An Experiential Report On The Thayer Method Of Teaching Across College-Level Chemistry, Biology, Math, And Physics Courses, 2020 Georgia Gwinnett College

#### An Experiential Report On The Thayer Method Of Teaching Across College-Level Chemistry, Biology, Math, And Physics Courses, Kevin P. O'Halloran, Sairam Tangirala, Fengjie Sun, Leonard E. Anagho, Gerald Agbegha, Clay Runck, David Roth, Amy H. Erickson

*Georgia Journal of Science*

The Thayer method of instruction is a little-known active learning technique that dates back to 1817 at the U.S. Military Academy. This study describes the implementation and statistical evaluation of an adaptation of the Thayer method in a variety of college science and math courses. All courses had five characteristics in common: (i) students were given a daily reading schedule and instructed to prepare before class, (ii) each class started with a question and answer session, (iii) class time minimized the use of lecture, (iv) class time maximized the use of active learning, and (v) students were frequently quizzed ...

Discovering Pascal's Triangle, 2020 Concordia University St. Paul

#### Discovering Pascal's Triangle, Cara Schmidtke

*Research and Scholarship Symposium Posters*

The Discovery of Pascal’s Triangle is a great lesson for students because it gives them a glimpse into the history of mathematics, patterns in upper level math topics, and connections between real life situations using combinations and more abstract math concepts, such as Pascal’s triangle. My research dives into how Bruner’s theory on discovery learning and the concept of constructivism can motivate my differentiated learners to understand Pascal’s Triangle and enhance their understanding of combinations. Educators can use this research to promote active learning in upper level mathematics classrooms. The discovery opportunities I provided to my ...

On The Application Of Multidimensional Logarithmic Residue To Systems Of Non-Algebraic Equations, 2020 Nukus State Pedagogical Institute

#### On The Application Of Multidimensional Logarithmic Residue To Systems Of Non-Algebraic Equations, Barlikbay Prenov

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

In this paper, the residue integrals over cycles associated with a system of non-algebraic equations and formulas for their calculation are given. Their connection with the power sums of the roots of the system is established. Some examples are considered.

Parameter Identification For Gompertz And Logistic Dynamic Equations, 2020 Missouri University of Science and Technology

#### Parameter Identification For Gompertz And Logistic Dynamic Equations, Elvan Akin, Neslihan Nesliye Pelen, Ismail Ugur Tiryaki, Fusun Yalcin

*Mathematics and Statistics Faculty Research & Creative Works*

In this paper, we generalize and compare Gompertz and Logistic dynamic equations in order to describe the growth patterns of bacteria and tumor. First of all, we introduce two types of Gompertz equations, where the first type 4-paramater and 3-parameter Gompertz curves do not include the logarithm of the number of individuals, and then we derive 4-parameter and 3-parameter Logistic equations. We notice that Logistic curves are better in modeling bacteria whereas the growth pattern of tumor is described better by Gompertz curves. Increasing the number of parameters of Logistic curves give favorable results for bacteria while decreasing the number ...

Tournaments And A Fibonacci Link, 2020 University of North Florida

#### Tournaments And A Fibonacci Link, Michael Long

*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 ...

Predator-Prey Model With Herding Behavior And Hunting Quota, 2020 University of North Florida

#### Predator-Prey Model With Herding Behavior And Hunting Quota, Randy Lee

*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, 2020 University of North Florida

#### Block Designs, Lucien Poulin

*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.

Insights From The Influx Of Prescription Painkillers In Northeast Florida: A Retrospective Analysis, 2020 University of North Florida

#### Insights From The Influx Of Prescription Painkillers In Northeast Florida: A Retrospective Analysis, Joseph Free

*Showcase of Osprey Advancements in Research and Scholarship (SOARS)*

The opioid epidemic has had, and will have, long-lasting ramifications in the United States. To better understand its impact in the Northeast Florida, this research seeks to identify relationships between hydro- and oxycodone pill concentration at the county and zip code levels and socio-economic factors such as average adjusted gross income and opioid related mortality. This project utilizes time series, regression, and GIS methods to examine local opioid saturation and has led to the development of an interactive Tableau dashboard which allows users to view opioid saturation at various levels of granularity. This analysis is made possible by longitudinal data ...

Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), 2020 Ursinus College

#### Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), Dave Ruch

*Analysis*

No abstract provided.

Binary Metrics, 2020 Missouri University of Science and Technology

#### Binary Metrics, Samer Assaf, Tom Cuchta, Matt Insall

*Mathematics and Statistics Faculty Research & Creative Works*

We define a binary metric as a symmetric, distributive lattice ordered magma-valued function of two variables, satisfying a “triangle inequality". Using the notion of a Kuratowski topology, in which topologies are specified by closed sets rather than open sets, we prove that every topology is induced by a binary metric. We conclude with a discussion on the relation between binary metrics and some separation axioms.

Structure-Activity Relationship Of Novel Diphenyl Ureas Targeting Mycobacterium, 2020 Grand Valley State University

#### Structure-Activity Relationship Of Novel Diphenyl Ureas Targeting Mycobacterium, Piper Burghduf

*Student Scholars Day Posters*

In 2017, the World Health Organization reported that 10 million people were infected with tuberculosis, 1.6 million of whom died. Tuberculosis is caused by a bacterium called Mycobacterium tuberculosis, which primarily infects an individual’s lungs. Unfortunately, failure to adhere to the long and arduous drug regimen has contributed to the emergence of antibiotic-resistant strains of M. tuberculosis. Therefore, the need for novel antibiotics is imperative to saving millions of lives. Our lab has recently developed a family of diphenyl ureas that exhibited increased antimicrobial activity toward Mycobacterium. Reported herein is the continuation of our previous research involving the ...

Doubly Chorded Cycles In Graphs, 2020 Grand Valley State University

#### Doubly Chorded Cycles In Graphs, Maia Wichman

*Student Scholars Day Oral Presentations*

In 1963, Corradi and Hajnal proved that for any positive integer k if a graph contains at least 3k vertices and has minimum degree at least 2k, then it contains k disjoint cycles. This result is sharp, meaning there are graphs on at least 3k vertices with a minimum degree of 2k-1 that do not contain k disjoint cycles. Their work is the motivation behind finding sharp conditions that guarantee the existence of specific structures, e.g. cycles, chorded cycles, theta graphs, etc. In this talk, we will explore minimum degree conditions which guarantee a specific number of doubly chorded ...

Non-Attacking Queen And Rook Placements, 2020 Grand Valley State University

#### Non-Attacking Queen And Rook Placements, Nicholas Layman

*Student Scholars Day Posters*

In 1848, Max Bezel introduced the problem of placing 8 queens on an 8 × 8 chess board so that none of the queens could attack each other. One generalization of this — the placement of n non-attacking queens on an n × n chess board — is the famous n-queens problem. A different but similar problem is that of placing non-attacking rooks on a generalized chess board which has connections to restricted permutations and has more general solutions known as compared to its queen counterpart. In this presentation, we investigate the intersection of these two problems — placing n pieces (either queens or rooks ...

Optimal Control Applied To Cancer Vaccine Protocols, 2020 Grand Valley State University

#### Optimal Control Applied To Cancer Vaccine Protocols, Brady Fritz

*Student Scholars Day Posters*

This research focused on a mathematical model for the administration of a cancer vaccine. This model involves time delays, making it a more difficult optimal control problem to solve. The mathematical model describes the administration of the vaccine along with certain groups of cells affected over time. The model was programmed into a specialized software called the Sparse Optimization Suite which could output a solution. This solution was then analyzed in order to properly describe it.

Automated Conjecture Making: Domination On Planar Graphs, 2020 Grand Valley State University

#### Automated Conjecture Making: Domination On Planar Graphs, Jose Garcia

*Student Scholars Day Posters*

A planar graph *G = (V,E)* is a graph that can be embedded in the plane, i.e. it can be drawn in the plane so that no edges intersect except at the vertices. A subset S of vertices in a graph G is called a dominating set if every vertex v ∈ V is either an element of S or is adjacent to an element of S. The domination number of a graph G is the smallest cardinality of a dominating set; we denote the domination number as γ(G). Automated conjecture making is the process of having a computer ...

Searching Games: A Bound For The Responder, 2020 Grand Valley State University

#### Searching Games: A Bound For The Responder, Jose Garcia

*Student Scholars Day Oral Presentations*

A searching game with two unknowns and a lie involves two players, the responder and the questioner. Before the start of the game, the two parties predetermine an amount of numbers n to consider, and how many questions k the questioner can ask before the game ends with a victory (or loss) for the responder. The responder thinks of two secret numbers. The questioner asks questions of the form "How many of your two numbers are in the subset Q of the set {0,...,n-1}?", in an attempt to search and find what the two secret numbers are. If the ...

Fern Or Fractal... Or Both?, 2020 Concordia University St. Paul

#### Fern Or Fractal... Or Both?, Christina Babcock

*Research and Scholarship Symposium Posters*

Fractals are series of self similar sets and can be found in nature. After researching the Barnsley Fern and the iterated function systems using to create the fractal, I was able to apply what I learned to create a fractal shell. This was done using iterated function systems, matrices, random numbers, and Python coding.

Infectious Disease Mortality Prediction, 2020 Graduate

#### Infectious Disease Mortality Prediction, Kazi Tanvir Hasan

*Mathematics*

When mortality statistics are reported for infectious diseases, they commonly reflect the ratio for the entire population impacted from it. This causes an underestimation since the frail members of the population are impacted at a higher rate. With the remaining healthy members, the mortality rate becomes skewed. With this project, we study predicting mortality under varying frailty conditions to account for the hidden heterogeneity's impact on the parameter estimates.

Decompositions Of Complete Uniform Multipartite Hypergraphs, 2020 Illinois Wesleyan University

#### Decompositions Of Complete Uniform Multipartite Hypergraphs, Patrick Ward

*Honors Projects*

In recent years, researchers have studied the existence of complete uniform hypergraphs into small-order hypergraphs. In particular, results on small 3-uniform graphs including loose 3, 4, and 5 cycles have been studied, as well as 4-uniform loose cycles of length 3. As part of these studies, decompositions of multipartite hypergraphs were constructed. In this paper, we extend this work to higher uniformity and order as well as expand the class of hypergraphs.

"What Country Is It In Africa?", 2020 Illinois Mathematics and Science Academy

#### "What Country Is It In Africa?", Kelly W. Remijan

*Teacher Resources*

No abstract provided.