Statement of Purpose

Over the past four years I have spent most of my time taking classes, studying from books, reading papers, doing homework, giving presentations, attending various events and seminars about mathematics. All of these studies made me understand how passionate I am about mathematics. However, my professors and friends in mathematics PhD programs tell me that this is just the tip of the iceberg. Now then I have decided to combine all these efforts to take me further at the world of researching. Despite the arduous nature of research, I am confident though that my resoluteness gives me the ability to reach my targets. The first time I discovered my determination was whilst I was playing chess at the National level. The hardest challenge at that stage was to prepare myself in order to compete in high level tournaments, in which I later managed to win awards. The second milestone was making the decision to become a researcher in my undergraduate years. After choosing such a route for my career, the significant increase in my GPA is attests to my ambitious and dedicated nature mentioned above. On the way to becoming a mathematician, I find nothing more striking than the simplicity and elegance of geometric ideas. As I attended my first lectures in Euclid’s fifth axiom, Gauss’ “Remarkable Theorem” and Einstein’s equations, my previous perceptions changed drastically under the pressure of these simple but powerful notions. Following that impact, it became crucial for me to keep track of new advances in the field of geometry. Delving into the depths of geometry, I came to appreciate its connections with many topics which appeared unrelated at first sight. One of these connections, namely to Groups and Symmetries, became my the topic of my undergraduate thesis. The Classification of the Wallpaper Groups was the title, and analyzing symmetries of two dimensional tessellations in terms of group theoretical notions was the goal of this study. During my educational life, I put