Physical Sciences and Mathematics Commons^™

Modeling The Spread Of Disease, James Hollister

Essential Studies UNDergraduate Showcase

Mathematically modeling the spread of disease in a population is a focus among epidemiologists. Using an SIR model (susceptible, infected, and recovered), we can create a system of differential equations to help better understand how a disease spreads in a simple environment. However, if we are to create a more realistic environment, computer simulations may be necessary. We can use the results from these simulations to try and find ways to eradicate the disease as efficiently as possible. In this poster, we will present the SIR model, present a system of differential equations that describe the movement of disease in …

Four Derivations Of Schrödinger’S Time Dependent Equation, Sydney Swanson

Essential Studies UNDergraduate Showcase

Physics and the natural world have been studied by humans since the first person wondered ‘Why?’ The Schrödinger equation is important because it attempts to describe a relatively new (to us) and unfamiliar part of our universe, behavior of subatomic particles, and helps modern scientists uncover secrets that have proven useful in technology and explaining our origins. The time dependent Schrödinger equation can be derived from various starting points in Classical such as the equation of a wave, the time independent Schrödinger equation, and Hamilton-Jacobi equations. Why Quantum mechanics exists, useful applications, and cases when it fails or is inaccurate …

Equations Of Motion In A Rotating Noninertial Reference Frame, Nicholas L. Sponsel

Essential Studies UNDergraduate Showcase

Measurement is an essential part of empirical research. As such, understanding whether the frame of reference in which a measurement occurs is inertial is essential for accurate data. As a rotating sphere, Earth is a non-inertial frame of reference and gives rise to fictitious forces. These forces are derived through vector algebra and further solved through matrix differential equations. The final solution for how velocity evolves over time results in sinusoidal functions with a period of 24 hours for Earth. To test the equations further, rational scenarios are proposed for different locations on the surface of Earth involving different initial …

A New Trend In Human Reproduction - Women In The Usa, Abby Rokke

Essential Studies UNDergraduate Showcase

The control a woman is allowed to have over her own reproductive system has been a recent popular topic of debate. Since the 1950's, women have made up over half of the total United States population. With women making up the majority of the country's citizens, it would be quite the contradiction for them to not have the right to make decisions about their own bodies. Over the last two decades many contraceptive and medical advances have assisted in a woman's ability to make her own choice. An interesting trend in childbearing has occurred from this new wave of technologies. …

Re-Describing Surface Roughness, Vincent Wagner

Essential Studies UNDergraduate Showcase

The purpose of this project is to explore a non-traditional method of identifying and describing variance in data. The original goal was to provide a more useful description of surface roughness for use in calculating pressure loss due to pipe friction in the oil and gas industry. This approach uses simple trigonometric calculations to capture more information about the point to point variance of a given data set, as well as information related to the ratio of measured length vs total contact length. This method utilizes steps similar to the bootstrap method in statistics, however, rather than sampling a data …

Mathematical Modelling Of English Coulee: Tanks In Series, Matthew Picklo

Essential Studies UNDergraduate Showcase

In the scope of the College of Arts and Science project: “Coulee Cleanway: Modelling and Analysis of the English Coulee Physiochemical Environment, UND Campus, Grand Forks”, a mathematical model attempting to describe the transportation of dissolved species within the English Coulee was developed based on “Tanks in Series”. By dividing the channel into discrete regions, a governing system of equations derived from conservation of mass equations and well-mixed assumptions is used to describe the spatial and temporal changes in concentration. The resulting system of differential equations was solved by a Runge-Kutta 4 numerical method, which allowed for the addition of …

Gödel’S Incompleteness Theorem, Emma Buntrock

Essential Studies UNDergraduate Showcase

In 1931 Gödel released his Incompleteness Theorem. His theorem was the opposite of what other mathematicians at the time wanted, but it was very influential to realize there is no perfectly complete formal systems. The incompleteness theorem is based of the idea that in a consistent system there are pieces that can not be proved or disproved, causing for incompleteness. The second part of that idea is that such a system can not prove that itself is consistent, which also makes it incomplete. I will verify theses proofs using a series of logic problems that show how a system is …

Improving The Problem With Problem Solving, Cole Thibert

Essential Studies UNDergraduate Showcase

As a prospective math educator who will be teaching in the near future, I was concerned with the idea of preparing my future students for college math courses. I decided to research the effects of teaching students how to appropriately use problem solving strategies in math. My research led me towards looking at the benefits of students becoming better problem solvers and how teachers can implement problem solving into their daily lessons.

When this implementation is successful, students can become more independent with their learning, they are able to work and persevere through challenging problems, and they have a greater …

The Most Important Statistics In Football, Jacob Holmen

Essential Studies UNDergraduate Showcase

This research is based on the Five Factors that were devised by Bill Connelly of SBNation. The Five Factors of football include Explosiveness, Efficiency, Field Position, Finishing Drives, and Turnovers. Each factor is composed of associated statistics that when put together make up the most important statistics in football. This research includes the analysis of all 857 FBS (the highest level of NCAA Division I football) games from the 2016 season. Data was analyzed through the use of an Excel spreadsheet. Five different statistics were looked at, each associated with one of the Five Factors. The statistics include Yards per …

Analytics And Baseball's New Generation, John Roche

Essential Studies UNDergraduate Showcase

Major League Baseball has been a catalyst for making decisions in sports and competition from a purely mathematical viewpoint. We have seen teams utilize unique on-field player alignments and roster-building strategies based on statistical observations and applications of math. This project examines the advantages Sabermetrics and analytics present within the sport. Untapped statistical categories that could further the success of teams in the future is also briefly discussed.