University Scholars Exploration Series – Influential Equations

Each semester, the University Scholars enroll in small-group, discussion-based seminars. In Spring 2016, Scholar Chloe Dixon ’17 taught the seminar “Exploring Influential Equations” as her Undergraduate Teacher Scholars capstone project. One of her students, computer science major Steven Leal ’18, reflects on the class and a few lessons learned.

University Scholar Steven Leal '18
University Scholar Steven Leal ’18

By Steven Leal

“What” is a simple question. It’s typical that the majority of modern society is equipped to handle this inquiry. Simple requests for knowledge are normally met with programmed responses.

Take for instance, “What’s the distance from London to Paris?” Instinctively, many of us reach into our pockets and answer, “I don’t know, let me ask google…”

What’s the best series on Netflix to binge?” We’d follow with an opinion from Rotten Tomatoes.

What’s the air speed velocity of an unladen swallow?”

As a collective, humanity has painstakingly timed the migrations of most birds species and rattled off about their favorite shows long enough to prepare a safety net of information we can rely on for our most common shared experiences.

But how about “why?” It’s a simple word, one less letter than “what,” but the syllable requires so many words in return. “Why do we fall back down when we jump? Why is the sky blue? Why is there an unexpected item in the bagging area?” Throughout history, we have always struggled to tie our simple experiences of the past together to explain the present and even predict the future.

Thankfully, there are and have been a few among us with crazy hair, crazy ideas, and that are crazy enough themselves to become offerings to the epiphany gods in our stead. They get these notions in their heads that wonderful phenomena are reproducible, that our natural world is governed by a set of rules we can understand and that answering tiresome questions like “why” can help widen the safety net for the rest of us common folk.

Over the spring semester, our Influential Equations seminar took it upon ourselves to find those with the craziest hair, the craziest ideas, and who were just crazy enough themselves to examine how reasoned insight can change our understanding of the world around us. From the simplicity of the Pythagorean Theorem to the echelons of Schrodinger’s wave equation, we discussed the derivation of these famous formulas, their widespread applications in today’s society, and how many women you must court before you can develop general relativity (and it was quite a few to say the least).

Toward the beginning of the semester, our class tackled our heroes of the past that developed the building blocks of calculation using, for example, the quadratic formula and the fundamental theorem of calculus. With more advanced methods of calculation, mathematicians such as Leonhard Euler could find common relationships in geometry that would later lead to uses in advanced computer rendering algorithms and applications far beyond expectations of the past.

Complex numbers, thermodynamics, and Maxwell’s equations all found their way into our discussions nearing the end of the school year. The applications of magnetism with bullet trains, rail guns, MRI machines, and many other advancements were among the multitude of other formulas we examined to understand just what became of us as a society after a few eureka moments.

The summation of our experience participating in this seminar boils down to a few important points. Firstly, if you are ever recognized for your profound contribution to aiding in the comprehension of the known universe, make sure you get your portrait painted with either an impressive hairdo or a towel on your head to compensate for your lack thereof (we’re looking at you, Euler). Secondly, you can make wonderful discoveries for humanity after coming from any background, as long as you have an obsession for knowledge or a personal rivalry you take a bit too far. It seems historically proven that a little bit of crazy can get you a little closer to answering “why” if you mix in a pen, paper and a little math.

Freshmen are recruited each spring to join the University Scholars program. To learn more, please see:

A class activity had Augustus Ellis ’17, Garrett Goble ’16, and James Felderhoff ’17 smash cups to demonstrate the second law of thermodynamics, that entropy always increases.
A class activity had Augustus Ellis ’17, Garrett Goble ’16, and James Felderhoff ’17 smash cups to demonstrate the second law of thermodynamics, that entropy always increases.

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