoroughly,I also started to like statistics as a subject.I also attended two full-semester courses on algorithm writing and programming--where I learnt Fortran and a little bit of C. The B.Stat. course offered three probability courses and also one in stochastic processes.In the M.Stat. course that I am attending now,I am having two more courses in each of these fields.I shall also do a reading course in stochastic integration in the next semester. In one of those courses on stochastic processes that I took in B.Stat., I learnt about application of stochastic processes in genetics and other fields. I liked it very much. In fact,as of now,probability theory and stochastic processes are my main subjects of interest and I intend to do something in these lines in future.

Having said that,I would like to mention that I would also like to widen my knowledge in fields hitherto unknown to me.I am also interested in problems involving applications -- regression, for instance.

I have had a course each in regression theory and time-series analysis which I enjoyed quite a bit-I had to do practical problem-based projects and class-presentations in those two courses, which not only increased my confidence in addressing a class,but also improved my data-anlysis skills.

With the kind of rigorous training in theoritical statistics,probability theory and mathematics that I am having here in my present institute,I am quite confident to live up to the graduate courses and research works in your department.I look forward for a successful career in statistics and I hope to contribute to the enrichment of the subject.

Thank you for considering my application,

(APRATIM GUHA)

Ever since my childhood, I have been fascinated by almost anything under the Sun. Interesting facts from a variety of topics attracted my attention. As I grew up, this diversity in interest remained in me. However, from quite early on, my interests became focussed mainly on the natural sciences - Physics, Mathematics, and to a lesser extent, Chemistry and Biology. The language of Mathematics, with its ability to convey so much while saying so little, impressed me immensely. And as I found the subject to be quite easy, it quickly became my favorite subject. Physics began to interest me when I learned that a few apparently simple laws and principles were enough to explain a host of practical everyday phenomena. I used to spend a lot of my spare time in making experiments and designing simple mechanical gadgets. I even participated in a Science Fair at a local science museum with some friends, where the "Mechanical Arm" we exhibited won a few kudos.

My first introduction to Statistics, in fact, came through Physics. As I learned more, I found that the apparent simplicity of most of the physical laws can be deceptive, and practical situations can arise where these laws are of almost no use. My first real glimpse of Statistics came when I found it coming to the rescue in one such situation - in the Kinetic Theory of Gases.

I started studying Statistics formally in my senior secondary school . After completing school, I was able to obtain admission to the Indian Statistical Institute, which is reputed to be one of the foremost centers for the study of Mathematics and Statistics in India. Here I have completed, with full stipend, the 3-year Bachelor's degree of the institute, and am currently in the 2nd and final year of my Master's degree program.

The Institute was a new world of knowledge. For the first time, we learned Mathematics and Probability in a completely rigorous manner. Statistics was presented in a new light, through practical solutions to real problems. These years at the Institute have been a broad and enriching experience, one which is difficult to summarize in a few words. Needless to say, there have been in-depth courses in both Mathematics and Statistics. Of these, the courses on Probability and Stochastic Processes deserve special mention. I have also enjoyed several courses on Applied Statistics, notable among them being those on Regression Techniques and Time Series Analysis. There were also several other optional courses, not directly related to Mathematics or Statistics, which were very instructive. Among them was a course in Geology which, in particular, I enjoyed immensely. But I think one of the most important gains from this whole experience has been that it has sharpened my ability to think in an organized and efficient way.

Another fascinating world which opened up here to me was the world of Computers. I feel that Statistics is above all a tool, with which one is much better equipped to tackle a vast gamut of problems. My views about computers are somewhat similar. With its speed and efficiency, it gives us a power unimaginable a few decades ago. At the Institute, over the last four years, I have had the opportunity to develop a considerable degree of familiarity with Computers. I am now fairly proficient in C and FORTRAN and am also familiar with Statistical packages like SPSS and S-Plus. Over these years, I have done a lot of programming, some of them implementing statistical methods taught in class, others unconnected with formal course work. This latter includes a lot of work in developing several graphics routines from scratch, without using any standard software. I am also particularly proud of writing a fairly complicated game in which the computer can participate as a pseudo-intelligent player.

Apart from subjects I have studied formally, there are numerous other topics which interest me. As I have already mentioned, I have a natural attraction towards what is usually categorized as "general knowledge". In fact, I have been a regular participant of various quiz programs for a long time. The topics which interest me are often unrelated. I have a love for music from my childhood, and have made amateurish attempts at learning quite a few musical instruments - e.g., the violin, flute and mouth organ. I have also had formal training in Indian music with the Hawaiian Guitar as a medium. All this contributed in my taking special interest in the frequency domain analysis of time series data, and in fact, I also made a presentation to my class on Wavelet Bases. In the early years at the Institute, I was fascinated for some time by fractals and Chaos theory. These are just two examples of my many interests. I know very little of most of them, but I hope that somewhere along the way, I would get the opportunity to learn more.

Throughout my student life, I have always given a lot effort to extra-curricular activities. For example, I learned Roller Skating when I was in school, and as I mentioned, I took Guitar lessons when I was older. However, my first priority has always been studies, and Academics is the career I feel is most suitable for me. I am also confident that I have the requisite background and ability to do well as a graduate student. This is the main reason for which I wish to pursue research in Statistics. At the same time, I want to further my knowledge and skills in Statistics and in the process , I hope to get opportunities to do inter-disciplinary work, which I think I would enjoy, given the diverse nature of my interests.

I am aware of the reputation enjoyed by your institute and your distinguished faculty in the field of Statistics. I am looking forward to getting a chance to pursue research at your university.

Thank you for considering my application.

Deepayan Sarkar

Like any Science student , I had interests in the Cause-Effect nature of our action s and felt happy whenever I managed to reason out the working of a machine. With these inclinations, Mathematics fell in place ,with its rigorous logical structure with no ambiguities. In School , I was always the topper in Mathematics, no matter how I fared in other subjects. Backed by my never failing grades , I began to pursue the subject more as a hobby rather than as a mere prerequisite for the annual promotion . This helped me get a glimpse of the many sides of the subject, which I started to explore.

When I moved to the Indian Statistical Institute(ISI), I found the atmosphere friendly and stimulating, living upto its reputation. And Statistics to me , seemed a logical continuation of what I did in school. I found out how for the uninitiated , Statistics could be no different from Astrology. A copy of Lehmann's Testing Statistical Hypotheses, is the best gift I have received till date and one of the cherished books in my collection. Through the years I became an ardent fan of Probability and was attracted by the way an intangible concept like randomness was rigorized. The Monte-Hall Paradox and its ilk of counter-intuitive examples indicated to me that the subject had more interesting things to offer , as one advances.

Throughout my stay at IS I, I received full scholarship from the Government of India and was always in that section of the class, which was inclined towards Academics and Research. The frequent Presentations to a large audience motivated me, complemented by the proximity to inspiring teachers . Even during my school-days, I liked to discuss the nuances of a concept or an abstruse solution with my classmates. Without doubt, teaching is one of the main points in my agenda for the coming years.

During the summer of 1997 , I attend ed the Mathematics Training and Talent Search programme conducted every year by the National Board of Higher Mathematics for a few selected students from all over the country. There I sharpened my blunt edges in Mathematics , which helped me succeed in the difficult mathematical courses that followed. During this period, I came in contact with many inspiring researchers and could get a feel for the work they were doing. Another event, which further fuelled my research interests besides introducing me to the myriad branches of Statistics was the International Conference in Statistics, organized jointly by ISI and the Bernoulli Society . Helping the organizers as a volunteer , I got the opportunity to interact with the Statisticians from all over the world.

Besides Statistics, programming Computers has always fascinated me. It has become a new source for Brain Twisters. I wrote several programs to do jobs that looked complicated at the first sight. I immensely enjoyed writing one particular program, that draws a Numeric spiral once the user specifies its size. I realized the potential of Programming, during one of my visits to the Library when I came across the collected papers of Claude E Shannon, of the Shannon entropy fame. There I came across the maze solving algorithm and Shannon's electric mouse that implemented his algorithms. Shannon's biography partly influenced my research interests thereafter.

I believe my strong point is the courage to face challenges added to my stress on Quality, in all my actions. My motivation for further research partly comes from my successful improvisations during examinations that lead to unconventional and totally new solutions. These were greatly supported and encouraged by my teachers. Currently, I am going through rigorous courses in Mathematical Statistics and Advanced Probability . I'm also attempting to learn topics like Graph Theory and Pattern Recognition besides Ergodic Theory.

I plan to put in use the theory I have learned so far, and eager to discover some of the applications myself. I would like to concentrate on applications of Stochastic Processes and Time Series for my further research. I believe that the only justification of my work lies in the help it offers in solving a problem . I would be happier to see my other varied interests ,music topping the list, helping me in my academics and vice-versa. To give back the society more than what I receive(d) is more or less what I have in mind. I am sure I will be able to achieve this as a graduate student in your Department.

I thank you for considering my application.

Ramprasath Lakshminarasimhan

I was introduced to statistics in the high school.Here the subjects like physics,chemistry and mathematics became more rigourous. The chapters which seemed to be so easy earlier were in front of me with their structured vastness.In this new form the topics became more enjoyable and exciting.I completed my high school with what I was told a satisfactory result.

Giving examinations was almost an obsession to me.In Calcutta there are some local organisations which conduct talent search tests.These tests are quite popular and not easy as such.I used to write all of them and my grades in general were among the highests.Success always gives one a great confidence.These tests have also taught me to think and use the known results quickly in order to solve a problem. I have written two board examinations leading to my school and high school degree and my rank was among the top hundred out of more than three hundred thousand students.

Statistics was something very new to me when I left high school,but my interest in the subject was not at all insignificant.I joined Indian Statistical Institute for my undergraduate studies in 1995.After getting my B.Stat degree with honours in 1998 I joined the same institution for the M.Stat curriculum.The latter I shall complete by June 2000.After that I would like to join your university as a graduate student with the aim of getting a Ph.D. degree.

In Indian Statistical Institute I got a thorough training in theoretical as well as practical statistics. Also Mathematics has been a constant companion throughout my studies. I have taken part in many class presentations on various topics .To give a few example I have given talks on ``Hastings algorithm",``Wavelet transforms" etc. The presentations were generally taken up from scratch and had to be explained to a certain depth.They were very interesting to listen to because that way I could get an introduction to topics which were much advanced than those discussed in a regular class.Making a presentation was much more challenging.It meant a lot of self-study besides the actual course work.Also sometimes one had to cover a large topic in a short period of time.I had to present the whole multiresolution analysis and generation of father ,mother in wavelet analysis within half an hour.Making such vast topics concise and at the same time lucid was a challenge. To be precise I had my first experience of teaching through these presentations.

Another important part of the curriculum was the practical data analysis and statistical programming projects.I designed a software for ANOVA and paired -t-tests. I took it as an intellectual challenge.All the standard softwares available in Indian Statistical Institute like Shazam,I.M.S.L.,SPSSX, S-plus,B.M.D.P. etc. are familiar to me in some way or the other. Also I have written computer codes for simulation in many different situations. Data analysis was an integral part of the course work.The problems I encountered in these analysis projects were very challenging.In one of the data sets I found that a twice integrated model gives a good fit but bad predicted values.After some study I found that the problem was actually created by over differencing.Such experiences have convinced me of the fact that statistics was only a tool to explain things and the actual knowledge about the field from which the data is obtained is also very important.Applying statistics in different fields has been my goal.I want to pursue my career in that direction.

Along with statistics I am also interested in physics.We have a strong department dealing with problems in physics and applied mathematics.I have credited all of the two courses available in physics in my undergraduate curriculum.I am also working in a project related to modeling of a dynamical system on convection rolls in a rotating fluid with low Prandl number with my physics teacher. The project is not yet complete, but I hope to get some interesting results soon.

With these experiences and realisations ,I am approaching the world of research in statistics.I am eager to contribute to the subject.I understand the excellence of your department and given a chance I am confident that I will be able to enrich the subject with my contribution.

Thank you for considering my application.

SANJAY CHAUDHURY

In school, I was amongst the best in my class. My strength lay in Mathematics and the science subjects. My consistent good performance in Mathematics was responsible for the development of a special interest in it and slowly I fell in love with the subject. Geometry fascinated me the most. I still remember, how I had tried to vindicate Pythagoras' Theorem. Drawing a right angled triangle with vertical sides of lengths 4cm and 6cm, I had cut three paper squares of sides equal to the three sides of the triangle and then tried to fit the two smaller ones onto the bigger one by cutting suitably. I was thrilled when I found that the pieces did really fall in their places perfectly.

It was in Class X that I won the prestigious National Talent Search Scholarship, which is awarded purely on the basis of merit by the National Council of Educational Research and Training in India. I went on to join the Science stream in my high school and by the end of it had decided to pursue Mathematics in my undergraduate studies. Therefore, I joined the Indian Statistical Institute, which is one of the premier institutions for undergraduate studies in mathematics in India.

As of now, I have spent four and a half years at the Indian Statistical Institute ( 3 years of B.Stat.( Hons.) and a year and a half of M.Stat.). My days in this institute has been an unforgettable experience. Here I was pitted against the very best in the country and was able to hold my own against them. Here, too, did I have the rare privilege of being taught by excellent professors. The formal training that I received in Mathematics and Statistics convinced me of the importance of rigour in proofs besides making me aware of the value of intuitions. With five courses each semester and three class tests and a semestral exam based on each course, I had to be diligent and methodical in my studies. In return, I have become a fast learner and am now confident to live up to the demands of any course work. Moreover, my training of computer languages and programming has been quite advanced in this institute, and my familiarity with statistical packages such as SPSS, STATA and SAS will help me in my Ph.D.

It was in the second year of B.Stat. that I had a formal encounter with Economics. Over the next two years, I did four basic courses in the subject - one each on Microeconomics, Macroeconomics, Indian Economic Structure and Econometric Methods, which succeeded in stirring up a lot of interest in me. Here was a subject which had so much practical applications, is concerned with individuals as well as institutions and yet had sufficient rigour and formalism in its structure to attract a mathematician. My interest in the subject was further aided by the gradual opening up of the Indian Economy. With economic liberalisation , as reports and articles on the country's economic performance got highlighted in newspapers and magazines, my interest in the subject was further aroused. Understanding of terms such as balance of payments, convertibility of currency and foreign direct investment helped me appreciate these reports and articles. I still remember the enthusiasm with which I followed the Annual Budget of 1997-98 which was presented during the semester in which I had Macroeconomics as a course. During the summer of that year, I read through Adam Smith's An Inquiry into Nature and Causes of the Wealth of Nations --- a book that fascinated me with its impeccable logical analyses and rational perspective. By the end of the final year of B.Stat., I had made up my mind to be an Economist. Enrolling for the M.Stat. programme with specialisation in Quantitative Economics was the first step towards it.

In the short stint that I had with Economics, I have developed an interest in Economic Theory (particularly General Equilibrium Theory) and Mathematical Economics. Another area that has attracted me is "Choice Under Uncertainty" to which I got introduced this semester. This is an area where I can relate my mathematical and statistical skills to real life economic problems quite easily.

My long term goal in life is to pursue a career of research and teaching. I feel that I have most of the qualities necessary to do original works of substance. In this respect, I want to mention my ability to work hard, my perseverence and the fact that neither success nor failure moves me deeply. Watching my mother, a high school teacher, and my father, a Chartered Accountant who used to teach in college until a few years ago, I have a deep regard for teaching as a profession and am myself attracted to it. The class presentations at the Indian Statistical Institute provided me the opportunity to sharpen and prove my communication skills and the ability to explain ideas clearly. I prepare meticulously for my presentations and if my audience understands and appreciates the concepts I am trying to convey, I feel extremely satisfied. This has generated in me an interest to pursue a teaching career. I also believe that teaching a group of intelligent students can be a stimulating experience besides helping me in my own research.

I believe that besides talent and motivation, a very good training in the subject is essential for a successful career in academics. Since I am relatively new to the subject, I consulted my course instructors and my seniors who have undertaken graduate studies in the US. All of them strongly recommended your department. As such, I have chosen to pursue graduate studies at your university because by working under the guidance of such distinguished researchers, I am confident of making original contributions in the field of Economics. And finally, the high frequency of contributions that members of your department make to the well known and highly acknowledged journals of Economics imply to me the greatly active nature of your department.Working with them will give me the broad exposure I am looking for which, surely, will bring out the best in me.

I hope to be a member of your department. Thank you for considering my application.

Sayan Chakraborty

I got interested in Mathematics at a very young age and I have decided to pursue a career in Mathematics. In the pursuit of Mathematics, I have always adopted a rigorous approach in order to attain an in-depth understanding of the subject at hand. I enjoy constructing counter examples in Mathematics and I like solving puzzles and Olympiad problems. All these are my favorite pastime.

I solved a problem on " puzzling rectangles " which was published in "RESONANCE", the nation's leading journal for science education, in December 1997. This Journal is published by the Indian Academy of Sciences. I participated in several Mathematical Olympiads both at the state and National level. I got the 5th rank in the state Math Olympiad (1993) and the 15th rank at the Indian Math Olympiad (1994). I received the Indian Mathematical Olympiad scholarship and also a certificate of proficiency in Mathematics in 1994. That puts me in the top 0.3 % among the participants at the national level. I received a M.Sc/M.A scholarship in 1998 which is conducted by the National board of Higher Mathematics (N.B.H.M), a government agency. Its aim is to promote Mathematics in our country and to encourage talented students through Olympiads and scholarships. I am a recipient of the science talent search merit certificate (1992). I participated in the Mathematics Training and Talent Search Programme which was conducted by the N.B.H.M in 1996.

I visited the Tata Institute of Fundamental Research (T.I.F.R) (a national centre of the Government of India for Mathematics and nuclear Science) thrice to participate in the visiting students research programme (V.S.R.P) where I got interested in Algebra and worked with Prof. Amit Roy. I studied Galois Theory and Group Theory when I first visited T.I.F.R in Dec. 1997 and later in June 1998 I was exposed to Semi-simple rings and Representations of Finite groups at T.I.F.R. I developed interest in Non-Commutative rings and I ended up studying the Golod-Safarevich theorem, Burnside and Kurosh problems and some general Non-Commutative theory in Dec 1998 at T.I.F.R. I scored 100 % in the course on Abstract Algebra in my M.Stat first year.

I have done many advanced courses in Mathematics in the last four years. I have been exposed to a lot of Analysis and Probability at I.S.I., and Algebra at T.I.F.R. during my V.S.R.P visits. While I was an undergraduate student I informally attended a course in General Topology which was offered for the graduate students. Last semester I had a course in Advanced Algebra in which I did Commutative Algebra and some basic Algebraic Number Theory as well. I find Algebra and Algebraic methods very alluring. Next semester I am taking courses in Algebraic Geometry, Algebraic Topology, Algebraic Number Theory and Graph Theory. At present I am engaged in learning some Homological methods in Commutative Algebra. I have decided to go in for research in pure Mathematics and contribute to the on-going research work. I can say confidently that I posses the motivation and intellectual ability to make original contributions in Mathematics. I look forward to joining your university as a graduate student in your esteemed department.

Sunil Kumar Chebolu.