Statement of purpose for Mathematics, Physics ans Statistics

Mathematics has always been my passion and obsession since my childhood. It always occupied most of my time and I never had any ambition in my life other than being a research mathematician.
I was introduced to mathematics at an age as early as two years through basic arithmetic operations. When I grew older to enter primary school I was haunted by the questions like what is addition and what is subtraction etc. I was not at all happy with the basic school level idea of computing the sum for two given numbers. I started asking the question to myself, what is a number. The non-rigorous nature of school level mathematics always pained me and I tried to have my own way of defining mathematical concepts for myself, which I came to know to be true later. When I was introduced to Euclidean Geometry, the book told me the conditions when two triangles are congruent. But it never told when two figures in a plane are called congruent. So I defined congruence for myself, and in the process I conceived the notions of isometry and equivalence relations. This way I always tried to rigorize the elementary mathematics. While leaving school I had developed my keen interest on number theory also.

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 Mathematical Olympiad. I also took part in several mathematics talent search examination that is widely taken by almost all school kids nowadays. And I never achieved anything except the top grade. I also took part in several national level quiz competitions and represented my state. I also received the top grade in Australian Mathematics Competition, in which students from all the countries participated.

After completing fourteen years of schooling I joined the Indian Statistical Institute (I.S.I) as an undergraduate student in 1997 and completed Bachelor of Statistics (Honors), a three years undergraduate course. After passing Bachelor of Statistics (Honors) with First Division in 2000, I joined the Master of Statistics - a two years Masters program. I am presently in my final year of Master of Statistics doing advanced courses in Mathematics. I.S.I is an Institute of National Importance in India and reputed for its high quality teaching and research in Mathematics, Statistics and Probability. Entry to I.S.I is a highly competitive business. Selection is done through a nation wide examination on mathematics followed by an interview by the I.S.I faculty. This selection carries substantial financial support apart from the tuition waiver all through the undergraduate years and the two years of masters. Besides the stipend we are provided with other facilities like contingency grant etc. I.S.I. is the only institute in the country that provides financial support for the undergraduates and hence the competition involved at the entry point is very keen.

In I.S.I., I got interested in Probability Theory and Analysis. I received a very strong and rigorous training in both analysis and probability theory. My advanced courses in analysis include courses on functional analysis, Fourier analysis on locally compact abelian groups and Brown-Douglas-Fillmore Theory. And as for probability I have been exposed to training in Brownian motion, Martingale Theory, Markov Processes, Diffusion Theory and Stochastic Calculus. I got interested in Differential Geometry when I was trying to understand the structure of Möbius Strip, whose non-orientability drew my attention. Then I visited our Bangalore Center to start my study on Differential Geometry under Prof. V. Pati. Then subsequently I visited the School of Mathematics of Tata Institute of Fundamental Research (T.I.F.R) (the national center of the Government of India for Mathematics and nuclear Science) twice to take part in Visiting Students’ Research Program (V.S.R.P.) where I worked with Dr. Pablo A. Gastesi on Differentiable Manifolds and Lie Groups. During my next visit to T.I.F.R. I worked with Prof. T. N. Venkataramana on Analytic Number Theory. I also attended acourse on Set Theory meant for fthe Doctoral students. While continuing my study on Differential Geometry I felt that I should have some knowledge of Algebraic Geometry also. So I started to learn Commutative Algebra and subsequently Algebraic Geometry also. This year I took part in International Conference on Algebra and Geometry held during 7th to 12th December 2001 at University of Hyderabad. I was the only student invitee in that conference. I am also attending the Workshop on Operator Theory and Operator Algebra in Indian Statistical Institute, Bangalore.

Presently I am working on deriving some known properties of Riemann zeta function using some probabilistic techniques, and metrizing certain class of figures in the plane and looking at the convergence of shapes. And also I am reading some materials about Brownian motion on smooth manifolds.

Throughout my student life I had also given a lot effort to extra-curricular activities also. I have been playing violin for quite a few years from now. I have always been interested in poetry also and have been publishing them from time to time. I have also borne the responsibility of editing a few magazines on literature and science awareness. I have been also acting in several stage performances of plays and audio-dramas from my childhood.

I have also put great effort in order to teach mathematics at elementary level in a rigorous fashion. I have been the in-charge of the mathematics cell of an organization that is involved in science awareness. Thus teaching has always been of great pleasure to me. I carried out several training camps in mathematics and many of my students performed excellently in Regional and National Mathematical Olympiads. And my background in acting has always enhanced my skill of presentation. I have also given several student seminars in my institute, which were widely appreciated. The topics of my seminar include Differential Geometry, Analytic Number Theory, Measure Theory and many more. But learning mathematics for myself has always remained at the center of my attention.

Apart from having the requisite background, I am confident that my dedication, hard work and strong will to achieve success will help me create a niche for myself in the areas of my interest. I am also confident that I will be able to meet the demands and requirements of the graduate courses and research work in your department. I hope to pursue a career in research in mathematics, and eventually contribute significantly to this branch of knowledge.

Thank you very much for considering my application.

E. coli bacteria binding to cell bilayer (liposome)

A picture of E.coli bacteria (blue) sticking to liposome (red)

This picture appeared on this week's cover of ACS journal "Langmuir". The cover is basically about E.coli bacteria (blue) that is chemically bonded to cell bilayer (liposome) (red). 

Background: Polydiacetylene (PDA) molecules might be the next big thing in the field of sensing. These molecules have an interesting property that they change colors (Blue to red) after chemical binding. Authors have used these molecules to prepare liposomes which can bind selectively to E. coli bacteria. 

Result and discussion: The authors synthesized glucose tagged liposomes, why glucose? because E.coli binds to glucose. The resulting liposomes can selectively bind to desired molecule i.e E. coli here. They observed that as the bacteria binds to PDA it changes color from blue to red and the more e. coli binds to cell bilayer it changes more and more reddish. Author also used a technique called "Fluorescence Resonance Energy Transfer" for checking the proximity of two molecules.

Liposome (red), E.coli bacteria (blue)

Conclusion:   Polydiacetylene molecules can be successfully used for biological sensing (famously called Biosensing).

Reference: "Investigating Ligand–Receptor Interactions at Bilayer Surface Using Electronic Absorption Spectroscopy and Fluorescence Resonance Energy Transfer" Langmuir, 2012, 28 (36), pp 12989–12998

sample SOP for Ph.D. program in Management

Statement of Purpose

Statement of Purpose

I xyz graduated in July 1996 with a degree in Civil Engineering from
Institute of Technology, Bombay. Many of my courses and research activities
in the final year were in the field of Structural Engineering and Damping
Techniques with a strong focus on strength of material. I am presently working
in Tata Technologies India Ltd., an information technology firm that is involved
in the areas of enterprise integration and CAD/CAM. I am applying for
admission and financial aid to the Ph.D. program in Operations Management
at the Krannert Graduate School of Management, Purdue University. Detailed
information about my academic record and my research and other experience
is attached to this statement.
I was introduced to mathematics and the physical sciences while at school
and it was in high school that I considered a career in this area. The desire to
study the applied physical sciences and mathematics prompted me to take
the Joint Entrance Examination (JEE) for admission to the Indian Institutes of
Technology. I was ranked in the top 0.25 % of the nearly 1,00,000 students
who took the examination.
My undergraduate education at IIT Bombay has not only given me a certain
set of skills but has also helped me understand my fields of interest and my
academic strengths and weaknesses. This understanding has made me
realize that though the applied physical sciences appeal to me, my strengths
lie in applied mathematics and in abstractions of reality. In particular, I am
interested in the managerial aspects of industrial and technological systems.
This interest developed during my junior year seminar titled ‘Productivity
Management’ in which I explored the relationship between manufacturing
strategy and productivity improvement. I continued further research in this
area through my senior year project titled ‘Decision Support System for
Quality Control’ which sought to investigate various decision making
mechanisms in the quality function and provide corresponding computer
support. The project also enabled me to appreciate the interaction between
manufacturing and the other functions of the firm especially information
systems. The reading of certain outstanding books during the course of my
research such as Skinner’s ‘Manufacturing in the Corporate Strategy’,
Deming’s ‘Out of the Crisis’ and Goldratt’s ‘The Goal’ finally convinced me to
pursue a Ph.D. in operations management and an academic career
thereafter.
My past work in the area of industrial engineering and operations research
was characterized by a dichotomy of approaches. The courses that I took in
this area dealt with various operational and tactical issues. The basic aim was
to understand a specific problem, model the problem appropriately and find an
optimal or reasonably optimal solution using the techniques of operations
research. This has given me a good background in issues related to
methodology, modeling, and heuristic solutions. On the other hand, my
research has been oriented towards strategic issues. The basic thrust of my
junior year seminar and senior year project has been ‘integrative’. Through my
future research efforts I would like to understand this dichotomy better.
Initially, I want to study rigorous model-based methods and do research on
operational and tactical topics. After gaining a thorough grounding in these
topics, I am interested in applying the same methodologies and techniques to
strategic topics in operations management.
I believe that I have the qualities to be a good researcher and teacher. I am a
creative person and often think in a contemplative way about various issues of
practical importance. Being able to identify patterns and relationships that are
not obvious to others is perhaps my greatest strength. This will prove very
valuable because an integral part of being a researcher and teacher is to
perceive the balance between theory and practice, analytical rigor and
intuition. My communication skills are good and I like expressing ideas and
concepts both in oral and written form - an ideal platform for the dissemination
of knowledge in my chosen field of specialization.
The Krannert Graduate School of Management is one of the best schools of
management in the world with a strong orientation towards research. The
diversity of research interests in the operations management group is of
particular interest to me. The eminent faculty and the individualized nature of
the doctoral program will definitely bring out the best in me. I would like to
reiterate that I possess the background, the ability and the motivation to make
a significant contribution to Operations Management. I hope you will take a
favorable decision regarding my admission to the Ph.D. program and I look
forward to joining the Krannert Graduate School of Management and Purdue
University.


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