Imagine a world in which nobody innovates. A world in which not a single human being strives to make changes. Mathematics has the power to change the world. Newton used his calculus to systematize physics, which has had a major impact on the world. The axiomatization of Mathematics, from Euclid’s Geometric methods to the analytic methods of Cauchy, Hilbert, Weierstrass, Cantor, Dedekind, etc., to the logical methods of De Morgan, Russel, Turing, etc., Mathematics is firmly built on the shoulders of innovators who took risks. In applying to grad school, I am taking a risk. I could have taken the more financially secure route of going into industry, but I would not be satisfied in my life. First and foremost, I am a scholar: a learner, a teacher, …show more content…
Winona State University opened my eyes to the plethora that is higher Mathematics. In the first class of my first semester here, Linear Algebra with Dr. Aaron Wangberg (who later became my research advisor and additionally my academic advisor), I learned the basics of mathematical objects and the maps between types of objects. Little did I know at the time, but those functions I was building every time I made a matrix, would later become more useful than vectors that were being operated on. That semester, I also took Numerical Analysis, in which I learned to thoroughly enjoy Scientific Computing, which would come in handy for my capstone project. A year later, I took Abstract Algebra with Dr. Joyati Debnath, and from there, my entire plan changed. Until that point, I had always thought of myself going into industry and getting a job, but she had other plans for me. She introduced our class to the land of Groups, Rings, and Fields, and I was hooked. From her class, I started my first major project: “On the Algebra of Rotations in R^3”, in which I studied the algebraic concepts behind the ways we represent 3D rotations. Joyati encouraged us to present our projects wherever possible, and with her, I did just that. I presented that project at PME WI ‘16, PME MN ‘17, MUMS ’17, MNSCU Undergraduate Research Festival ’17, Mathfest ’17, and finally