Physical Sciences and Mathematics Commons^™

Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma

Undergraduate Student Research Internships Conference

First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.

Tournaments And A Fibonacci Link, Michael Long, Daniela Genova

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Round robin tournaments are a type of directed graphs with applications to athletic competitions and transportation logistics. The presentation begins with a brief series of informative theorems and properties of directed graphs, which are imperative to our understanding of the properties that make directed graphs (and, subsequently, round robin tournaments) uniquely interesting. We then present a number of results about the properties of tournaments (defined as a complete directed graph), including transitivity–a relatively uncommon property used to determine domination in a round robin tournament–and connectivity, which can most often be seen in determining means of transportation between any two locations. …

Predator-Prey Model With Herding Behavior And Hunting Quota, Randy Lee, Mahbubar Rahman Phd

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The Lotka-Volterra predator-prey model is widely studied and used in many disciplines such as biology, ecology and economics. It is used to describe the growth and coexistence of two interacting populations. The model consists of a pair of first-order nonlinear differential equations. In this paper, we studied steady states, stability of steady states, existence of limit cycles, and bifurcation behavior of the predator-prey model by modifying the existing model with hunting quota. We also illustrated our results with numerical simulations.

Block Designs, Lucien Poulin, Daniela Genova

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Block designs are a type of combinatorial structures that can be used to model many different types of problems ranging from experimental design to computer software testing. They can be used to construct schemes that ensure complete optimization and efficiency of the given experiment. We focus mainly on Steiner and Kirkman triple systems, as well as, on different ways for constructing block designs. Well known results in combinatorics such as Fisher’s inequality and Kirkman’s schoolgirl problem are also discussed.

Simulation Environment For Object Manipulation With Soft Robots In Shared Autonomy, Devin Hunter, Fabio Stroppa, Allison Okamura

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The robots of today have grown to be of much more significant use than their predecessors. Robots are now being used in industries outside of the factory setting which can be seen primarily in the medical, transportation, and social fields. With robots taking on all of these new roles within our society, the establishment of robust human-robot collaboration is crucial in order for robots to be able to successfully complete desired tasks without becoming a hinderance to nearby humans. We explored this concept by implementing a shared-autonomy algorithm named MBSA (Motion Based Smart Assistance) to a soft robot simulation and …

Embedding Graphs On Surfaces And Graph Minors, Tracy Leung, Mya Salas, Dylan Wilson

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

A planar graph is a graph that can be drawn in such a way in the plane, so that no edges cross each other. In other words, it is a graph that can be embedded in the plane. We discuss the conditions that make a graph embeddable on a sphere with k handles. Then, using vertex deletions and edge contractions, which produce graph minors, we examine if a graph is minimally nonembeddable on a surface. To conclude, we discuss an important result, that the set of minimally nonembeddable graphs on a surface is finite.

University Scholar Series: Tatiana Shubin, Tatiana Shubin

University Scholar Series

Moving in Circles: the Beauty and Joy of Mathematics for Everyone

Tatiana Shubin joined the faculty of San Jose State University in 1985 after earning her Ph.D. in Math­ematics from University of California, Santa Barbara. In 1998, she founded San Jose Math Circle and the Bay Area Math Adventures. In 2006, Shubin became a co-founder of the first Math Teachers' Circle in the US. This circle proved to be a seed which germinated to produce the entire Math Teachers' Circle Network. She launched the Navajo Nation Math Circles project in 2012, became a co-founder and co-director of the Alliance of …