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Articles 91 - 120 of 255
Full-Text Articles in Mathematics
Orca Research Report, Jeanna Chilton, Dr. Gary Lawlor
Orca Research Report, Jeanna Chilton, Dr. Gary Lawlor
Journal of Undergraduate Research
The work I was able to do for the research on the minimal surface area of the octahedron was time consuming, but unfortunately did not bring about any profound knowledge for anyone besides myself.
A Mathematical Model Of Collagen Lattice Contraction, J. C. Dallon, Emily J. Evans, H Paul Erhlich
A Mathematical Model Of Collagen Lattice Contraction, J. C. Dallon, Emily J. Evans, H Paul Erhlich
Faculty Publications
Two mathematical models for fibroblast-collagen interaction are proposed which reproduce qualitative features of fibroblast populated collagen lattice contraction in time. Both models are force based and model the cells as individual entities with discrete attachment sites however the collagen lattice is modeled differently for each model. In the collagen lattice model the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fiber model the nodes are not triangulated, are less interconnected, and the collagen fibers are modeled as a string of nodes. Both models suggest that the overall increase in stress of …
Counting Threshold Graphs And Finding Inertia Sets, Christopher Abraham Guzman
Counting Threshold Graphs And Finding Inertia Sets, Christopher Abraham Guzman
Theses and Dissertations
This thesis is separated into two parts: threshold graphs and inertia sets. First we present an algorithmic approach to finding the minimum rank of threshold graphs and then progress to counting the number of threshold graphs with a specific minimum rank. Second, we find an algorithmic and more automated way of determining the inertia set of graphs with seven or fewer vertices using theorems and lemmata found in previous papers. Inertia sets are a relaxation of the inverse eigenvalue problem. Instead of determining all the possible eigenvalues that can be obtained by matrices with a specific zero/nonzero pattern we restrict …
Record Linkage, Stasha Ann Bown Larsen
Record Linkage, Stasha Ann Bown Larsen
Theses and Dissertations
This document explains the use of different metrics involved with record linkage. There are two forms of record linkage: deterministic and probabilistic. We will focus on probabilistic record linkage used in merging and updating two databases. Record pairs will be compared using character-based and phonetic-based similarity metrics to determine at what level they match. Performance measures are then calculated and Receiver Operating Characteristic (ROC) curves are formed. Finally, an economic model is applied that returns the optimal tolerance level two databases should use to determine a record pair match in order to maximize profit.
Minimum Rank Problems For Cographs, Nicole Andrea Malloy
Minimum Rank Problems For Cographs, Nicole Andrea Malloy
Theses and Dissertations
Let G be a simple graph on n vertices, and let S(G) be the class of all real-valued symmetric nxn matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The smallest rank achieved by a matrix in S(G) is called the minimum rank of G, denoted mr(G). The maximum nullity achieved by a matrix in S(G) is denoted M(G). For each graph G, there is an associated minimum rank class, MR(G) consisting of all matrices A in S(G) with rank A = mr(G). Although no restrictions are applied to the diagonal entries of …
A Topics Analysis Model For Health Insurance Claims, Jared Anthony Webb
A Topics Analysis Model For Health Insurance Claims, Jared Anthony Webb
Theses and Dissertations
Mathematical probability has a rich theory and powerful applications. Of particular note is the Markov chain Monte Carlo (MCMC) method for sampling from high dimensional distributions that may not admit a naive analysis. We develop the theory of the MCMC method from first principles and prove its relevance. We also define a Bayesian hierarchical model for generating data. By understanding how data are generated we may infer hidden structure about these models. We use a specific MCMC method called a Gibbs' sampler to discover topic distributions in a hierarchical Bayesian model called Topics Over Time. We propose an innovative use …
Probable Frames: Using A Probability Task To Explore Fraction Multiplication, Joseph G. Curtis, Dr. Robert Speiser
Probable Frames: Using A Probability Task To Explore Fraction Multiplication, Joseph G. Curtis, Dr. Robert Speiser
Journal of Undergraduate Research
When you toss a coin at the start of a football game and call “Heads!” the probability the coin will land “heads-up” is one-half. If the referee does not hear your prediction, he must toss again. The probability the second toss will land heads is again one-half. But what is the probability that both tosses were heads? In the double coin toss, the probability of two heads in a row is one-half times one-half: one-fourth. Although the rule (multiply the probabilities of the two independent events in order to calculate the probability of both events) is simple to carry out, …
Orca, Kourtney Peters
Orca, Kourtney Peters
Journal of Undergraduate Research
Throughout my research, the students were rarely given a verbal introduction to the tasks they faced. Instead, they had to rely on their intuition, pre-conceptions, and any previous knowledge to find solutions to the tasks at hand. They were given time and resources to explore their already existing understanding. This balance of time to think and distance from the teacher’s guidance is key, I think, to encouraging students to use their intuition and past experience to solve problems. According to Duckworth (Bransford, 2000), “Accomplished teachers ‘give learners reason’ by respecting and understanding learners’ prior experiences and understandings, assuming that these …
Computer Aided Complex Analysis, Jared Whitehead, Adam Rich, Dr. Michael Dorff
Computer Aided Complex Analysis, Jared Whitehead, Adam Rich, Dr. Michael Dorff
Journal of Undergraduate Research
Complex analysis is a fundamental course in mathematics required by some engineering and physical science disciplines. Since complex numbers are two dimensional – they have a real and imaginary part – visualizing their graphs, a very important part of practical and theoretical analysis, can be difficult. Complex valued functions of complex numbers can only be graphed in a space of four or more dimensions. To see the entire graph at once is not a feasible option for the human mind. Instead, analysts concern themselves with small sets of the plane and the effect that complex functions have on them. For …
Linguistic Invention In Mathematical Communication Among Practicing Elementary School Teachers, Christine Johnson, Janet Walter
Linguistic Invention In Mathematical Communication Among Practicing Elementary School Teachers, Christine Johnson, Janet Walter
Journal of Undergraduate Research
As a tutor in the BYU Math Lab, I attempted to model correct vocabulary to be consistent with the students’ textbooks and professors. However, at times it seemed as though I needed to use more creative language to effectively communicate mathematical concepts. I began to wonder if it was possible to model correct mathematical vocabulary and convey my intended meanings at the same time. As an undergraduate in the Mathematics Education program, I knew that studying mathematical communication would make me a more effective teacher.
Traveling Waves, Keith Rudd, Dr. Jeffery Humpherys
Traveling Waves, Keith Rudd, Dr. Jeffery Humpherys
Journal of Undergraduate Research
Traveling waves are, mathematically speaking, partial differential equations which can be expresses as U(x-ct), where x is the spatial variable, t is time, and c is the speed of the wave. Traveling waves have applications in fluid dynamics, optics, and many other areas.
Foundations Of Tropical Geometry Classification Of Polynomials, Nathan Manwaring, Dr. Tyler Jarvis
Foundations Of Tropical Geometry Classification Of Polynomials, Nathan Manwaring, Dr. Tyler Jarvis
Journal of Undergraduate Research
Tropical Mathematics is a relatively new field of mathematics that is getting a lot of attention recently. It is applicable in the field of Combinatorics as well as Phylogenetics, and more uses are being found each day. Our goal was to find a way to classify Tropical Polynomials so that they may be better understood and ultimately bridge the gap between different applications and discoveries in Tropical Mathematics.
Finding A Galois Representation Corresponding To A Hecke Eigenclass, Meghan De Witt, Dr. Darrin Doud
Finding A Galois Representation Corresponding To A Hecke Eigenclass, Meghan De Witt, Dr. Darrin Doud
Journal of Undergraduate Research
My project was to finish a thirteen year old unsolved problem that provided an important computational example of a conjecture in the field of Algebraic Number Theory.
Exploring The Open-Response Task As A Tool For Assessing The Understanding Of Fifth- Grade Students In The Content Area Of Fractions, Heather Bahlmann, Janet G. Walter
Exploring The Open-Response Task As A Tool For Assessing The Understanding Of Fifth- Grade Students In The Content Area Of Fractions, Heather Bahlmann, Janet G. Walter
Journal of Undergraduate Research
Inferring student understanding is at the heart of improvement in mathematics learning and teaching. Assessment provides valuable information which can be used to “promote growth, modify programs, recognize student accomplishments, and improve instruction” (NCTM, 1995, p.27). It is imperative that the methods for assessing student understanding be constantly explored and evaluated. Ou decision to research the open-response task as an assessment tool results from our perspective that students make sense of mathematics by exercising personal agency. Personal agency is the freedom and responsibility to choose to act (Walter & Gerson, 2006). Open-response tasks allow students to exercise personal agency, hence …
The Effect Of A Long-Term Professional Development Course In Standards-Based Mathematics On The Attitudes And Practices Of Inservice Teachers, Destiny Turner, Dr. Candice Ridlon
The Effect Of A Long-Term Professional Development Course In Standards-Based Mathematics On The Attitudes And Practices Of Inservice Teachers, Destiny Turner, Dr. Candice Ridlon
Journal of Undergraduate Research
In 2000, the National Council of Teachers of Mathematics (NCTM) developed a set of principles and standards to guide mathematics teaching in grades K-12. These principles outline pedagogy that encourages students to discover and understand math on a conceptual level. These monumental standards are widely recognized, but unfortunately, are not as widely implemented in actual classrooms. Most often, this problem is addressed through short-term professional development workshops.
Factorization Of Tropical Polynomials, Nathan Grigg, Dr. Tyler Jarvis
Factorization Of Tropical Polynomials, Nathan Grigg, Dr. Tyler Jarvis
Journal of Undergraduate Research
Tropical algebra, also called “min-plus” or “max-plus” algebra, is a relatively new topic in mathematics that has recently caught the interest of algebraic geometers, computer scientists, combinatorists, and other mathematicians. According to Andreas Gathmann , tropical algebra was pioneered by mathematician and computer scientist Imre Simon in the 1980s but did not receive widespread attention until a few years ago. Interestingly, the title “tropical algebra” is nothing more than a reference to Simon’s home country—Brazil.
Non-Linear Ray Tracing Visualizing The Impossible, Jared Duke, Dr. Matthew Anderson
Non-Linear Ray Tracing Visualizing The Impossible, Jared Duke, Dr. Matthew Anderson
Journal of Undergraduate Research
Ray tracing is a common technique for computational, photo-realistic simulation of the “real world.” However, most current approaches assume light propagation is linear: that is, light always travels in a straight line. Our aim was to create a ray tracing program that would handle the “bending” of light waves at relativistic speeds or by gravitational forces. This could in turn be used to assist scientists in understanding the numerical results from their research and to help others understand and visualize such complex natural phenomenon.
Assessing Cognitive Construction In Learning Statistics As Applied Through Mathematics Education, Aubrey Baxter, Dr. Hope Gerson
Assessing Cognitive Construction In Learning Statistics As Applied Through Mathematics Education, Aubrey Baxter, Dr. Hope Gerson
Journal of Undergraduate Research
Paul Fields in the statistics department was my first mentor. Together we tried to develop a new pedagogy for teaching statistics. This interested me because I may teach advanced placement statistics after I graduate from the Mathematics Education program. A position then came available to me as a research assistant for Dr. Hope Gerson. It was a better opportunity because it is in my field of study and it allowed me work with statistics and apply calculus. Together with Dr. Walter, Dr. Gerson taught an Honors Calculus 1 class for two semesters and an Honors Calculus 2 class for one …
Calculus Excel At Byu: Increasing Student Potential For Success, Karla Jeanese Hendricks, Dr. Michael Dorff
Calculus Excel At Byu: Increasing Student Potential For Success, Karla Jeanese Hendricks, Dr. Michael Dorff
Journal of Undergraduate Research
Success in calculus can have significant implications both within an intended field of study and throughout academic pursuits. Of the 34 science, technology, engineering, and mathematics (STEM) majors at BYU, 25 of them require calculus for graduation and 20 of them require it as a prerequisite for other courses. A study at Bryant University in Rhode Island examined mathematics SAT scores, verbal SAT scores, percentile rank in high school graduating class, percentage score on a college mathematics placement exam, and calculus grades of actuarial students; it was found that the calculus grades were the “single best predictor of a student’s …
Constructing Wavelets With Good Frequency Response And Two Vanishing Moments, Chad Lillian, Dr. Andrew D. Pollington
Constructing Wavelets With Good Frequency Response And Two Vanishing Moments, Chad Lillian, Dr. Andrew D. Pollington
Journal of Undergraduate Research
Recruitment of loudness is a hearing impairment in which certain frequency ranges are not as audible as others. If a common hearing aid is used to remedy this problem all frequencies will be amplified and there will be no advantage. The solution to this problem is a hearing aid that only selectively amplifies those frequencies that are less audible.
Metacalibration Proof Of The Triple Bubble Conjecture In R3, Donald Sampson, Dr. Gary Lawlor
Metacalibration Proof Of The Triple Bubble Conjecture In R3, Donald Sampson, Dr. Gary Lawlor
Journal of Undergraduate Research
My project was to further develop the technique of metacalibration, a new method of minimization proof, in order to prove the triple bubble conjecture: that the standard triple bubble is the least surface area way to separately enclose three given volumes.
Option Pricing For Inventory Management And Control, Bryant Angelos, Dr. Jeffrey Humpherys
Option Pricing For Inventory Management And Control, Bryant Angelos, Dr. Jeffrey Humpherys
Journal of Undergraduate Research
In recent years, capital markets have experience remarkable growth in both the total volume of trades and in the complexity of the financial instruments being traded. Investors are becoming increasingly sophisticated as they search for newer and more effective ways of managing and protecting themselves from risk. Retail markets have undergone a similar transformation as retailers seek to maximize profit while minimizing risk. Supply chains are becoming more interconnected, and the contracts governing them have become more complex in recent years.
Nonnegative Matrix Factorization, Gretchen Schillemat, Dr. Jeffrey Humpherys
Nonnegative Matrix Factorization, Gretchen Schillemat, Dr. Jeffrey Humpherys
Journal of Undergraduate Research
The purpose of this project was to study the nonnegative matrix factorization (NNMF) problem: Given a nonnegative matrix V, find the” best” nonnegative matrices W and H, such that V WH. The main focus in our project was when the data was sparse.
A Class Of Univalent Convolutions Of Harmonic Mappings, Matthew Daniel Romney
A Class Of Univalent Convolutions Of Harmonic Mappings, Matthew Daniel Romney
Theses and Dissertations
A planar harmonic mapping is a complex-valued function ƒ : D → C of the form ƒ(x+iy) = u(x,y) + iv(x,y), where u and v are both real harmonic. Such a function can be written as ƒ = h+g where h and g are both analytic; the function w = g'/h' is called the dilatation of ƒ. This thesis considers the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping p;(z) = z/(1-z) with respective dilatations e^iθz and e^ipz, θ, p ∈ R. We prove that any such convolution is univalent. …
The Minimum Rank Problem For Outerplanar Graphs, John Henry Sinkovic
The Minimum Rank Problem For Outerplanar Graphs, John Henry Sinkovic
Theses and Dissertations
Given a simple graph G with vertex set V(G)={1,2,...,n} define S(G) to be the set of all real symmetric matrices A such that for all i not equal to j, the ijth entry of A is nonzero if and only if ij is in E(G). The range of the ranks of matrices in S(G) is of interest and can be determined by finding the minimum rank. The minimum rank of a graph, denoted mr(G), is the minimum rank achieved by a matrix in S(G). The maximum nullity of a graph, denoted M(G), is the maximum nullity achieved by a matrix …
Bounding The Norm Of Matrix Powers, Daniel Ammon Dowler
Bounding The Norm Of Matrix Powers, Daniel Ammon Dowler
Theses and Dissertations
In this paper I investigate properties of square complex matrices of the form Ak, where A is also a complex matrix, and k is a nonnegative integer. I look at several ways of representing Ak. In particular, I present an identity expressing the kth power of the Schur form T of A in terms of the elements of T, which can be used together with the Schur decomposition to provide an expression of Ak. I also explain bounds on the norm of Ak, including some based on the element-based expression of …
Integral Traces Of Weak Maass Forms Of Genus Zero Odd Prime Level, Nathan Eric Green
Integral Traces Of Weak Maass Forms Of Genus Zero Odd Prime Level, Nathan Eric Green
Theses and Dissertations
Duke and Jenkins defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and showed that these lifts preserve the integrality of Fourier coefficients. We show that the generalization of these lifts to modular forms of genus 0 odd prime level also preserves the integrality of Fourier coefficients.
Spectral Stability Of Weak Detonations In The Majda Model, Jeffrey James Hendricks
Spectral Stability Of Weak Detonations In The Majda Model, Jeffrey James Hendricks
Theses and Dissertations
Using analytical and numerical Evans-function techniques, we examine the spectral stability of weak-detonation-wave solutions of Majda's scalar model for a reacting gas mixture. We provide a proof of monotonicity of solutions. Using monotonicity we obtain a bound on possible unstable eigenvalues for weak-detonation-wave solutions that improves on the more general bound given by Humpherys, Lyng, and Zumbrun. We use a numerical approximation of the Evans function to search for possible unstable eigenvalues in the bounded region obtained by the energy estimate. For the parameter values tested, our results combined with the result of Lyng, Raoofi, Texier, and Zumbrun demonstrate that …
The Frobenius Manifold Structure Of The Landau-Ginzburg A-Model For Sums Of An And Dn Singularities, Rachel Megan Webb
The Frobenius Manifold Structure Of The Landau-Ginzburg A-Model For Sums Of An And Dn Singularities, Rachel Megan Webb
Theses and Dissertations
In this thesis we compute the Frobenius manifold of the Landau-Ginzburg A-model (FJRW theory) for certain polynomials. Specifically, our computations apply to polynomials that are sums of An and Dn singularities, paired with the corresponding maximal symmetry group. In particular this computation applies to several K3 surfaces. We compute the necessary correlators using reconstruction, the concavity axiom, and new techniques. We also compute the Frobenius manifold of the D3 singularity.
Market Dynamics With Non-Homogeneous Poisson Processes, Preston T. Redd
Market Dynamics With Non-Homogeneous Poisson Processes, Preston T. Redd
Theses and Dissertations
The Bertrand Duopoly model for demand in economics is a well-used model. Although this model has important insights towards pricing strategy, it does not accurately depict true market behaviors. In this paper, we will examine the advantages and disadvantages of the current model and its assumptions.We then take a whole new approach towards modeling this phenomena, using Poisson processes to model the demand of goods. We will discuss why this is a better approach and explain how we can extend this to better understand pricing strategies and market dynamics. We then apply our findings to the newsvendor problem, a commonly …