Nathan Manwaring and Dr. Tyler Jarvis, Mathematics Tropical Mathematics is a relatively new field of mathematics that is getting a lot of attention recently. It is applicable in the field of Combinatorics as well as Phylogenetics, and more uses are being found each day. Our goal was to find a way to classify Tropical Polynomials […]

## Finding a Galois Representation Corresponding to a Hecke Eigenclass

Meghan De Witt and Dr. Darrin Doud, Mathematics Department My project was to finish a thirteen year old unsolved problem that provided an important computational example of a conjecture in the field of Algebraic Number Theory. Originally, we worked with the techniques of elliptic curves and class field theory to try and isolate the objects […]

## Factorization of Tropical Polynomials

Nathan Grigg and Dr. Tyler Jarvis, Mathematics Tropical algebra, also called “min-plus” or “max-plus” algebra, is a relatively new topic in mathematics that has recently caught the interest of algebraic geometers, computer scientists, combinatorists, and other mathematicians. According to Andreas Gathmann , tropical algebra was pioneered by mathematician and computer scientist Imre Simon in the […]

## Calculus Excel at BYU: Increasing Student Potential for Success

Karla Jeanese Hendricks and Dr. Michael Dorff, Mathematics Success in calculus can have significant implications both within an intended field of study and throughout academic pursuits. Of the 34 science, technology, engineering, and mathematics (STEM) majors at BYU, 25 of them require calculus for graduation and 20 of them require it as a prerequisite for […]

## Non-Linear Ray Tracing Visualizing the Impossible

Jared Duke and Dr. Matthew Anderson, Math Department Ray tracing is a common technique for computational, photo-realistic simulation of the “real world.” However, most current approaches assume light propagation is linear: that is, light always travels in a straight line. Our aim was to create a ray tracing program that would handle the “bending” of […]

## CONSTRUCTING WAVELETS WITH GOOD FREQUENCY RESPONSE AND TWO VANISHING MOMENTS

Chad Lillian and Dr. Andrew D. Pollington, Mathematics Recruitment of loudness is a hearing impairment in which certain frequency ranges are not as audible as others. If a common hearing aid is used to remedy this problem all frequencies will be amplified and there will be no advantage. The solution to this problem is a […]

## Metacalibration Proof of the Triple Bubble Conjecture in R3

Donald Sampson and Dr. Gary Lawlor, Mathematics Education Goal/Purpose My project was to further develop the technique of metacalibration, a new method of minimization proof, in order to prove the triple bubble conjecture: that the standard triple bubble is the least surface area way to separately enclose three given volumes. Importance of Project Over the […]

## Option Pricing for Inventory Management and Control

Bryant Angelos and Dr. Jeffrey Humpherys, Math Department In recent years, capital markets have experience remarkable growth in both the total volume of trades and in the complexity of the financial instruments being traded. Investors are becoming increasingly sophisticated as they search for newer and more effective ways of managing and protecting themselves from risk. […]

## NONNEGATIVE MATRIX FACTORIZATION

Gretchen Schillemat and Dr. Jeffrey Humpherys, Mathematics The purpose of this project was to study the nonnegative matrix factorization (NNMF) problem: Given a nonnegative matrix V, find the” best” nonnegative matrices W and H, such that V WH. The main focus in our project was when the data was sparse. We began by exploring […]

## Metacalibration Proof of the Triple Bubble Conjecture in R3

Donald Sampson and Dr. Gary Lawlor, Mathematics Education Goal/Purpose My project was to further develop the technique of metacalibration, a new method of minimization proof, leading to a proof of the triple bubble conjecture: that the standard triple bubble is the least surface area way to separately enclose three given volumes. Importance of Purpose Over […]