UCSD Math 20C

This fall I took a UCSD mathematics course on multivariable calculus to extend my learning. I got to experience both the lecture-style teaching and fast pace of college. Whether it was learning about vectors, polor coordinates or ititerated integrals, my brain got to relish in the world of numbers :)

An Essay on Fubini's Theorem

By: Erica Lee

When I taught my sister how to solve for a variable’s answer when given two simple equations, I realized how philosophical math could be. By teaching her a method of substitution - putting “x” in terms of “y,” solving for “y,” then getting “x” – I realized that there were multiple ways of getting an answer.

A more complex version of this substitution strategy is derived from Fubini’s theorem, which I recently learned in my UCSD calc class. Fubini's theorem computes double integrals by allowing the order of integration to be changed.

By being able to switch the “x,” “y” and “z” variables when I tediously solved the equations, I came to the realization that in life – just like math - one can take different routes to find the same solutions. The answers to life are not always easily accessible, but for those who pursue them often find them rewarding.

While some students avoid these difficult problems because they ignite frustration, I relish in them. The world of math has become my niche, allowing me to combine my reasoning skills and excitement to better understand the world. Just as I attempt difficult mathematical problems to better understand their underlying principles, I undertake other challenges – whether academic, athletic or social - so that I can learn more about myself, but more importantly, my potential.

In addition to Fubini’s theorem, the principles of calculus have enlightened my mind about the characteristics of life. Differential calculus deals with the derivative: by finding the derivative of a function at every point in its domain, it’s possible to produce a new function. This derivative function, molded from the original one, highlights the importance of growth - for a new function can be spawned off of the old one, while still maintaining relativity to its origins.

Each step I take in life creates a rippling effect, building a trail of footprints as I discover more. Even though my aspirations move me farther from my simplistic childhood, I’m still able to see where I’ve come from and what I’ve done - my path of achievements, but also my mistakes, being evidence of my progression. Calculus has bestowed upon me not just academic knowledge, but also insight into life.

In addition, math has changed my attitude when approaching situations. Although my drive used to be fueled by peers and friends, I became intrinsically-motivated when I gained an understanding about the theories of math. Although philosophy may be composed of different arguments tearing each other down, mathematics is fundamentally-based on collaborative work over an extended amount of time. A proven theorem forever follows from its axioms; if other mathematicians return to work on it, they come to build on the axiom, not argue. The only inherently competitive part of math is the race for more knowledge. The only competitor in my life is myself.

Although I harbor uncertainty about what I want do in life – with my aspirations open to as much change as a variable - I know that I’ll always want to enrich the lives of others - whether scientifically, emotionally or artistically.

However, what I pursue in life isn’t as important as the pursuit in general. I’ll always maintain a belief in myself to succeed. I base my life off of words spoken by Emerson: “Make the most of yourself, for that is all there is of you.”