# Оценить Statement of Purpose

тут очень много пиздежа, но надеюсь, прокатит

Текст хорош тем, что содержит необходимые факты, недостатком же является то, что их невозможно в этой простыне быстро найти. По структуре сейчас это не statement of purpose, а помесь развёрнутой автобиографии в свободной форме, statement of research interests и cover letter.

Принимающие в аспирантуру хотят взять того, кто защитится. Для этого во всех подаваемых документах они ищут подтверждения трёх пунктов: (1) человек знает, что его ждёт в этой аспирантуре; (2) он этого хочет; (3) он это может.

Пункт (1) включает в себя представление о теме будущих исследований, о программе и об аспирантской жизни вообще, в частности, откуда деньги возьмутся. Сам по себе не требует фактического подтверждения и демонстрируется скорее текстом в целом. Денежный вопрос может потребовать пары фраз отдельно.

Пункт (2) надо в явном виде сформулировать, лучше в самом начале. Также полезно показать, что желание не вчера появилось (одна фраза со ссылками на биографию) и что оно завтра не исчезнет (для это полезно сказать, чем applicant собирается заниматься после получения PhD и почему он не может этим заняться прямо сейчас; в текущей версии этого или вообще нет, или я не заметил).

Пункт (3) является самым объёмным и требует перечисления relevant skills, experience and personal attributes с подтверждающими примерами из биографии; заодно надо ненавязчиво раскрывать (1) и (2). Список того, что в конкретном месте считают relevant, обычно есть у них на сайте и им можно руководствоваться. Отдельная задача: попутно объяснить всё необычное в CV.

Короче: текущий текст надо разобрать на кусочки и пересобрать в текст, позволяющий легко tick the box при просматривании. Воду вылить.

то есть, условно разделить стейтмент на 3 части: в 1ой расписать о своем желании, во 2ой о теме исследований на пхд и аспирантской жизни в целом, в 3 о том чем ты будешь заниматься после пхд и как пхд тебе поможет в дальнейшем - правильно понимаю? в йеле надо 2 стейтмента прикладывать оф перпос и биографию. Вопрос в том, как показать то, что мне пхд нужен не для халявной гринкарты, а то, что я всей этой мутью србираюсь заниматься?

Intending to apply advanced quantitative methods in the modern financial industry, I need a world-class research-level qualification in probability theory and stochastic calculus. After thorough investigation of almost 50 US universities, I am confident that the Yale university Applied Maths PhD program best suits my educational background, research experience and interests, and career goals. Faculty expertise ranging from statistics, functional analysis and SDE to efficient algorithms and distributed and parallel programming as well as low ratio of grad students to faculty would guarantee me supporting and stimulating environment for my PhD research and study.Формулировки мои за образец брать не надо, а надо смотреть на принцип организации. В начале прямо и ясно сообщается цель получения PhD. Больше к этому возвращаться не надо, про будущее ничего содержательного не скажешь, а главное уже сказано. Тут же сообщается область: читающий может сразу прикинуть, скажем, что надо это переслать Jones'у и Wu, которые этим занимаются. Далее сообщается, что решение подать именно сюда было обдуманным, а заодно упоминается о наличии у аппликанта необходимого образования и опыта научной работы (про это подробнее надо написать в дальнейшем!). Затем уточняется исследовательская область (поскольку явно имеется в виду пересечение названных тем) и указываются ожидания аппликанта: самостоятельная работа (supporting and stimulating environment) и широкое сотрудничество. В результате уже покрыта большая часть того, что я выше назвал (1) (кроме денег) и (2) (оставшееся автоматически раскроется рассказом о предыдущем опыте). В идеале в таком тексте каждое слово работает и достигает сразу нескольких целей, и при этом текст легко и приятно читается (я так писать не умею).

Далее можно рассказать о прошлом, но не хронологически (это есть в CV а по skills and personal attributes (при этом experience будет покрыт автоматически). Далее можно написать что-то вроде research proposal: тема, почему она интересна миру и тебе самому, что известно, как планируешь работать. Всё очень сжато. В заключительном абзаце сказать, откуда ты ожидаешь деньги на оплату fees and expenses (собственные сбережения, работа, TA, RA - чтобы читающий мог убедиться, что ты не бросишь из-за нехватки денег и не будешь слишком сильно отвлекаться на их зарабатывание) и повторить про свои ожидания от аспирантуры.

I consider Stochastic Calculus as a primary area of my research during PhD. Probability and Stochastic Calculus have been an area of my particular interest since the 2nd year of study in Moscow, where I not only took relevant classes but also conducted independent research in optimal stopping rules, game theory and random graph theory under guidance of professor Bulinski. Probability Seminars Series at CU and Minerva Foundations Lectures enhanced my interest in the field. Correspondence with professor Protter, professor Karatzas and professor Bulinski also convinced me to continue research in this field.

Limit theorems for stochastic processes is the area that attracts me by a huge number of challenging problems. Writing my diploma thesis on random graph theory I used well-known results from discrete mathematics, mathematical analysis differential geometry, functional as well as stochastic analysis and was able to prove a result on relationship between k-nearest graph and a convex hull of random graph – it could be considered as a limit theorem, though. Discrete mathematics allowed me to analyze random graphs from deterministic point of view. Mathematical and convex analysis were particularly useful in the analysis of the convergence and convergence rate. Differential geometry enabled me with properties of Minkowski metric on manifolds. Fusion of these seemingly unrelated concepts from different mathematical fields produced a new result in random graph theory. Given to my initial success, though small, I am eager to leverage all my skills and expertise in other mathematical fields to make my own contribution.

Apart from my sheer enthusiasm and motivation, research on Limit theorems could be facilitated by further study of complex analysis, constant interaction with faculty members and my familiarity with the subject matter. Although 1 year class on complex analysis course in MSU gave me fundamental basis and necessary technical as well as theoretical skills, a number of advanced level classes and scientific seminars on complex analysis could facilitate further my study of characteristic functions. Having attended professor Bulinski scientific seminar on Limit Theorems for Stochastic Fields for 3 academic years I was able to learn about a number interesting techniques that I used in my course works as well as diploma thesis. On the other hand, such names as David Pollard and Andrew Barron who are well known on their research on U-statistics, K-statistics and weak convergence make me believe that I will get qualified assistance in my research on Limit Theorems, especially on their functional versions.

My research experience and solid theoretical background in functional analysis will also be helpful and useful on research on a convergence in functional spaces. Professor Bogachev’s lectures on real and functional analysis equipped me with all necessary tools to further study functional spaces and their properties. Moreover on Undergraduate special courses and seminars on functional spaces and operator theory we were taught recent results in those areas. I first applied those skills during research on spectral properties of differential operators. Specifically, I focused on Hilbert spaces. Properties of linear operators, classical measure theory inequalities, topology and properties of polynomial functions allowed me to derive some interesting inequalities and boundary conditions for eigen functions of differential operators that were further used by professor ... in his research papers on properties of elliptic and hyperbolic type of differential operators. This practice of learning of properties of one functional space in terms of another, well studied space, could be used in a study of a convergence properties of stochastic processes, distributional as well as sample path properties,

Limit theorems is not the only area of my interest, another area that interest me is Levy processes. Although I studied Poisson process and Brownian motion properties while in Moscow, true understanding of how important this class of processes came when I was at CU. Wide range of areas where Levy processes could be applied makes Levy processes an interesting field of research. I would like to start my initial research from dependence structure, sample path and distributional properties and move onwards. Professor Protter advised me to learn about Malliavin calculus and I started my own study of it in order to make further progress in the field. Also I would like to employ recent discoveries that are available in magazines such as Annals of Probability, Annals of Applied probability and many others.

What makes applied math program truly unique is a chance to collaborate with those whose primary focus is application of theoretical concepts into real life solutions. Analysis of convergence, and exploration on Levy processes require deep understanding of how those results will be applied in practice. Unfortunately, due to my theoretical background, I rarely focused on the practice side. Applied math programs offers an opportunity to collaborate with specialists in machine learning, data mining and signal processing fields and may help to apply theoretical discoveries into real-life applications.

Given to my preference to stochastic calculus it seems natural that I have an interest in Stochastic differential equations after graduation and after successful completion of Applied Math PhD program. Filtering problem being one of the future areas of specialization. Stochastic Differential Equations came to my life when I was writing a coursework paper on game theory and have become an important part of my research interest. My interest in Stochastic analysis and former exposition to research on functional analysis could be explained by long term research interest in SDE field. Since analysis of a filtering problem deals with a minimization problem of a certain functional on a Hilbert Space advanced courses and seminars on optimization at Yale, will give me knowledge in the field I am not familiar with and will be used in the future. Research done on Limit theorems could also be employed by approximating solutions of SDE by stochastic integrals.

My interest in numerical analysis and algorithms classes en route to fulfilment of PhD requirements seem pretty natural given to my future interest in SDE and PhD research. Numerical solutions of SDE involve a number of interesting aspects. I would like to work on new numerical schemes under a variety of conditions. Although, I worked mostly with numerical schemes for ODE and PDE, numerical schemes for SDE rely heavily on stochastic analysis and my previous exposition to stochastic processes and advanced stochastic analysis coupled with classes on algorithms and numerical computation I am going to take from applied math school as well as CS school may play an important role in the analysis of various schemes. Although I learned some elementary simulation techniques while at Columbia and I continued my study of simulation techniques by reading books of P. Glasserman, DJ Highham and PE Cloeden, I believe that simulation of random variables on a computer software may be improved by further analysis of randomized algorithms. Applied math program offers an opportunity to get an excellent fundamental training in advanced numerical methods, parallel programming, distributed computation and randomized algorithms which will be used heavily in my future research.

В целом Statement неплохой, я уверен, что у половины подающих туда заявления будет что-то похожее. Просто надо составить его таким образом, чтобы человек, прочитавший его по диагонали (а примерно так их и читают выделил его из остальных или по крайней мере составил себе представление о себе.

Из того, что я прочитал:

- apply to, а не in или я не понял, о чём ты пишешь. Ещё, economics, а не economy

- во втором предложении снова повторяется world-class research-level qualification. Во-первых это тяжело читать, во-вторых не стоит повторяться.

- Ты пишешь о переписке с несколькими профессорами, однако для читателя остаётся загадкой, какова природа вашего общения. Если вы общались о чём-то не важном, не стоит об этом писать, если о науке, то надо об этом написать.

спс, щя переделаю

Intending to apply advanced mathematical and statistical methods in computer science as well as economy I need a world-class research-level qualification in statistics and computer science. After thorough investigation of almost 50 US universities, where research interests of faculty members, research scientists and postdoctoral students was my primary consideration, I am confident that the Yale university Applied Maths PhD program best suits my educational background, research experience and interests, and career goals. Faculty expertise ranging from statistics to efficient algorithms and distributed and parallel programming as well as low ratio of grad students to faculty would guarantee me supporting and stimulating environment for my PhD research and study.

I consider Stochastic Calculus as a primary area of my research during PhD. Probability and Stochastic Calculus have been an area of my interest from my 1st year of study in The Departments of Mechanics and Mathematics of Lomonosov Moscow State Universityю During his lectures on basic probability theory special class for 1st year students professor Bulinski captivated with beauty and simplicity of probability theory and motivated me to study Probability theory class with zeal and enthusiasm following academic year. By my 2nd year of study I already knew that probability will be my future area of specialization and asked professor Bulinski be my scientific advisor. I conducted independent research in optimal stopping rules, game theory and random graph theory under guidance of professor Bulinski. Probability Seminars Series at CU and Minerva Foundations Lectures enhanced my interest in the field.

My first independent research on probability and statistics came at my 3rd year of study at MSU. It was a problem in Optimal Stopping Rules for Heterogeneous Markov Processes and involved heavy use of stochastic calculus and Operator Theory, specifically properties of Markov Chains, Self Conjugate Operators and their eigenvalues. Although I did not take those classes at the time I could research topic using mathematical analysis, statistics and linear algebra tools that I was familiar with. However, I having studied stochastic calculus and operator theory next term I could figure out points at further research that could and should be done and researched the topic more thoroughly during my summer vacations. The research involved advanced properties of Markov chains and minimization problem of special type of linear operators on a Hilbert space. It was my first serious project that instigated my interest in distributional and sample path properties of stochastic processes as well as those of Linear operators on Hilbert Space.

An opportunity to research functional spaces and Operators came when I worked as a research assistant in Mathematical institute. Professor Bogachev’s lectures on real and functional analysis equipped me with all necessary tools that allowed me to start a research, although it required a great deal of self study since functional analysis was not my area of specialization. Specifically, I focused on Hilbert spaces. Thorough research and study of advanced properties of linear operators, topology and of polynomial functions as well as well-known measure theory inequalities allowed me to derive some interesting inequalities and boundary conditions for eigen functions of differential operators that were further used by professor ... in his research papers on properties of elliptic and hyperbolic types of differential operators and I presented the result on a conference in ... . This practice of learning of properties of one functional space in terms of another, well I would like to apply in my research on Levy processes

One reason for my particular interest in Levy processes came from my involvement in Math Finance program at CU. Although I studied Poisson process and Brownian motion properties while in Moscow, true understanding of how important this class of processes came when I at my time at CU. Wide range of areas where Levy processes, such as Physics and Biology, makes Levy processes an interesting field of research. Due to availability of spare time after graduation of CU I started my own study of Maliavin calculus and learned fundamental concepts of the theory. However, I need qualified assistance on a number of challenging issues such as martingale expansion and levy measures that will improve my understanding of the subject and could be employed in research. Analysis of fundamental breakthroughs in the field as well as close collaboration with Applied Math faculty members and research scientists make dependence structure, sample path and distributional properties of Levy processes an ideal initial point research that will allow me to make further progress in the analysis of Levy processes and Applied Math PhD program an ideal place that will offer nurturing environment to my research

Limit theorems for stochastic processes is another the area that attracts me by a huge number of challenging problems. Writing my diploma thesis on random graph theory I used results from discrete mathematics, mathematical analysis, differential geometry, functional as well as stochastic analysis and was able to prove a result on relationship between k-nearest graph and a convex hull of random graph – it could be considered as a limit theorem, though. Exposure to discrete mathematics for 1 academic year allowed me to analyze random graph and its convex hull from deterministic point of view. Huge involvement in Mathematical and convex analysis for almost 3 academic years through special seminars and required classes allowed me make thorough analysis of the convergence and convergence rate. Having attended prerequisite classes on differential geometry and topology for 1 academic I was able to use properties of Minkowski metric on manifolds. Fusion of these seemingly unrelated concepts from different mathematical fields produced a new result in random graph theory, that was proudly presented in Lomonosov conference in 2011. And now I am eager to leverage all my skills and expertise in other mathematical fields to make my own contribution.

Apart from my sheer enthusiasm and motivation, research on Limit theorems could be facilitated by further study of complex analysis, constant interaction with faculty members and my familiarity with the subject matter. Although 1 year class on complex analysis course in MSU gave me fundamental basis and necessary technical as well as theoretical skills, a number of advanced level classes and sciintific seminars could facilitate my further study of characteristic functions. Having attended professor Bulinski scientific seminar on Limit Theorems for Stochastic Fields for 3 academic years I was able to learn about a number interesting techniques that I plan to use in my work on functional limit theorems. On the other hand, I feel a need on a further study in asymptotic theory in order to make fundamental breakthroughs in the field. And such names as David Pollard and Andrew Barron who are well known on their research on U-statistics, K-statistics and weak convergence make me believe that I will get qualified assistance in my study and research on Limit Theorems, especially on their functional versions.

Talking about my long-term career goal I would like to mention SDE. My interest in SDE came when I was writing my coursework on Game theory at my 4th year of study and have became inherent part of my research interest. The coursework problem dealt with Nash equilibrium strategy in a game. As a matter of fact, it was a filtering problem with Poisson processes being noise generating processes. My involvement in a Variations calculus class, good theoretical foundation in statistics and stochastic calculus as well as excellent grade on Optimal control allowed me to derive better estimate for a particular constant, a characteristic of the optimal strategy.

Being CU Math Finance program student I noted a heavy use of SDE in financial industry that instigated my further interest in the subject. Having attended Math finance seminar series at Statistics department and prerequisite Math Finance practitioners seminar for the program students I learned about most challenging problems in the field

My interest in the study of Levy processes and Limit theorems is attributed to my long-term interest in SDE. On one hand, excellent research done on properties of Levy processes may result in a prolific study of filtering of a noise generated by Levy processes and broaden research on ergodicity properties of stochastic integrals. On the other hand study on limit theorems may be used in approximation of a solution of SDE by stochastic integrals.

I am also interested in application of my results into practice and research on SDE may be considered complete only after an efficient computational algorithm and simulation technique have been proposed. Analysis and design of an algorithm require knowledge in such fields as numerical analysis, harmonic analysis and algorithms.Although I studied complex analysis and numerical analysis for 1 academic and got a solid understanding of fundamental concepts, I feel need in advanced studies of modern techniques. On the other hand applied math faculty members research interests and graduate level classes as well as scientific seminars on Fourier analysis, scientific computing and randomized algorithms will give me necessary theoretical and practical foundation to start my future research on numerical computation and simulation of a SDE solution. Collaboration and study on such issues as distributed computing and parallel programming with Applied math researchers will also contribute to the development of efficient computation and simulation techniques.

Study and research on all those areas as well as teaching activities to cover my living expenses and tuition fees will require huge efforts and time to spend but this is a prerequisite to everybody who consider scientific career. Playing water polo in MSU varsity water polo team and studying math I learned how to distribute my energy and time efficiently. Study in CU allowed me to make most from the available time and material. And now I feel myself ready to embark to the long and challenging academic career path. By conducting research in Yale being PhD program participant, I can find ways to bring scientific results into applications where the products make differences in human lives. It is a critical stage in my life and career, which I am ready to face and prepared to go beyond my best

Когда то у меня была очень похожая ситуация и мой SoP был близок по духу с Вашим. К сожалению, мне тогда никто не объянил, что такой SoP будет смотреться блекло относительно других апликантов (для меня это плохо кончилось). Скорее всего, у Вас очень сильный пакет и отличные рекомендации и Вас везде примут (SoP - это не самый важный элемент но зачем играть с судьбой, когда на кону стоит будущая карьера.

Если коротко, то

1) После дороботки стоит отдать SoP for proofreading to a professional copy editor. Тяжело читается, длинные предложения, бывает тяжело понять что имеется ввиду. В интернете полно контор которые это сделают баксов за 30-40 (но мало кто из них будет делать серьезные правки). Много всего по мелочи, e.g., "as well as economy" should be "and economics" - каждый отдельный случай нестрашен, но когда их много, то это негативный сигнал

2) Члены комиссии по приему очень занятые люди, которые в добавок получают 100-200 applications на ПхД - что то около 3-4 минуты на человека. Первый параграф SoP должен четко и ясно объяснить членам комиссии почему нужно взять *именно Вас* а не остальных 199 апликантов. В текущим варианте, первый параграф дает Йелю понять, что они Вас достойны, а не наоборот (что если SoP попадет к человеку, который не в курсе что русские не rude and arrogant, а просто мы так мысли излагаем?). SoP - это самореклама, а не автобиография, здесь каждое слово на вес золота.

Например, "After thorough investigation of almost 50 US universities" - что это должно сказать члену комиссии? Вы конечно хотели сказать что Йель самый-самый, но члены комиссии могут это прочитать как то что Вы сомнивались есть ли Йель в ТОП50 по процессам Леви?!

Все прекрасно понимают, что Вы будете подаваться еще как минимум в 15-20 мест.

How about ... I want to do research in applications of Levy processes to computer science and economics. Yale's Prof. XXX and Prof. XYZ are world leading experts in this area whom I would love learning from/working with. После этого если сильно хочется в Йель то можно написать товарищам XXX и XYZ - как правило, это очень отзывчивые и приятные люди

вопрос в том с чего лучше начать

A problem on number theory I came over while reading a book on a biography of Leonard Euler engendered my interest in mathematics which became a full blown passion upon my graduation of Republic Specialized Physics Mathematics School. My intellectual hunger as well as curiosity led me the department of Mechanics and mathematics of Moscow State University – well-known around the world for its discoveries and contributions into the field of mathematics.

At Moscow State University Probability and Stochastic Calculus have been an area of my interest from my 1st year of study, During his lectures on basic probability theory class for 1st year students professor Bulinski captivated with beauty and simplicity of probability theory and motivated me to study Probability theory class with zeal and enthusiasm following academic year. By my 2nd year of study I already knew that probability will be my future area of specialization and asked professor Bulinski to be my scientific advisor. I conducted independent research in optimal stopping rules, game theory and random graph theory under guidance of professor Bulinski. Probability Seminars Series at CU and Minerva Foundations Lectures enhanced my interest in the field.

Intending to apply advanced mathematical and statistical methods in computer science as well as economy I need a world-class research-level qualification in statistics and computer science. After thorough investigation of almost 50 US universities, where research interests of faculty members, research scientists and postdoctoral students was my primary consideration, I am confident that my educational background, research experience and interests, and career goals best suits expectations put upon PhD students. Faculty expertise ranging from statistics to efficient algorithms and distributed and parallel programming as well as low ratio of grad students to faculty would guarantee me supporting and stimulating environment for my PhD research and study.

My first independent research on probability and statistics came at my 3rd year of study at MSU. It was a problem in Optimal Stopping Rules for Heterogeneous Markov Processes and involved heavy use of stochastic calculus and Operator Theory, specifically properties of Markov Chains, Self Conjugate Operators and their eigenvalues. Although I did not take those classes at the time I could research topic using tools of mathematical analysis, statistics and linear algebra that I was familiar with. However, I having studied stochastic calculus and operator theory next term I could figure out points at further research that could and should be done and researched the topic more thoroughly during my summer vacations. The research involved estimates of transitional probabilities of Markov chains and minimization problem of self-conjugate linear operators on a Hilbert space. Although I derived a solution for optimal stopping problem under more general conditions, due to lack of time and expertise in operator theory I could not continue research on the topic.

An opportunity to research functional spaces and Operators came when I worked as a research assistant in Mathematical institute. Professor Bogachev’s lectures on real and functional analysis equipped me with all necessary tools that allowed me to start a research, although it required a great deal of self study since functional analysis was not my area of specialization. Specifically, I focused on Hilbert spaces. Thorough research and study of advanced properties of linear operators, topology and of polynomial functions as well as well-known measure theory inequalities allowed me to derive some interesting inequalities and boundary conditions for eigen functions. Specifically, I considered properties a functional space by means of another well-studied space and construction of an appropriate linear operator.

I would like to apply this approach in my study of Levy processes at phd in Yale Wide range of , such as Physics and Biology, makes Levy processes an interesting field of research. Having read a number of scientific articles I learned a number of methods of use of linear operators. These methods could be applied in a study of dependence structure and weak convergence of Levy processes. On the other hand, I started my own study of Malliavin calculus .However, such issues as martingale expansion and Levy measures are to be addressed more thoroughly. At this point I expect close collaboration with Applied math as well as Stat department members.

Limit theorems for stochastic processes is another the area that attracts me by a huge number of challenging problems. Writing my diploma thesis on random graph theory I used results from discrete mathematics, mathematical analysis, differential geometry, functional as well as stochastic analysis and was able to prove a result on relationship between k-nearest graph and a convex hull of random graph – it could be considered as a limit theorem, though. Discrete mathematics allowed me consider special relationship between k-nearest graph and convex hull or the graph. Using tools of mathematical and convex analysis I considered a minimization problem for a certain functional of Poisson processes. Knowledge frm Classes on differential geometry and topology allowed me to use properties of Minkowski metric on manifolds. Fusion of these seemingly unrelated concepts from different mathematical fields produced a new result in random graph theory, that was proudly presented in Lomonosov conference in 2011. And now I am eager to leverage all my skills and expertise in other mathematical fields to make my own contribution.

Apart from my sheer enthusiasm and motivation, my research on Limit theorems is dictated by practical needs. Limit theorems especially functional versions are primary tools to build estimates. That is why I expect assistance from faculty embers such as David Pollard and Andrew Barron who are well known on their research on U-statistics, K-statistics and weak convergence. A number of advanced level classes and scientific seminars on complex analysis could facilitate my further study of characteristic functions. Having attended professor Bulinski scientific seminar on Limit Theorems for Stochastic Fields for 3 academic years I was able to learn about a number interesting techniques that I plan to use in my work on limit theorems such as Stein method,

Talking about my long-term career goal I would like to mention SDE. My interest in SDE came when I was writing my coursework on Game theory at my 4th year of study and have became inherent part of my research interest. The coursework problem a Nash equilibrium strategy problem. As a matter of fact it was a filtering problem. I could not understand a concept of stochastic integral at that time. As a result worked mostly on technical side, such as better estimates for integrals and more generalized class of integral functions . On the other hand my familiarity stochastic calculus as well as with Optimal control and allowed me to derive better estimate for a particular constant, a characteristic of the optimal strategy.

My research on SDE I would like to start from filtering problems. Better understanding of the concept of a stochastic integral came on Probability Theory 2 class taught by Philip Protter. Math finance seminar series at Statistics department gave me an overview of current state of the field. Prerequisite Math Finance practitioners seminar demonstrated most challenging areas in the field. Although I have an excellent background in stochastic calculus, graduate level classes and scientific seminars will be very helpful in a study of optimization. This in turn allows me to consider wider range of functional and corresponding minimization rpoblems.

My interest in the study of Levy processes and Limit theorems is attributed to my long-term interest in SDE. On one hand, excellent research done on properties of Levy processes may result in a prolific study of filtering of a noise generated by Levy processes and facilitate research on ergodicity properties of stochastic integrals. On the other hand study on limit theorems may be used in approximation of a solution of SDE by stochastic integrals.

I am also interested in application of my results into practice and research on SDE may be considered complete only after an efficient computational algorithm and simulation technique have been proposed. Analysis and design of an algorithm require knowledge in such fields as numerical analysis, harmonic analysis and algorithms. Although I studied complex analysis and numerical analysis and got a solid understanding of fundamental concepts, I feel need in advanced studies of modern techniques. On the other hand applied math faculty members research interests and graduate level classes as well as scientific seminars on Fourier analysis, scientific computing, distributed computing , parallel programming and randomized algorithms will give me necessary theoretical and practical foundation to start my future research on numerical computation and simulation of a SDE solution.

Study and research on all those areas as well as teaching activities to cover my living expenses and tuition fees will require huge efforts and time to spend but this is a prerequisite to everybody who consider scientific career. Playing water polo in MSU varsity water polo team and studying math I learned how to distribute my energy and time efficiently. Study in CU allowed me to make most from the available time and material. And now I feel myself ready to embark to the long and challenging academic career path. By conducting research in Yale being PhD program participant, I can find ways to bring scientific results into applications where the products make differences in human lives. It is a critical stage in my life and career, which I am ready to face and prepared to go beyond my best

Что за мемуары, бл. Сократи в два раза, изложи суть, каждое предложение не длиннее 10 слов, никаких тяжеловесных языковых изворотов и разнесенных на несколько строк начала/конца фразы, никаких пафосных и смешных "My intellectual hunger", в идеале, суть в первом параграфе, разжевывание во втором, заключение в третьем.

Да ладно тебе, пусть пишет говно и остается в своем великом и прекрасном Казахстане.

мсье Бонапарт, Вы соизволили посетить сей раздел? Какая милость

Ты лучше расскажи как ты собрался трать стасярину сидя в еле?

Я хотел сначала трахнуть, а потом свалить

A problem on number theory I came over while reading a book about biography of Leonard Euler engendered my interest in mathematics. That interest became full-blown passion upon my graduation form Republican Specialized Physics Mathematics School. That passion was a governing force behind my study at MSU, CU Math Finance program and research activities in Mathematical Institute.

Intending to apply advanced mathematical and statistical methods in computer science as well as economy I need a world-class research-level qualification in statistics and computer science. In my investigation of almost 50 US universities my primary consideration was research interest of faculty members, research scientists and postdoctoral students. I am confident now that my educational background, research experience, interests and career goals best suits expectations put upon perspective PhD students. Faculty expertise ranging from statistics to efficient algorithms and distributed and parallel programming as well as low ratio of graduate students to faculty would guarantee me supporting and stimulating environment for my PhD research and study.

Probability and Stochastic Calculus have been an area of my interest from my 1st year of study. During lectures on basic probability theory class professor Bulinski captivated with beauty and simplicity of probability theory By my 2nd year of study I had already known that probability would be my future area of specialization and asked professor Bulinski to be my scientific advisor. I conducted independent research in optimal stopping rules, game theory and random graph theory under his supervision.

At Yale I would like to make a research on Levy processes. Extensive applicability of Levy processes from finance to biology and chemistry makes this type of processes very attractive area of research.

I started to focus on Levy processes during my research at my 3rd year in Moscow. It was a problem in Optimal Stopping Rules for Heterogeneous Levy Processes. The solution involved a use of stochastic calculus and Operator Theory, specifically properties of Brownian Motion, Self Conjugate Operators and their eigenvalues. Although I did not take those classes at the time I could research the problem using tools of mathematical analysis, statistics and linear algebra that I was familiar with. I studied stochastic calculus and operator theory the next term. During my summer vacations I researched the topic more thoroughly. The research involved functional as well as statistical estimates of transitional probabilities of Markov chains and minimization problem of self-conjugate linear operator. Although I derived a solution for optimal stopping problem under more general conditions, due to lack of time and expertise in operator theory I could not continue research on the topic.

An opportunity to research functional spaces and operators came when I worked as a research assistant in Mathematical institute. Professor Bogachev’s lectures on real and functional analysis allowed me to start a research, although it required a great deal of self study. Specifically, I focused on Hilbert spaces. Study of advanced properties of linear operators, topology and of polynomial functions as well as well-known measure theory inequalities allowed me to derive some interesting inequalities and boundary conditions for eigen functions of a particular type of differential operators.

At Yale I plan to study Malliavin calculus en route to a comprehensive research of Levy Processes. I started my own study of Malliavin calculus. However, such issues as martingale expansion and Levy measures are to be addressed more thoroughly. Better understanding of Malliavin calculus and my research experience in functional as well as stochastic analysis will allow me to start research of dependence structure, sample path and distributional properties and move onwards.

Limit theorems for stochastic processes is an area that attracts me by a huge number of challenging problem and wide applicability. Writing my diploma thesis on random graph theory I used results from discrete mathematics, mathematical analysis, differential geometry, functional as well as stochastic analysis and was able to prove a result on relationship between k-nearest graph and a convex hull of random graph – it could be considered as a limit theorem. Discrete mathematics allowed me to consider special relationship between k-nearest graph and convex hull or the graph. Using tools of mathematical and convex analysis I considered a minimization problem for a certain functional of Poisson processes. Differential geometry and topology allowed me to use properties of Minkowski metric on manifolds. Fusion of these seemingly unrelated concepts from different mathematical fields produced a new result in random graph theory, that was proudly presented in Lomonosov conference in 2011. And now I am eager to leverage all my skills and expertise in other mathematical fields to make my own contribution.

Apart from my sheer enthusiasm and motivation, my research on Limit theorems is dictated by practical needs. Limit theorems especially functional versions are primary tools to build estimates and statistics. Assistance from faculty members such as David Pollard and Andrew Barron who are well known on their research on U-statistics, K-statistics and weak convergence will facilitate my progress in the field. Having attended professor Bulinski scientific seminar on Limit Theorems for Stochastic Fields for 3 academic years I was able to learn about interesting techniques such as Stein and Dvoretsky as well as a number of other methods. Functional analysis techniques will allow me to reduce existing problems to already studied ones by means of an appropriate linear operator.

Writing about my long-term career goal I would like to mention SDE. My interest in SDE came when I was writing my coursework on Game theory at my 4th year of study and have become inherent part of my research interest. The coursework problem was Nash equilibrium strategy problem. As a matter of fact it was a filtering problem. I could not understand a concept of stochastic integral at that time. On the other hand my familiarity with stochastic calculus as well as with Optimal control allowed me to derive better estimate for a particular constant, a characteristic of the optimal strategy. Scientific seminar on Math finance at Columbia University and prerequisite classes there gave me foundation of stochastic differential equations and current state of affairs.

My research on SDE I would like to start from filtering problems. In general, filtering problems deal with a minimization problem of functional on a Hilbert space. Due to my familiarity with functional and stochastic analysis the field is an ideal point to start a research. Applied Math program offers a number of courses on optimization and asymptotics which I would like to attend in order to start comprehensive research.

An efficient computational algorithm and simulation technique should be proposed. Analysis and design of algorithms require knowledge in such fields as numerical analysis, harmonic analysis and algorithms. Due to my previous focus on probability theory and functional analysis I lack expertise in those areas. On the other hand applied math faculty members research interests, graduate level classes as well as scientific seminars on Fourier analysis, scientific computing, distributed computing , parallel programming and randomized algorithms will give me necessary theoretical and practical foundation to start my future research on numerical computation and simulation of a SDE solution.

Study and research on all those areas as well as teaching activities to cover my living expenses and tuition fees will require huge efforts and time to spend but this is a prerequisite to everybody who considers scientific career. Playing water polo in MSU varsity water polo team and studying math I learned how to distribute my energy and time efficiently. Study in CU allowed me to get most from the available time and material. And now I feel myself ready to embark on a long and challenging academic career path. By conducting research in Yale being PhD program student, I can find ways to bring scientific results into applications where the products make differences in human lives. It is a critical stage in my life and career, which I am ready to face and prepared to go beyond my best.

да, теперь по крайней мере можно прочитать. суждение насколько это хорошо как SoP - оставлю знатокам.

Probability and Stochastic Calculus have been an area of my interest from my 1st year of study.Конечно звучит пафосно, но это же пиздеж явный, особенно про Stochastic Calculus.

Какой-то бессвязный поток сознания, впечатление, что главное - употребить побольше терминов, продемонстрировать якобы опыт исследований чуть ли не во всех областях, а хотя б минимальная конкретика, не говоря о связности текста, его подчинении какой-то одной общей идее, грамотность в конце концов - дело десятое. Общие слова, штампы.

Нормальные математические результаты можно описать конкретно и только словами - доказано то, получено это, предложено сё (см. абстракты к статьям).

Абсолютный ноль конкретики на две страницы убористого наукоподобного бла-бла-бла - это плохо. Фразы типа "Я применил дискру, комплан, дифгем, топологию, функан, подействовал на полученное линейным оператором и получил мега-результат по случайным графам" - это вода, даже если ты даешь ссылку или прилагаешь саму статью.

Линия повествования не выдержана, Лукина пишет о двух схемах построения эссе - хронологической и тематической. Тут ни то, ни другое.

Далее, если это окончательный вариант, то тема конкретного университета не раскрыта. Если ты подаешь в 10 школ, и просто меняешь названия университетов, то это однозначный минус.

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sven1969

любая критика и предложения крайне приветствуютсяLooking at math class bullitin at age of 11 I did not expect math would become my lifelong passion. At age of 13, my interest in math led me to Republic Physics Math School – best math school in … . There my familiarity with math became a passion and I decided to pursue scientific career in the field of mathematics.

After successful graduation of the school I passed exams and was accepted to The Department of Mechanics and Math of Lomonosov MSU – one of the best math schools in the world. I had an honour to be a student of professor Bulinski, Shiryaev, Bogachev and Fomenko. However, the man who captivated me with beauty of probability theory was professor Bulinski. After his first lecture on probability theory I knew exactly that he will be scientific advisor and probability theory would be my future area of specialization. Having graduated from MSU I started to work in … mathematical institute. There I concentrated primarily on ODE and Functional Analysis. Solving problems in Differential Equations I started to realize what role an idea plays in formulation of a mathematical model and real life applications of scientific results.

To get first class experience in applications of probabilistic concepts I applied to CU Math Finance program. Such names as Ionanis Karatzas and Philip Protter were and important factors having a direct impact on my decision to CU. On the other hand a large number of part-time students allowed me to get insight on applications of scientific results in financial as well as other industries. Andrey Solodski from safra bank gave me an opportunity to view how all those concepts work in real-life. To understand intuition behind such concepts as Risk Neutral Probability I attended PhD Level courses and in finance and economics departments. Although, I spent much time studying courses I was not registered to I was able to tie together real life intuition and abstract mathematical concepts. A sudden blow came when my sponsor went bankrupt and I was forced to pay my living expenses and tuition fees. To cover my expenses I had to find a job, and could not attend my regular classes. However, I continued to study myself and visit classes at first availability. This experience had a direct impact on my grades, since I was not able to attend midterm exams and submit my home works by deadlines. On the other hand, studying on my own I had to do all the research myself without any external help, which gave an important experience of self-study.

Instead of applying to PhD program during my masters study I decided to take a year off after graduation from CU. A year away from school allowed me to recuperate from an extensive and exhaustive math Finance Program study at CU, gain some prospective about my goals and prepare for prerequisite exams. Moreover, a year off allowed me to make proper research of doctorate programs that best suits my educational background, research experience and research interests. Research interests of faculty members, research scientists and postdoctoral students was my primary consideration in choosing PhD program. After thorough investigation of faculty members research interests of almost 50 US universities I can say with full confidence and resolution that Yale university Applied math PhD program best suits my research interests and career goals. Low ratio of grad students to faculty members guarantee my regular interaction with top academicians. A wide range of scientific interests of faculty members and research scientists Recent research publications of applied math faculty members in scientific magazines make me believe that I will work on frontiers of modern mathematics and computer science.

I consider Probability theory and Stochastic Calculus as my primary areas of research during my PhD. Levy processes is a very interesting point of initial research since there are a number of unanswered questions on dependence structure, distributional and sample path properties. At this point I plan to broaden my expertise in Maliavin calculus, which I have started to study in September, and which is necessary to make progress in the field. My previous experience with functional analysis, especially familiarity with functional spaces, will be useful in research on properties of finite-dimensional distributions of Levy processes. Specifically, I plan to use Operator theory in a study of distributional properties and dependence structure of Levy processes.

Limit theorems for stochastic processes is also the area that attracts me by a huge number of challenging problems. Writing my diploma thesis on random graph theory I used well-known results from discrete mathematics, mathematical analysis differential geometry, functional and stochastic analysis and was able to prove a result on relationship between k-nearest graph and a convex hull of random graph – it could be considered as a limit theorem, though. Discrete mathematics allowed me to analyze random graphs from deterministic point of view. Mathematical and convex analysis were particularly useful in the analysis of the convergence and convergence rate. Differential geometry enabled me with properties of Minkowski metric on manifolds. Fusion of these seemingly unrelated concepts from different mathematical fields produced a new result in random graph theory that was presented in Lomonosov conference in 2011..

My interest in Limit Theorems is also explained by my participation in Professor Bulinski’s special seminar on Limit theorems for Stochastic Fields for 3 academic years and interest in complex analysis. Although, I have an excellent training in complex analysis I believe a number of grad level classes and participation at scientific seminars will expand my expertise in complex analysis, which could be further used in a study of characteristic functions. Close collaboration with applied Math faculty members and research scientists as well as those from Math and Stat departments will be extremely helpful. Publications of David Pollard and Andrew Barron on their research on U-statistics, K-statistics and weak convergence make me believe that I will get qualified assistance in my research on Limit Theorems, especially on their functional versions.

Stochastic Differential Equations came to my life when I was writing a coursework paper on game theory and have become an important part of my research interest. Probability Theory 2 class, taught by professor Protter, allowed me to get first hand training in the field from one of its godfathers. Stochastic methods in Finance class in CU demonstrated applications of SDE in real-life. I would like to concentrate on filtering problems, both linear and nonlinear. Since filtering problem deals with minimization problem in Hilbert spaces, my familiarity with variations calculus and optimal control, functional analysis and stochastic calculus could be employed at this point. I would also like to apply results of my future research on limit theorems to SDE, so that to obtain convergence of stochastic integrals to the solution of a given stochastic differential equation.

My interest in numerical and harmonic analysis seem pretty natural given to my future interest in SDE. Theoretical results would be worthless without application and applications Numerical solutions of SDE involve a number of interesting aspects. First, I would like to work on new numerical schemes under a variety of conditions. Although, I worked mostly with numerical schemes for ODE and PDE, numerical schemes for SDE rely heavily on stochastic analysis and my previous exposition to stochastic processes and advanced stochastic analysis coupled with classes on algorithms and numerical computation may play an important role in the analysis of various schemes. Then it would be a natural to consider properties of those schemes, such as stability and convergence rate, given my previous experience with numerical analysis and a solid background in stochastic analysis those questions may be answered. An efficient path-simulation methods should also be proposed to make an SDE result applicable in real-life. On numerical methods in finance class in CU Math Finance program I was given a couple of simple path-simulation techniques. I continued my study of path-simulation techniques by reading books of P. Glasserman, DJ Highham and PE Cloeden. Professor Protter also gave me a number of valuable advices. Despite that, I plan to consult with a number of Applied math faculty, statistics faculty and CS faculty members on this topic.

In order to make my theoretical results applicable in real-life new and efficient computational algorithms should be implemented. I already started my self study of algorithms, their design and analysis. Research interest of the department faculty members and research scientists on distributed computing, parallel programming and distributed algorithms makes Applied PhD program even more appealing, since I will be able to collaborate with statisticians and computer scientists at the same time and in the same place.

Study and research on all those areas require huge efforts and time to spend but this is a prerequisite to everybody who consider scientific career. Playing water polo in MSU varsity water polo team and studying math I learned how to distribute my energy and time efficiently. Study in CU allowed me to make most from the available time and material. And now I feel myself ready to embark to the long and challenging academic career path. By conducting research in Yale being Ph.D program participant, I can find ways to bring scientific results into applications where the products make differences in human lives. It is a critical stage in my life and career, which I am ready to face and prepared to go beyond my best.