Mathematics Commons^™

The Riemann Curvature Tensor, Jennifer Cox

Mathematics Senior Capstone Papers

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 …

Blackjack: The Math Behind The Cards, Hanna Blanchard

Mathematics Senior Capstone Papers

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 …

Personality & How Sound Affects Moods, Joe Pham

Mathematics Senior Capstone Papers

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 …

Making The Cut: Receivers Of The National Football League, Anthony Kent Davis

Mathematics Senior Capstone Papers

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 …

Pisano Periods: A Comparison Study, Katherine Willrich

Mathematics Senior Capstone Papers

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. …

Folding Mathematics: A Mathematical Approach To Origami, Zachary Davis

Mathematics Senior Capstone Papers

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 …

Factors That Predict Success Of A Beaumont Student, Tara Limestoll

Masters Essays

This project is an attempt to discover predictors of high school performance through the use of data science techniques and analysis of the Beaumont school 2017-2018 student body. High school success is an important factor for college admission, so being able to forecast a student's performance or identify those in need of assistance is paramount. Analysis shows that there is a strong correlation and predictive quality in the quantitative assessment results examined in this study. While results for both success and failure were significant, predictions of student success measures were more accurate than those of the failure group.

Connectedness- Its Evolution And Applications, Nicholas A. Scoville

Topology

No abstract provided.

Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

Number Theory

No abstract provided.

The Role Of Sampling Variability In Developing K-8 Preservice Teachers’ Informal Inferential Reasoning, Omar Abu-Ghalyoun

Dissertations

Recent influential policy reports, such as the Common Core State Standards (CCSS-M, 2010) and Guidelines for Assessment and Instruction in Statistics Education Report, (GAISE, 2007), have called for dramatic changes in the statistics content included in the K-8 curriculum. In particular, students in these grades are now expected to develop Informal Inferential Reasoning (IIR) as a way of preparing them for formal concepts of inferential statistics such as confidence intervals and testing hypotheses. Ben-Zvi, Gil, & Apel, (2007) describe IIR as the cognitive activities involved in informally making statistical inferences. Over this path from informal to formal inference, many important …

Uniformly Connected Graphs, Nasreen Almohanna

Dissertations

Perhaps the most fundamental property that a graph can possess is that of being connected. Two vertices u and v of a graph G are connected if G contains a u-v path. The graph G itself is connected if every two vertices of G are connected. The well-studied concept of connectivity provides a measure on how strongly connected a graph may be. There are many other degrees of connectedness for a graph. A Hamiltonian path in a graph G is a path containing every vertex of G. Among the best-known classes of highly connected graph are the Hamiltonian-connected graphs, …

The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?, Chloe Munroe

Mathematics Undergraduate Theses

The hyperreal number system *ℝ forms an ordered field that contains ℝ as a subfield as well as infinitely many large and small numbers. A number is defined to be infinitely large if |ω| > n for all n = 1, 2, 3, ... and infinitely small if |ε| < 1/n for all n = 1, 2, 3... This number system is built out of the real number system analogous to Cantor’s construcion of ℝ out of ℚ. The new entities in *ℝ and the relationship between the reals and hyperreals provides an appealing alternate approach to real (standard) analysis …

The Name Tag Problem, Christian Carley

Mathematics Undergraduate Theses

A group of n people sit around a table, according to an assignment of name tags in which only one person is paired with the correct name tag. Curious to see if it will improve the number of correct pairings, everybody passes their name tag to the person on their left. Oddly, a new person, and only that person, receives the correct name tag. Indeed, every rotation provides the correct name tag to exactly one new person, until the nth rotation, whereby every person has received the correct name tag one at a time. Given any group of people, …

Accurate Inference For Repeated Measures In High Dimensions, Xiaoli Kong, Solomon W. Harrar

Mathematics and Statistics: Faculty Publications and Other Works

This paper proposes inferential methods for high-dimensional repeated measures in factorial designs. High-dimensional refers to the situation where the dimension is growing with sample size such that either one could be larger than the other. The most important contribution relates to high-accuracy of the methods in the sense that p-values, for example, are accurate up to the second-order. Second-order accuracy in sample size as well as dimension is achieved by obtaining asymptotic expansion of the distribution of the test statistics, and estimation of the parameters of the approximate distribution with second-order consistency. The methods are presented in a unified and …

Confidence Intervals For The Area Under The Receiver Operating Characteristic Curve In The Presence Of Ignorable Missing Data, Hunyong Cho, Gregory J. Matthews, Ofer Harel

Mathematics and Statistics: Faculty Publications and Other Works

Receiver operating characteristic curves are widely used as a measure of accuracy of diagnostic tests and can be summarised using the area under the receiver operating characteristic curve (AUC). Often, it is useful to construct a confidence interval for the AUC; however, because there are a number of different proposed methods to measure variance of the AUC, there are thus many different resulting methods for constructing these intervals. In this article, we compare different methods of constructing Wald‐type confidence interval in the presence of missing data where the missingness mechanism is ignorable. We find that constructing confidence intervals using multiple …

Deciphering The Transport Of Elastic Filaments By Antagonistic Motor Proteins, Stephanie Portet, Cecil Leduc, Sandrine Etienne-Manneville, J. C. Dallon

Faculty Publications

Intermediate filaments are long elastic fibres that are transported by microtubule-associated motor proteins kinesin and dynein inside the cell. How elastic filaments are efficiently transported by antagonistic motors is not well understood and difficult to measure with current experimental techniques. Adapting the tug-of-war paradigm for vesicle-like cargos, we develop a mathematical model to describe the motion of an elastic filament punctually bound to antagonistic motors. As observed in cells, up to 3 modes of transport are obtained; dynein-driven retrograde, kinesin-driven anterograde fast motions and a slow motion. Motor properties and initial conditions that depend on intracellular context, regulate the transport …

Classification Of Non-Singular Cubic Surfaces Up To E-Invariants, Mohammed Alabbood

Theses and Dissertations

In this thesis, we use the Clebsch map to construct cubic surfaces with twenty-seven lines in PG(3, q) from 6 points in general position in PG(2, q) for q = 17, 19, 23, 29, 31. We classify the cubic surfaces with twenty-seven lines in three dimensions (up to e- invariants) by introducing computational and geometrical procedures for the classi- fication. All elliptic and hyperbolic lines on a non-singular cubic surface in PG(3, q) for q = 17, 19, 23, 29 …

Sequential Differences In Nabla Fractional Calculus, Ariel Setniker

Department of Mathematics: Dissertations, Theses, and Student Research

We study the composition of nabla fractional differences of unequal orders, known as "sequential" nabla fractional differences. The sequential differences we examine possess different bases — specifically, we establish the outer operator as having a base larger than the inner operator by at least an integer factor of 1. Further, we consider two cases of orders: first the case when the outer difference has a larger power, and second when the inner difference has a larger power.

We develop rules for sequential nabla fractional differences and present connections between the sign of a sequential difference of a function and the …

Variations In Ramsey Theory, Drake Olejniczak

Dissertations

The Ramsey number R(F,H) of two graphs F and H is the smallest positive integer n for which every red-blue coloring of the (edges of a) complete graph of order n results in a graph isomorphic to F all of whose edges are colored red (a red F) or a blue H. Beineke and Schwenk extended this concept to a bipartite version of Ramsey numbers, namely the bipartite Ramsey number BR(F,H) of two bipartite graphs F and H is the smallest positive integer rsuch that every red-blue coloring of the r-regular complete bipartite graph results in either …

Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg

Computer Science: Faculty Publications and Other Works

This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics.

The Number Of Fixed Points Of And-Or Networks With Chain Topology, Lauren Geiser

Honors Theses

Boolean networks are sets of Boolean functions, which are functions that contain Boolean variables and the logical operators AND, OR, and NOT. In the simple case, the variables can be in one of two states—either 1 or 0, which can be interpreted in different ways such as ON or OFF, or TRUE or FALSE, depending on the application. Arranging model systems into Boolean functions, we can study steady states of these networks. This refers to the overall state of the dynamical system given an initial condition and another theoretical condition such as a subsequent point in time. Boolean networks have …

Topology Of Fractals, Amelia Pompilio

Honors Theses

No abstract provided.

Leveraging Variation Of Historical Number Systems To Build Understanding Of The Base-Ten Place-Value System, Eva Thanheiser, Kathleen Melhuish

Mathematics and Statistics Faculty Publications and Presentations

Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-ten place-value system (i.e., grouping, place value, base). Understanding these features is crucial to understanding and teaching number and place value. The research aims of this paper are (1) to present a local instructional theory (LIT), designed to familiarize PTs with these features through comparison with historical number systems and (2) to present the effects of using the LIT in the PT classroom. A theory of learning …

Cryptography: Mathematical Advancements On Cyber Security, Kristin Bower

Senior Honors Theses

The origin of cryptography, the study of encoding and decoding messages, dates back to ancient times around 1900 BC. The ancient Egyptians enlisted the use of basic encryption techniques to conceal personal information. Eventually, the realm of cryptography grew to include the concealment of more important information, and cryptography quickly became the backbone of cyber security. Many companies today use encryption to protect online data, and the government even uses encryption to conceal confidential information. Mathematics played a huge role in advancing the methods of cryptography. By looking at the math behind the most basic methods to the newest methods …

On Analytic Nonlinear Input-Output Systems: Expanded Global Convergence And System Interconnections, Irina M. Winter Arboleda

Electrical & Computer Engineering Theses & Dissertations

Functional series representations of nonlinear systems first appeared in engineering in the early 1950’s. One common representation of a nonlinear input-output system are Chen-Fliess series or Fliess operators. Such operators are described by functional series indexed by words over a noncommutative alphabet. They can be viewed as a noncommutative generalization of a Taylor series. A Fliess operator is said to be globally convergent when its radius of convergence is infinite, in other words, when there is no a priori upper bound on both the L1-norm of an admissible input and the length of time over which the corresponding output is …

Determinants Of Incidence And Hessian Matrices Arising From The Vector Space Lattice, Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe

Department of Mathematics: Faculty Publications

Let V = ⁿi= _o V^I bethe lattice of subspaces of the n-dimensional vector space over the finite field Fq, and let A be the graded Gorenstein algebra defined over Q which has V as a Q basis. Let F be the Macaulay dual generator for A. We explicitly compute the Hessian determinant j 2F= Xi Xj j, evaluated at the point X1 = X2 = ... = XN = 1, and relate it to the determinant of the incidence matrix between V1 and Vn-1. Our exploration is motivated by the fact that both of these matrices naturally …

An Examination Of Kinetic Monte Carlo Methods With Application To A Model Of Epitaxial Growth, Dylana Ashton Wilhelm

Theses and Dissertations

Through the assembly of procedural information about physical processes, the kinetic Monte Carlo method offers a simple and efficient stochastic approach to model the temporal evolution of a system. While suitable for a variety of systems, the approach has found widespread use in the simulation of epitaxial growth. Motivated by chem- ically reacting systems, we discuss the developments and elaborations of the kinetic Monte Carlo method, highlighting the computational cost associated with realizing a given algorithm. We then formulate a solid-on-solid bond counting model of epitax- ial growth which permits surface atoms to advance the state of the system through …

On The Characteristic Polynomial Of A Hypergraph, Gregory J. Clark

Theses and Dissertations

We consider the computation of the adjacency characteristic polynomial of a uniform hypergraph. Computing the aforementioned polynomial is intractable, in general; however, we present two mechanisms for computing partial information about the spectrum of a hypergraph as well as a methodology (and in particular, an algo- rithm) for combining this information to determine complete information about said spectrum. The first mechanism is a generalization of the Harary-Sachs Theorem for hypergraphs which yields an explicit formula for each coefficient of the characteristic polynomial of a hypergraph as a weighted sum over a special family of its subgraphs. The second is a …

Successful Pressing Sequences In Simple Pseudo-Graphs, Hays Wimsatt Whitlatch

Theses and Dissertations

Motivated by the study of genomes evolving by reversals, the primary topic of this thesis is “successful pressing sequences” in simple pseudo-graphs. Pressing sequences where first introduced by Hannenhali and Pevzner in 1999 where they showed that sorting signed permutation problem can be solved in polynomial time, therefore demonstrating that the length of a most parsimonious solution to the genome in- version only rearrangement problem can be determined efficiently.

A signed permutation is an integer permutation where each entry is given a sign: plus or minus. A reversal in a signed permutation is the operation of reversing a subword and …

Dynamical Entropy Of Quantum Random Walks, Duncan Wright

Theses and Dissertations

In this manuscript, we study discrete-time dynamics of systems that arise in physics and information theory, and the measure of disorder in these systems known as dy- namical entropy. The study of dynamics in classical systems is done from two distinct viewpoints: random walks and dynamical systems. Random walks are probabilistic in nature and are described by stochastic processes. On the other hand, dynami- cal systems are described algebraically and deterministic in nature. The measure of disorder from either viewpoint is known as dynamical entropy.

Entropy is an essential notion in physics and information theory. Motivated by the study of …