When I was younger, I was the kind of kid who would read math textbooks the way other kids would read novels. I was in awe of the mysterious people who were responsible for the concepts contained in those textbooks, and I secretly hoped that one day I might be able to make a contribution as significant as theirs. Participating in something as significant as such advancement was the greatest honor I could have asked for as a child like me.
Throughout my childhood, I devoted a lot of energy to pursuing my interest in mathematics, which was fueled both by my natural curiosity and by the desire to fulfill this dream.
Prior to beginning my studies at a university, I competed in a number of mathematics competitions, which tested students’ speed, accuracy, and originality in problem-solving.
As a result of such efforts, my talents in the area gained me the highest possible mark on the examinations given at my school, as well as the opportunity to attend a summer camp at Cornell University. I always had a good time talking about difficult arithmetic problems with my classmates and my teachers, exchanging ideas and gaining fresh perspectives. Calculating numbers or locating a key were just two examples of the kinds of challenges that might be tackled with the assistance of mathematics, which I found both practical and fascinating. In spite of this, there came a time when I could no longer derive satisfaction from overcoming challenging challenges; the fact that I could always locate the solution made it appear to be a routine activity. In my first year of college, I learned the hard way that no one can do anything worthwhile without putting in a lot of work and that I had to pay the price for my cockiness.
To my great good fortune, I have never lost my interest in mathematics. When I found out that mathematics could foresee the future, I was astounded since an accurate mathematical model included everything.
After gaining this fresh understanding of the subject matter, I was able to see that mathematics holds the potential to make my life and the lives of others better. My emphasis shifted at this point away from finding solutions to equations and toward developing models.
Among the many subfields of mathematics, ordinary differential equations and dynamical systems are the ones that most pique my attention. I have studied a lot of material pertaining to these topics in a variety of classes, and I have learnt a lot of fascinating theories, such as bifurcation, chaos, and nonlinear systems.
In the meantime, my hard work and dedication allowed me to achieve success in these classes. As I went deeper into my studies, I came to the realization that each idea, regardless of how straightforward it may appear, always includes additional complex information that calls for in-depth reflection. For instance, Professor XXX discovered that for a continuous function, the presence of a point with period three indicates chaos. This concept intrigued me owing to the fact that it is both straightforward and intricate at the same time. The comparable property is reflected in the work that I’m doing right now, which is related to a theorem about central manifolds in finite dimensions. I attempted to demonstrate its correctness in a finite dimension while maintaining its qualities in a lower dimension with a reduced number of dimensions. This thus makes it possible to forecast what takes place in a higher level just by taking into consideration what one may infer about a lower dimension.
Dynamical systems are, without a shadow of a doubt, effective and helpful. When I was an undergraduate, I realized that the solid foundation in mathematics that I have can help me in my pursuit of additional study on many applications. In order to better prepare myself for conducting independent research as part of the Ph.D. program I intend to continue my research on this subject when I am a student in graduate school. A depiction of a mathematical model is not as realistic as a dynamic system since dynamic systems are intrinsically linked to the natural world. As a result, following the conclusion of my doctoral studies, one of my career goals is to do research related to this field. I hope that the classes that I take here in Maryland will help me figure out the specific path that my future research will take. In particular, I have an interest in the articles that Professor XXX has written on medical and physical models. These publications would be an excellent springboard for me to contemplate where I want to go with my research in the future.