SENIOR  COMPS PRESENTATIONS

in Mathematics

  

 

“n = 2 is great, but the fun starts at n = 3” 

  Jorge Torres Perez

The goal of this project is to present in an organized and easily coherent fashion the proof for Fermat’s Last Conjecture in the Diophantine Equation \( x^n+y^n=z^n\) for when \(n=3\). The proof is partially accredited to Euler, who was the first to carry out the rigorous proof, although he failed to recognize a fallacy in the procession of his logic. This project emphasizes concepts integrated from Euler’s own previous works in sums of squares to prove a lemma that fortifies and bridges that gap. The importance of this specific Diophantine example is that it is the first case in Fermat’s Last Theorem, also known as Fermat’s Last Conjecture, for which states that there are no nonzero integer solutions of \(x, y\) and \( z \) for the equation \(x^3+y^3=z^3.\)

 

An Introduction To
Singular Perturbation Theory

Erika May

Often, we come across mathematical problems that cannot be solved exactly. Singular perturbation theory explores methods of approximating solutions to such problems by identifying a small parameter for which a solution exists, and observing the behavior of the solution as the parameter approaches zero. In this presentation, we will explore an example of a singular perturbation problem, in which we introduce the method of matched asymptotic expansions as our method of approximation. We will also discuss boundary layers and how they affect the solution. Ultimately, we will visually and analytically compare our approximation with the exact solution.

 
 

Modelling Economic Growth Using  Differential Equations

Chad Tanioka

The use of differential equations is prevalent in the world of physical sciences because they are an essentail tool in understanding complex dynamic systems in the real world. In this presentation, we will investigate Robert Solow's growth model that features a differential equation used to describe equilibrium solutions to our economics system.  We will discuss the mathematical and economical interpretations of the Solow-Swan economic growth model, address its key assumptions and then will attempt to solve for equilibrium solutions using two different techniques.

 

 

Thursday, February 25th, 2016

5:00-6:30pm

Fowler 302

 

**Refreshments Will Be Served**

Everyone is invited!