Here's the topic of choice essay for common app; I've just finished the rough draft, and I would appreciate it if you guys could edit it some. Here it is, and thank you.

Topic of Choice:

How has taking a certain risk reevaluated who you are; how has this new found yearning taken from the risk revitalized education and learning for you?

I've Caught This Cold

Ubiquitous, yet despised. It's like a disease that dissipates through the human body; though many may rid themselves of the spreading through many self-created orifices, the select few have it ingrained into their central nervous systems and minds. It's not the plague, cholera, or even an actual contagion, but mathematics.

I was beginning my senior year, and already, I had upset the administration. Not my high-school administration, but the local college's; I had registered for a math class well beyond what prerequisites I needed, and essentially lied to get into it. I was at least two college years behind and had barely scratched the surface of calculus BC. Though I convinced myself that taking an independent study in multivariate calculus would be sufficient to get me where I needed, I know now discipline was more essential for this course than was my actual math ability.

The course began with a comfortable review, solving non-homogeneous differential equations using Laplace Transformations, and progressed into partial differential equations. I was baffled by my sudden mathematical impotence, and as the instructor, Dr. Kelly Cline, continued through the course from such subjects as Fourier Series, non-linear differential equations, or even heat-diffusion, I cannot say I felt more comfortable and adjusted. Despite having consistent conflicts with the subject material, I began to notice how mathematics begins to all connect; how, simple multiplication can be expressed as an infinite series, how the motion of a spring can be expressed as a non-linear differential equation, how natural logarithms can confuse the transitive property, and how infinity can create solutions that just don't exist.

I found myself, in my free time, finding multiple solutions to a single-integral, experimenting with integrals I knew couldn't be solved, or even trying to mix Archimedes' formula of exhaustion with modern integration. While I was doing this, however, I was severely neglecting the course I was thoroughly unprepared for. I was averaging a C-, endeavoring desperately to eke by tests, and literally begging my teacher for help on occasion.

The class itself was a disaster; I learned much about real-world usage of differential equations, historical gaffes made by mathematics as the Tacoma Narrows Bridge incident in 1940, but I could not competently keep up with the material. However, the class itself, the risk in doing poorly as I had never done before, gave me a subject I now love to do, a hobby with a realistic usage. It's hard to describe how I can view something as byzantine as an infinite series of trigonometric functions as beautiful, but I've finally found that subject where I don't need an explanation. I just know that I love it, and will always love the mercurial form that is mathematics.