Tag: MATH 499

Jackson Findlay

Game Theory, Economics and Tennis

This presentation provides an overview of game theory, an influential branch of mathematical economics that studies strategic interactions and decision making.  I introduce some basic tools used by game theorists, including strict and weak dominance and iterated deletion procedures, and discuss applications ranging from auction theory to sports. 

MATH 499, Senior Capstone

Connie Wilmarth

P003

1:30 – 2 PM

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Mackenzie Hunton

Gamification in the Math Classroom

A recent trend in K-12 education is gamification, or the use of games to motivate learning in the math classroom. This presentation surveys some practices and the current research into their effectiveness as a teaching tool.

MATH 499, Senior Capstone

Connie Wilmarth

P003

2 – 2:30 PM

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Andrew Lindley

Bushnell Cafeteria Offerings Survey and Analysis

This study seeks to improve the Bushnell dining experience by utilizing statistical methods. Using data gathered by a specific survey process, this project will uncover what meals students like, what meals students don’t like, and what can be done to better the cafeteria in light of these discoveries. The data collection design, data visualization, and statistical methods used in determining results will all be presented and explained. The end goal is an unbiased and accurate study that equips our staff to provide the best possible dining experience at Bushnell.

MATH499- Senior Capstone

Dr. Connie Wilmarth

10:30am – P003

Alessia Righi

Einstein’s Theory of Special Relativity

This thesis examines the topic of Einstein’s special relativity. Starting from Aristotle’s ‘locus naturalis’ through Newton’s laws of dynamics all the way to Maxwell’s equations, the paper looks at the historical progress made in the human understanding of space and time, with a particular focus on the contradiction that brought Einstein to develop the relativity theory.

MATH 499 – Senior Capstone

Connie Wilmarth

11:30am-Noon Bucher Room

Courtney Weinberger

Actuarial P-Test

Actuaries need to be masters of probability. Hence the reason why the very first exam Actuaries will take is primarily on the mastery of probability. To master the different forms of probability, you must do several problems until you have the equations memorized. For the very first test, people interested in Actuarial work must master the conditional, discrete, continuous, and multivariable forms of probability. These forms of probability each have some unique difficult problems which will be shown and thoroughly explained. Additionally, all of these forms of probability have their own set of equations as well as requirements that must be fulfilled. Knowing when and where to use each form is crucial because of this reason.

MATH 499 – Senior Capstone

Connie Wilmarth

10:00am – 10:30am P103

David Schwartz

The Introduction of Statcast to Major League Baseball

Major League Baseball has been a driving force in American sports and statistical developments with the introduction of Statcast. Statcast uses the combination of doppler radar and video to obtain advanced statistics that are utilized for the development of baseball players. Prior to Statcast the general focus when it came to statistics in baseball were simple stats like Earned Run Average, Hits, Runs Batted In, etc. With the introduction of Statcast, we can focus more on predictive statistics that helps coaches scout players from a different perspective. For example, statistics like Expected Batting Average, Expected Weighted On Base Percentage, and many other recently introduced advanced stats that are discussed to show the benefit of using Statcast data for creating the most successful team possible. The introduction of Statcast, along with many other technological advances Major League Baseball has made created a window of growth for the baseball community as a whole by introducing new ways to analyze players and their development.

MATH 499 – Senior Capstone

Brian Carrigan

10:30am – 11:00am P103

Julia Kassing

Long-Term Financing and Capital Structure

The role of a financial manager is unique and vital in relation to a company’s ability to thrive. They must decide how best to utilize resources in order to maximize shareholder value. When a company needs an increase in capital, they may turn to a form of long-term capital financing. This is generally in the form of either debt or equity. In deciding how to obtain new capital, a financial manager must evaluate the health of the company, the desired level of risk and leverage, and the state of the greater economic environment. To delve into this topic, it will be imagined that Yeti Holdings, Inc. (YETI) requires increased capital. We will examine the company’s financial statements and the position of the firm in relation to both the current and projected economic conditions to determine in what matter the company should obtain new capital and the resulting implications of this decision.

MATH 499 – Senior Capstone

Connie Wilmarth

3:30pm – 4:00pm P103

Nicolas Cazares

Modern Approaches to Spinal Cord Repair

Spinal cords are one of the most sensitive parts of the human body and damage to them can massively hinder one’s quality of life. This presentation will go over medical research of spinal cord repair. The first section is an overview of what the spinal cord is including, cellular make-up, biological function, and detailed anatomy. The second section of this presentation will discuss the history of research within this field dating back to the 1960s. Following this I will look at modern approaches to spinal cord repair and discuss the pros and cons of each method.

MATH 499

Brian Carrigan

P103

1 – 1:30 PM

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Tiffany Hilkey

Infinity in Mathematics

I will be doing a comprehensive survey of infinity in mathematics. Infinity is much larger and more complex than human calculation can handle, but it happens to appear quite often in mathematics. It is introduced as a limit in Calculus, and this is usually the first real encounter with it. Looking at set theory and infinite sets reveals that infinity actually comes in different sizes, even though it is infinite. There are still things that mathematicians can’t figure out about infinity, and that goes to show how complex it is.

MATH 499, Senior Capstone

Connie Wilmarth

P114

Noon – 12:30 PM

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Payton Martin

Portfolio Management

In this presentation, we will explore vital concepts that are the building blocks of quantitative portfolio management. We will discuss the mathematical expression of expected return and risk on an investment and how they are used. We will examine weights within a portfolio and how risk is minimized while compromising as little as possible on expected return. Building blocks of the several-security model will direct us towards multiple interesting insights as well as lay the foundation for the beta factor and the Capital Asset Pricing Model (CAPM).

MATH 499, Senior Capstone

Connie Wilmarth

L203

10:30 – 11 AM

View stream here

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Kevin Kaelin

Alternative Power Sources: Electrifying Commercial Aircraft 

In a world with an ever-increasing demand for transportation, solutions are needed to limit the amount of pollution generated by vehicles.  One solution for limiting emissions from vehicles is to make them electric.  This research seeks to answer this question: is an electrically powered jet engine feasible for commercial aircraft?  This project takes a standard CFM56-7B24 turbofan jet engine that powers a Boeing 737-800 plane and explores the conceptual use of electric motors to drive the fan and compressor assembly.  The overall weight of this concept is compared to the maximum operating weight of the Boeing 737-800.  The total amount of kilowatt-hours required is calculated as well as the total weight of batteries needed to satisfy the energy requirements of this concept.  Based on the findings of this research: current battery densities are too low to provide a weight-effective solution to petroleum-based jet fuel.   

MATH 499, Capstone 

Brian Carrigan 

P103 

2:30 – 3 PM 

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Jonathan Messiers

A Bridge to Space: The Mechanics and Design Considerations for a Space Elevator

Achieving orbit is currently an extremely expensive and resource-heavy venture. Current rockets cost anywhere from $10,000 to $20,000 to lift a single kilogram of payload to low earth orbit. A space elevator may be able to lift a kilogram to orbit for as little as $200. A space elevator is a cable anchored at the equator that extends into space past geostationary orbit, using the centrifugal force of Earth’s rotation to hold itself upright under tension. Such a cable may be constructed using materials with extremely high strength-to-weight ratios. The overall design of a space elevator consists of the cable itself, a counterweight to suspend the cable via centrifugal force, climbers to deliver payload to and from orbit, and a base station anchoring the cable to the Earth somewhere along the equator. Craft released from the space elevator at a height of 53,000 kilometers would be at escape velocity, allowing them to reach other celestial bodies without the thousands of tons of fuel and stages conventional rockets require for the same velocity. Challenges faced include weather conditions within the atmosphere, the effects of solar radiation on the cable, collisions with orbital debris, cable oscillations, research and development costs, and political complications.

MATH 499, Capstone

Brian Carrigan

SPS 100

2:30 – 3 PM

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Hans Coburn

Solving The Rubik’s Cube, Analyzing The Fridrich Method

The Rubik’s Cube was made famous in the 1980s when they were distributed to stores nearly world wide. In 1982 the first speed cubing competition took place. Ever since, there have been different solving methods and strategies to decrease the number of moves needed to solve and lower the amount of time needed to solve it. One of the original competitors in that first completion, Jessica Fridrich, invented her own method for solving the cube. Over the years her original method has been added to by other speed cubers. That method, which is used to some degree by most every speed cuber today, is known as the Fridrich Method.

In this capstone, I will be setting out to analyze some of the very basic algebra behind the Rubik’s Cube. This will allow a better understanding of how to finish the last layer of the cube using the Fridrich Method. This final step in the method is the permutation of the last layer (also referred to as PLL). These PLL algorithms that will result are not the only algorithms needed to solve the cube using the Fridrich method; however, the same type of group theory is behind the construction of all algorithms for the cube. I will also include an intuitive guide to solving the cube that anyone can use to solve without the use of the internet to look up algorithms.

MATH 499, Capstone

Connie Wilmarth

PFB 103

2:30 – 3:00 PM

Hayley Leno

Cryptography: From Expanding an Empire to Winning World War II

This research looks at how mathematics, through cryptography, has affected our world history. From expanding an empire to possibly winning World War II, codes and ciphers have played an important role in world history. In general, the basics and key terms of cryptography are explained here, as well as example ciphers. One cipher explored here is the Caesar cipher. The creation, use and weaknesses of this easily broken, simple cipher are discussed. The Enigma, a far more complex code, is also discussed. This research looks at the creation and use of the Enigma and how, through mathematicians’ work, cracking the Enigma may have affected the outcome of World War II.

MATH 499, Capstone

Connie Wilmarth

PFB 103

2:00 – 2:30 PM

Chris Zirkle

The Revealing of the Infinite

The Revealing of the Infinite, is a brief look at the history, the mystery, and the revealing truths about the concept of infinity, as well as its practical uses. Since the start of mathematics, there has been much debate over the idea of infinity. Initially being too hard to grasp, for centuries it was deemed as being that of an illusion. Something that appeared to be there, but, in reality, was not. As history moved forward, and infinity’s presents remand prevalent in the world of mathematics, vital uses for it began to be discovered and applied, thus, changing the world forever. But, although paramount in applied mathematics, much mystery about its nature still remand unrevealed up until the late 1880’s, where more concepts about it essence were finally discovered. The ideas floating around about infinity during the late 1800’s, were essential in revealing small snap shot of what infinity is like, but it still remains, to this day, not a fully resolved mystery, and yet seems to hold the secrets of the universe inside of it.

MATH 499 Capstone

Connie Wilmarth

P114

11:30 AM

Allison Duvenez

Ethnomathematics

The goal of this presentation is to broaden the scope of how mathematics can be used. Historically the information has been presented from a narrow frame of western culture. As an example of how there is meaning for mathematics within other cultures I will focus on the history of Native American and African tribes. It is the attempt to challenge the assumption that our western culture’s use of mathematics is more sophisticated or shows greater intelligence. Mathematics merely reflects the cultural need of a society. It is continually adapted through time by the culture at hand.

MATH 499, Senior Capstone

Connie Wilmarth

A201

10:30 – 11 AM

William Jones

Fractals: the Geometry of Chaos

Fractals are self-similar objects with fractional dimension . These objects can be constructed using dynamical systems, and expressed geometrically. The dynamical systems used in these constructions have chaotic properties. These properties are density, transitivity, and sensitivity to initial conditions. The most primitive fractal set is the cantor middle thirds set. Fractal geometry is distinct from Euclidean geometry and can be used to better model natural phenomenon.

MATH 499, Senior Capstone

Connie Wilmarth

Banquet Room

1 – 3 PM

Scott Perkins

History in Mathematics Education

Differentiated instruction is an educational philosophy and the current driving force behind modern education. Differentiated methods take into account the various learning styles and needs of students, by employing various methods of instruction to generate interest, promote learning, and improve assessment of student progress, as opposed to the method of direct instruction, which treats all students as equal. This research presentation attempts to answer the question of whether it is useful and viable to incorporate the history of mathematics in mathematics classrooms and curricula as a method of differentiating mathematics instruction.

MATH 499, Senior Capstone

Connie Wilmarth

P103

9 – 9:30 AM

Ethan Souers

The Mathematics of Rock Guitar

Society places math geeks and rock stars in two very different baskets. However, without mathematics there would be no rock n’ roll. In this study the mathematics of the electric guitar were examined by scanning existing knowledge in the field. From Pythagorean fret placement to standing waves, mathematics exists in every element of a guitar from its build design to the sounds it makes. The expressive, emotional phenomenon that is rock music can be conceptualized and understood in grounded mathematics.

MATH 499, Senior Capstone

Connie Wilmarth

P103

9:30 – 10 AM

Annie Jo Wilson

Math Anxiety

Math is a subject that almost everyone has struggled with in one way or another. Many could say that they get anxiety from just hearing the word. In this study, we will look at math anxiety and the effects it has on student performance. The goal of this research is to find a way to ease the fear that comes from this particular subject and enhance student learning. The research covers timed tests, how you present the test as well as whether girls or boys have a greater sense of anxiety when it comes to math.

MATH 499, Senior Capstone

Connie Wilmarth

P103

10 – 10:30 AM

Brooke Davis

Construction of a Simple Securities Market Model

The securities market includes stocks and bonds, but also many more less common types of securities. This presentation will introduce viewers to the basics of the market, including risk and the no-arbitrage principle. This principle requires that no risk-free investments with a guarantee of gain can be made, and once it is assumed to be true, many other facts and interesting truths can be derived. The presentation will explore this in more depth, and provide an equation for determining the future value of investments.

MATH 499, Senior Capstone

Connie Wilmarth

Banquet Room

9 – 11 AM

Karli Vath

Assessment in Math Education

Many times in Math education, the assessment used tells teachers and students too little, and too late, how well students are understanding material. There is a push now for alternative assessment which emphasizes deep learning strategies, as opposed to solely recognition or recall. The ideal form of assessment promotes students’ best performance across time and uses a range of methods.

MATH 499, Senior Capstone

Connie Wilmarth

Banquet Room

9 – 11 AM

Ashley King

A Study on Golf Physics

The sport of golf involves many actions that can be analyzed using the mathematical properties of physics. Studies have been conducted regarding the nature of a golf ball in flight, the properties of golf clubs, and the mechanics of a golf swing. This capstone will survey some of the research on golf ball design with regard to general goals of minimization of draft, reaction to compression, and the maximization of spin. In addition, this capstone will investigate the physical dynamics of the golf swing and the golf club, with a goal of optimizing performance.

MATH 499, Senior Capstone

Connie Wilmarth

L203B

9 – 9:30 AM

Michael Van Loon

Effective Methods of Teaching Mathematics

Mathematics is widely known as one of the most difficult subjects to learn. Imagine teaching it! I am a math major and have been through many classes in my education career. Through my own experiences and through that of many resources I have developed a presentation/paper and poster to help you understand how effective, successful, and happy math instructors teach, guide, and help their students through the highest levels of achievement.

MATH 499, Senior Capstone

Connie Wilmarth

Banquet Room

1 – 3 PM

Daniel Norland

A Brief History of Greek Mathematics

This paper is a brief history of Greek mathematics.  It will cover how the Greek era of mathematics began and go through the development of mathematics in the Greek era, covering some of the great mathematicians.  It will then discuss the end of the Greek era of mathematics and the legacy.

MATH 499, Senior Capstone

Connie Wilmarth

L203A

1:30 – 2 PM