Physical Sciences and Mathematics Commons^™

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Computational Number Theory: Modular Forms, Paul Jenkins

Journal of Undergraduate Research

In 2017 and 2018, the following students participated in the BYU Computational Number Theory research group under my direction and produced the following deliverables.

Geometric Optimization, Analysis, And Design, Denise Halverson

Journal of Undergraduate Research

1. Evaluation of how well the academic objectives of the proposal were met

The goals for the mentoring environment were reached:

• Academic Development – Each student had the opportunity to work on a cutting edge research problem, as indicated below. Papers are in various stages of completion, a few submitted or accepted for publication, but all have drafted papers.
• Community Development – Several students were able to attend the MAA Math Fest in both 2014 and 2015. Most students gave presentations at the CPMS Student Research Conference. My students have been able to interact with engineering student working on similar …

Spectral Graph Theory For Weighted Digraphs, Alexander Zaitzeff, Jeffrey Humpherys

Journal of Undergraduate Research

For digraphs weighted and unweighted, one important application is ranking: Given a directed graph, whether it be the Internet or a social network, which node (representing a web page or a person) is the most important? There are many different methods to find answer this question. A few are highest indegree, closeness centrality¹, betweeness centrality², eigenvector centrality, Katz Centrality³, and PageRank⁴. Our idea is to use sparsity, or the idea that in a network only has a few important nodes, to determine the ranking on a graph.

The Fourier Coefficients Of Modular Forms, Kyle Pratt, Dr. Paul Jenkins

Journal of Undergraduate Research

Modular forms are complex analytic functions with remarkable properties. Modular forms possess interesting and surprising connections to many different branches of mathematics. For example, it is well-known that Andrew Wiles’ proof of Fermat’s Last Theorem, a conjecture that had been unresolved for more than three centuries, utilized modular forms in a crucial way.

Zeros Of Poincare Series Of Level 2, Andrew Haddock, Paul Jenkins

Journal of Undergraduate Research

Introduction Poincaré series are a certain type of modular form. Modular forms are complex-valued functions that satisfy certain symmetry properties. There are many different types of modular forms, and one way to classify modular forms is by their level, such as 1, 2, 3, etc. They are of much interest as a research subject because they are connected in surprising ways to many different fields in number theory—e.g., elliptic curves, quadratic forms, and partition functions, to name just a few. As we gain more insight into the various properties of modular forms, we gain more insight into how these various …

Transpose Symmetry Groups Of Noninvertible Polynomials, Nathan Cordner, Dr. Tyler Jarvis

Journal of Undergraduate Research

Introduction Mirror symmetry is an area of mathematical research that stems from theoretical physics, particularly from string theory. Solutions of problems in mirror symmetry yield not only interesting mathematical results, but also have important theoretical implications for high energy particle physics.

Byu Computational Number Theory Research Group David Cardon, Darrin Doud, Paul Jenkins, And Pace Nielsen, Pace Nielsen

Journal of Undergraduate Research

In the years 2013-2014 we held a weekly seminar in which every supported student gave presentations at least once (but usually twice or more) per semester. This gave the students opportunities to learn and develop presentations skills, which will help them later in their careers. It also gave them opportunities to work together in a tight-knit group setting. This learning was augmented by regular, one-on-one weekly meetings with their advisors. Many of the students wrote professional research papers published in peer-reviewed journals, presented their research at conferences, and many won prestigious university and even national awards.

Leveraging Mosts (Mathematically Significant Pedagogical Opportunities To Build On Student Thinking), Keith R. Leatham, Blake E. Peterson

Journal of Undergraduate Research

Phase 1, Goal 1: Purposefully create a data set of videotapes and transcripts of secondary classroom mathematics discourse that reflects the student mathematical thinking that can occur in diverse classrooms.

Computational Modeling Of Wave Propagation In Metamaterials, Shue-Sum Chow

Journal of Undergraduate Research

The project is concerned with the study of wave propagation in metamaterials. We recall the work plan described in the original proposal and provide an evaluation of the academic objectives.

Defining The Transpose Group In Landau-Ginzburg Mirror Symmetry, Lisa Bendall, Dr. Tyler Jarvis

Journal of Undergraduate Research

Introduction. Mirror symmetry is a phenomenon first observed in theoretical physics, which has garnered interest among mathematicians. The Landau-Ginzburg mirror symmetry conjecture proposes two algebraic structures which are isomorphic, or in some sense “mirror” each other. These structures are built from polynomials and corresponding symmetry groups.