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 […]

## An Explanation of Strange Duality in terms of Landau-Ginzburg Mirror Symmetry

Rachel Suggs and Dr. Tyler Jarvis, Department of Mathematics Suppose you have a physical system that can jump suddenly between two stable states. Then a function modeling the system will have a singularity at the jump. Our singularities will all be dened by polynomials, such as x3y + y5 + z2. Mathematician V.I. Arnol’d studied such singularities in […]

## Quadratic Fields with 2-Skylow Class Group Isomorphic to C2kC2

Adele Lopez and Dr. Paul Jenkins, Department of Mathematics We prove that there are innitely many imaginary quadratic fields with 2-class group isomorphic to C2kC2 for any given positive integer k. This work is based on a related result for cyclic 2-class groups by Dominguez, Miller and Wong, and our proof proceeds similarly. However, we […]