Mathematics Senior Capstone PapersCopyright (c) 2019 Louisiana Tech University All rights reserved.
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers
Recent documents in Mathematics Senior Capstone Papersen-usThu, 01 Aug 2019 23:02:11 PDT3600Folding Mathematics: A Mathematical Approach to Origami
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/11
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/11Fri, 28 Jun 2019 06:47:06 PDT
From constructing a midpoint on a line to observing specific divisions of a plane, the art form of Origami borrows many mathematical tools in order to create complex, and often symmetrical, patterns in a paper medium known as a fold. For this project, the traditional fold known as the Origami Crane/Swan will be thoroughly examined as it contains the unique property to lie completely flat when complete. This phenomenon occurs because the vertices holding the fold together are not all considered to be flat folds. The different types of vertices interacting with each other create a natural locking mechanism within the medium and make it impossible for the medium to unravel. Using established geometrical and origami theorems, this project intends to deconstruct these locks and investigate the mathematics behind how the construction works.
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Zachary DavisPisano Periods: A Comparison Study
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/10
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/10Fri, 28 Jun 2019 06:46:51 PDT
The Pisano period, denoted π(n), is the period during which the Fibonacci sequence repeats after reducing the original sequence modulo n. More generally, one can similarly define Pisano periods for any linear recurrence sequence; in this paper we compare the Pisano periods of certain linear recurrence sequences with the Pisano periods of the Fibonacci sequence. We first construct recurrence sequences, defining the initial values as integers from 2 to 1000 and second values as 1. This paper discusses how the constructed sequences are related to the matrix M = [(first row) 1 1 (second row) 1 0] reduced modulo n. We offer a proof to show that the order of M is equal to the Pisano period of the Fibonacci sequence reduced modulo n. Further, we provide data showing that there are few discrepancies between the order of M and the Pisano periods of the constructed sequences reduced modulo n, for n from 2 to 1000. Finally, we detail progress made in the analysis of the comparison between the Pisano periods of the Fibonacci and Lucas sequences.
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Katherine WillrichMaking the Cut: Receivers of the National Football League
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/9
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/9Fri, 28 Jun 2019 06:46:35 PDT
In this paper the prospects of the National Football League, or NFL, are studied in order to determine the relationships between past college statistics, other “measurables,” and how they translate to successful careers in the league. When referring to measurables, this consists of all of the numerical data from each player that should, in theory, help teams get an idea of the players strengths or weaknesses. The data being used comes from an annual scouting combine for NFL teams that is held prior to each season. Information about the player’s college statistics and pre-draft measurables are being compared to several individual player statistics that are commonly indicative of successful careers. The goal is not only to benefit teams in identifying productive players, but also for the young men with dreams of competing at the highest level. It is often difficult to get a concrete idea of what teams are looking for, because many teams having differing opinions about which players will provide the most value. This investigation deals specifically with receivers and analyzing data collected from their past in order to make predictions on future careers. Multiple regression models are necessary due to several important independent variables (measurables) for each dependent variable (player statistics). Analyzing these relationships leads to the construction of several mathematical models which aim to predict the success of future prospective NFL receivers.
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Anthony Kent DavisThe Housing Bubble
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/8
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/8Fri, 28 Jun 2019 06:46:17 PDT
The housing market is constantly changing. Fluctuating housing prices and a flooded market have home buyers hesitant to commit and sellers on edge. What if the prospective buyer or seller could take this financial step already knowing the state of the market? The purpose of this project is to attempt to predict the next housing bubble. A multivariable regression analysis is conducted using relevant data including variables such as average property prices, number of foreclosures, etc. in the United States beginning in the year 2009. The trends, patterns, and models created from the regression analysis are compared against data models from the housing bubble of 2008. This comparison is used to identify similarities between trends that led to the previous housing bubble. Using the different sets of models, a time-line that predicts the next housing bubble is created.
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Shelby BrownPersonality & How Sound Affects Moods
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/7
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/7Fri, 28 Jun 2019 06:46:03 PDT
This research seeks to determine the personality and relationship between current moods of individuals at Louisiana Tech University by conducting a sound test of a can opening with a pre and post mood assessment, Brief Mood Introspection Scale (BMIS). The real question is “Can a sound test change mood?” Using one-way analysis of variance (ANOVA), the study is intended to examine the relationship between the pre and post (BMIS). The results indicate that there is a statistically significant relationship between both BMIS assessments. To determine if the data is significant, we must show the analysis of both BMIS and its outcome. Concluding this study, the personality assessment, Big Five Factor Inventory extra short form (BFI-2-XS), results will be shown in context while the pre and post BMIS assessment will be compared.
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Joe PhamThe Mathematical Modeling of Ballet
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/6
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/6Fri, 28 Jun 2019 06:45:48 PDT
This project aims to analyze the connections between ballet and mathematics. Specifically, this project focuses on analyzing the three-dimensional surfaces created as a dancer performs ballet choreography. The primary goal is to use a Vicon motion capture system in conjunction with MATLAB to model the three-dimensional lines and surfaces created by a dancer’s legs as she performs specific ballet movements. The movements used for this experiment were a pique turn and a rond de jambe. The data was collected using sensors to create objects in Vicon to record the position of the ankle, knee, and hip of the working leg while the dancer performed specific ballet movements. The position data was first analyzed in Excel, where specific criteria were used to eliminate data points that were incorrect due to errors while recording. Then the position data was exported to MATLAB for analysis. The data points were used to create fitted polynomials through the ankle, knee, and hip. Next, line segments were constructed between the ankle and knee and between the knee and hip. The ultimate goal is to find a closed form equation to mathematically describe the surfaces created by the dancers legs for each move and to find a general model for future experiments.
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Kendall GibsonSemiclassically modeling Hydrogen at Rydberg states immersed in electromagnetic fields
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/5
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/5Fri, 28 Jun 2019 06:45:34 PDT
Originally, closed-orbit theory was developed in order to analyze oscillations in the near ionization threshold (Rydberg) densities of states for atoms in strong external electric and magnetic fields. Oscillations in the density of states were ascribed to classical orbits that began and ended near the atom. In essence, observed outgoing waves following the classical path return and interfere with original outgoing waves, giving rise to oscillations. Elastic scattering from one closed orbit to another gives additional oscillations in the cross-section. This study examines how quantum theory can be properly used in combination with classical orbit theory in order to study inelastic scattering for atoms in an external field. At Rydberg states, an electron wave function can be modeled numerically through semiclassical means, using the Coulombic interaction from the atom, but as it approaches lower states, it must be modeled quantum mechanically, using a ‘Modified Coulombic’ potential.
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Jaron WilliamsBlackjack: the math behind the cards
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/4
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/4Fri, 28 Jun 2019 06:45:19 PDT
In this paper the reader will learn about the math behind the cards in the game of Blackjack. Blackjack or “21” has been played around the world with various rules and regulations in both professional and informal environments. The ultimate objective of the game is to receive a total card value of 21, or as close to 21 as possible without exceeding it, from the cards in a player’s hand in order to beat the dealer’s total. The goal of this project is to calculate the probabilities of various hands to determine the best strategies to win 21. The probabilities of receiving each combination of a two-card pair, as well as the probabilities of a player’s best and worst case of receiving a third card to remain in the game, are calculated. These calculations are done for scenarios involving three players and a dealer using two to six card decks per scenario. The results indicate consistent probabilities of receiving the same two-card pair regardless of the number of decks used, but decreasing probabilities of receiving a third card to remain in the game. Thus, casinos are more likely to administer games with more decks in play. The goal is to determine whether to “hit” or “stand” when dealt certain a pair.
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Hanna BlanchardThe Riemann Curvature Tensor
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/3
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/3Fri, 28 Jun 2019 06:45:04 PDT
A tensor is a mathematical object that has applications in areas including physics, psychology, and artificial intelligence. The Riemann curvature tensor is a tool used to describe the curvature of n-dimensional spaces such as Riemannian manifolds in the field of differential geometry. The Riemann tensor plays an important role in the theories of general relativity and gravity as well as the curvature of spacetime. This paper will provide an overview of tensors and tensor operations. In particular, properties of the Riemann tensor will be examined. Calculations of the Riemann tensor for several two and three dimensional surfaces such as that of the sphere and torus will be demonstrated. The relationship between the Riemann tensor for the 2-sphere and 3-sphere will be studied, and it will be shown that these tensors satisfy the general equation of the Riemann tensor for an n-dimensional sphere. The connection between the Gaussian curvature and the Riemann curvature tensor will also be shown using Gauss’s Theorem Egregium.
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Jennifer CoxMathematical Analysis of the Duck Migration to Louisiana
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/2
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/2Fri, 28 Jun 2019 06:44:49 PDT
The purpose of this project is to research the relationship between duck migration and weather patterns, more specifically trying to determine if the rainfall and temperature in a given year affects the migration patterns of ducks. Duck hunters and conservation- ists alike have observed an overall decrease in the duck population in Louisiana over the past 70 years. Though some years have seen an increase, the population has not recovered to the level from the 1950s. These observations have led to many questions about what have happened to the ducks or where have the ducks gone. Using differ- ent forms of Regression in Excel and Minitab this project investigates recent national patterns to try and correlate a pattern between the duck population and natural occur- rences. At the end of the project it was discovered that there is a correlation between the duck population in Louisiana to Louisiana Temperature, Louisiana Precipitation, Minnesota Temperature, and Ontario Precipitation. This correlation provides a better understanding of how nature has an impact on a population of a single species and allows us to better predict the duck population at the end of the year from statistics in the beginning of the year.
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Brandon GarciaPredicting Win Rates in Competitive OverwatchTM
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/1
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/1Fri, 28 Jun 2019 06:44:33 PDT
OverwatchTM is a video game published by Blizzard Entertainment R where two teams comprised of six people each compete against one another to accomplish a specific goal. The goal of each game is dependent on which map is being played. The maps are divided into four categories: Assault, Escort, Control, and Hybrid. A data set comprised of 3000 games of competitive OverwatchTM is used to determine how likely a team is to win their match. The factors used to determine the likelihood of winning are the map type and the skill ranking for each team. The data set is pre-processed by standardizing and encoding the data through Python. After the data is encoded, 80% of the data is divided into a training set and 20% of the data is divided into a testing set. Classification algorithms are tested against the data to determine which classifying method returns the highest accuracy. After using the training set, the Bagging Classifier shows the highest accuracy when compared to the testing set.
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Andrea Sibley