My Statement Of Purpose as a Mathematics PhD Student

The Statement of Purpose, also known as the SOP, is the most important part of your university application. It introduces you to the admissions committee and gives them a chance to get to know you better. Its objective is to convince the committee that you deserve to be a part of the university’s community. If written well, your Statement of Purpose can get you into your dream university.

Statement Of Purpose Sample

My reasons for wanting to do a PhD are (in my eyes) the obvious ones. I am interested in Mathematics and I enjoy doing it, I hope this is reason enough. Ideally, I would like a career in academia as I have enjoyed studying mathematics thus far and want to continue.

I am now in my final year of a Maths degree at the University of Warwick, UK. In previous years I achieved high grades, high enough to alleviate the worry concerning graduating with a classification (equivalent to a GPA of 4.0). This grade from my previous year’s examination success has enabled me to take the courses which interest me most, regardless of their difficulty; this is evidenced by the fact that I am only taking graduate-level courses this year. By far my favourite courses this term are Algebraic Geometry, Modular Forms and Elliptic Curves; it is somehow rewarding to use the tools and knowledge I gained from technical, purely abstract subjects such as Group Theory, Commutative Algebra, and Complex Analysis in a much more tangible fashion. In particular I nd Modular Forms very interesting: I am continually surprised by the subject’s order and `niceness’. I hope to learn more about how modular forms relate to algebraic geometry and number theory over the coming academic year. Being in the final and master’s years of my degree I am required to write a dissertation. Under the supervision of Professor Miles Reid FRS, I am writing a dissertation in the area of algebraic geometry and modular forms. The exact title is yet to be decided, but the project will most probably be concerning Hilbert Modular Forms and their associated surfaces with an emphasis on resolving their singularities and toric varieties. I aim to give examples of some of the more abstract concepts using toric varieties. Currently, I am reading about cyclic quotient singularities and their resolutions using Herzebruch’s continued fractions method.

I have written projects in both my second and third year; an exposition on Waring’s problem and the Hardy-Littlewood Circle Method, and last year a paper titled `Primes of the Form x2 + ny2′, which was a basic introduction to Quadratic Forms and Hilbert Class Field Theory. I particularly enjoyed my project last year, the member of the faculty who supervised me, Dr Johan Bosman, really encouraged and motivated me; my time spent working with him has inspired me to study algebraic number theory further. During my second year, I was awarded the Ron Lockhart scholarship. It is awarded once every three years to an undergraduate mathematician who has shown potential during their first year. Each year since starting university, I have taken the maximum number of extra mathematics courses permitted by my department. Some of my favourite courses from previous years include Galois Theory, Rings and Modules, Groups and Representations, Algebraic Number Theory and Manifolds. During my Galois Theory course, I enjoyed seeing applications to Algebraic Number Theory and Classical Number Theory; for example, seeing a proof of quadratic reciprocity using cyclotomic elds. Although I have never taken a course in topology, I have read the rest two chapters of Hatcher’s Algebraic Topology while on an REU last summer in Minnesota. Thus, I do have a working knowledge of point-set topology, homotopy, the fundamental group and simplicial homology. I plan to take a course in algebraic topology next term. I hope to learn more algebraic topology during graduate school; it is a subject in which I am becoming very interested. During my time at the University Of War-wick, I have given many seminars to fellow undergraduates, the last of which was on quadratic forms and genus theory. In general, I am a big supporter of discussing mathematics: I spend a good portion of my time in the mathematics common room arguing and discussing mathematics with friends. I hope to nd a similar dynamic at graduate school.

I have a good amount of teaching experience, both at the university level and below. During my second year of university, I took part in a government-funded teaching scheme, which entailed learning basic teaching theory during weekly seminars juxtaposed with teaching Mathematics in a local secondary school (high school) for half a day a week. I was then selected to take part in a charitable programme organised by the university, teaching Mathematics in underprivileged schools in Der es Salaam, Tanzania, for six weeks of the summer vacation. At the university level, I worked as a teaching assistant for a first-year Analysis course for two consecutive years. I am currently working as a supervisor; a group of first-year mathematics students are assigned to me, I am responsible for marking all their assignments as well as organising twice-weekly meetings during which I cover topics including analysis, linear algebra, abstract algebra and differential equations.

During the course of my degree, I have become close with Dr John Moody, my academic tutor. Over the years we have had many conversations during which he exposed me to new and cool mathematics. In my opinion, the most important lesson he has taught me is to forget about the course syllabus; to learn mathematics instead of a mathematics course. This is a philosophy I plan to implement further at graduate school.

This year I have taken advantage of the many seminars and talks given by my department. The department has a strong number theory/algebra group, hosting regular talks on current research areas. The talks are motivating and inspirational, perhaps best of all they give me a sense of perspective and direction. It is nice to get away from the rigidity of formal lecture courses and get away from the Definition, Theorem, Proof style of learning, to get a taste of the big picture. I recently attended a talk by Professor Roger Heath-Brown titled Diophantine Equations: Algebra, Geometry, Analysis and Logic, during which he exhibited some of the many ways to study Diophantine equations. I left the talk motivated and wanting to know more; in general, the more mathematics I learn and see, the more I am amazed by its `niceness’ and the more I want to understand it.

I am applying to Ohio State because of its strong algebraic geometry and number theory groups, more importantly, the current research topics of some department members immediately interest me. For example, I see that Professor Christian Friesen has done work on the class number of quadratic extensions. I brei y touched on this subject during my algebraic number theory course and also during an essay I wrote on primes of the form x2 + ny2, and I would love the opportunity to learn more. Also, I am currently learning about the resolutions of singularities in relation to the dissertation that I am doing under Professor Miles Reid. I would be interested in continuing this work, possibly under the advisement of Professor Mirel Caibar, who I see as doing research in related areas. In general, I hope to understand more about algebraic geometry, elliptic curves, modular forms and homological algebra at graduate school, and I believe Ohio State is a good place to achieve this.