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Σary, Minnesota State University Moorhead, Mathematics Department

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Compressed Sensing For Multiple Input-Multiple Output Radar Imaging, Juan F. Lopez Jr.

Theses and Dissertations - UTB/UTPA

Multiple input - multiple output (MIMO) radar utilizes the transmission of spatially diverse waveforms from a static antenna array to gather information about the desired scene. We will demonstrate how techniques from compressed sensing can be applied to image formation in MIMO radar when in the presence of undersampling. We analyze the problem under the general theoretical framework of inverse scattering.

Actual Vs. Perceived Value Of Players Of The National Basketball Association, Stephen Righini

Honors Projects in Mathematics

Over the past few decades the media has played an increasingly large role in shaping how player effectiveness in the National Basketball Association (NBA) is perceived. Several factors have caused fans, announcers, and even NBA team management to have unintentional bias toward certain players. This study aims to utilize various formulas created by NBA statisticians, called Player Raters, to identify how efficient each NBA player actually is in comparison to the rest of the league. Data from the past 12 seasons was compiled and six Player Raters were used to place values on every NBA player since the 2000-2001 season. …

Time Series Data Mining: A Retail Application Using Sas Enterprise Miner, Daniel Hebert

Honors Projects in Mathematics

Modern technologies have allowed for the amassment of data at a rate never encountered before. Organizations are now able to routinely collect and process massive volumes of data. A plethora of regularly collected information can be ordered using an appropriate time interval. The data would thus be developed into a time series. With such data, analytical techniques can be employed to collect information pertaining to historical trends and seasonality. Time series data mining methodology allows users to identify commonalities between sets of time-ordered data. This technique is supported by a variety of algorithms, notably dynamic time warping (DTW). This mathematical …

The Fibonacci Sequence: Its History, Significance, And Manifestations In Nature, Anna Grigas

Senior Honors Theses

The discoveries of Leonard of Pisa, better known as Fibonacci, are revolutionary contributions to the mathematical world. His best-known work is the Fibonacci sequence, in which each new number is the sum of the two numbers preceding it. When various operations and manipulations are performed on the numbers of this sequence, beautiful and incredible patterns begin to emerge. The numbers from this sequence are manifested throughout nature in the forms and designs of many plants and animals and have also been reproduced in various manners in art, architecture, and music.

Logics And The Sorites Paradox, Devin Neubrander

Journal of Interdisciplinary Undergraduate Research

Renderings of the ancient Sorites paradox in classical first-order logic, Lukasiewicz’s three-valued first-order logic, and a Pavelka-style derivation system for Lukasiewicz’s fuzzy first-order logic are derived. It can be seen that only in the last logic mentioned is the conclusion of the Sorites paradox false while the premises are true thus resolving the paradox.

Quantitative Approaches To Sustainability Seminars, Rachel Levy

All HMC Faculty Publications and Research

How can mathematicians contribute to education of about sustainability? Mathematicians study climate change, energy-related technologies, models of energy availability, production and consumption, and even the political and social aspects of sustainable legislation and practices. However, at this point, few courses on sustainability can be found in math department offerings. When we consider problems that our current and future students will face, energy sustainability certainly seems important. But how many of these ideas reach our classrooms?

Customer Age As A Predictor Of Contact Volume, Tollan Renner

Honors Theses and Capstones

A two stage modeling approach for modeling customer age as a predictor of contact volume was conducted using a real-world data set of approximately 2,000,000 contacts from a company call center. Two models were constructed in the first stage, one a straightforward regression and the other a series of regressions. One was selected as better performing and scaled up to predict calls received from calls answered. The second stage of the modeling included a day of the week covariate and performed the best of the models created. This model uses age bins as model effects, of which the youngest age …

Equations Of Light - The Steam Journal Inaugural Issue, The Cover Art, Chris Brownell

The STEAM Journal

This is the background to some of the work, art and thinking that went into the cover art for the inaugural issue.

Creating A Faculty Learning Community To Support Scholarship Of Teaching And Learning Among Stem University Faculty, Cher C. Hendricks, Myrna Gantner

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

In this session, we describe the creation of a Faculty Learning Community for university faculty in science, mathematics, and computer science. These faculty, recipients of mini-grants funded by the USG STEM Initiative, are studying ways to improve their instruction and increase student learning in STEM courses. Through the FLC, they are able to collaborate and support each others’ work.

Trig-Star, James M. Anderson

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

A TRIG-STAR is a mathematics student who has demonstrated in competition that he or she is the most skilled among classmates in the practical application of trigonometry. The competition for the honor is a timed exercise which is the solving of a trigonometry problem that incorporates the use of right triangle formulas, circle formulas, the law of sines, and the law of cosines. The contest helps to promote careers in surveying and mapping to students at the High Schools across the country. The award is sponsored by the National Society of Professional Surveyors and cosponsored locally. State winners also have …

Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

Many students are overwhelmed by mathematics because the language is too difficult, the teaching strategies are insufficient or they have lost motivation. With a recent emphasis on meeting the Common Core expectations, using manipulatives to eliminate misconceptions in the mathematical classroom has become even more prevalent. I explored the misconceptions that many students struggle with and provided possible methods of eliminating them at all levels for learning. During this investigation, I studied the effect of manipulatives on students’ understanding of fraction concepts and the students’ conceptions of the unit of reference when working with fraction word problems. I learned that …

Duncan, Benjamin, 1772-1809 (Sc 678), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 678. Cipher book kept by Benjamin Duncan, of Culpeper County, Virginia and Fayette County, Kentucky. Includes samples of legal forms and letters.

Brown, James Monroe, 1800-1886 (Sc 806), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 806. Ciphering book, 1822-1827 (40 p.), of James M. Brown, Butler County, Kentucky, which also contains a few pages of account entries and other various notations, (806a). Photocopy of ciphering book is also included. Also letter, 1989, from donor relating family data.

Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients, Morgan Cole

Theses and Dissertations

Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some integer b greater than or equal to 2. We will investigate the size of the coefficients of the polynomial and establish a largest such bound on the coefficients that would imply that f(x) is irreducible. A result of Filaseta and Gross has established sharp bounds on the coefficients of such a polynomial in the case that b = 10. We will expand these results for b in {8, 9, ..., 20}.

Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan

Theses Digitization Project

The purpose of this project is to investigate blow-up properties of solutions for specific initial-value problems that involve Bernoulli Ordinary Differential Equations (ODE's). The objective is to find conditions on the coefficients and on the initial-values that lead to unbounded growth of solutions in finite time.

The Machete Number, David Freund

Senior Independent Study Theses

Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.

Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations, Tracy Layden

Scripps Senior Theses

This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.

Undergraduate And Graduate Teaching Assistants' Perceptions Of Their Responsibilities - Factors That Help Or Hinder, Alena Moon, Hyunyi Jung, Farshid Marbouti, Kelsey Joy Rodgers, Heidi A. Diefes-Dux

Mathematics, Statistics and Computer Science Faculty Research and Publications

Effective teaching assistants (TAs) are crucial for effective student learning. This is especially true in science, technology, engineering, and mathematics (STEM) programs, where TAs are enabling large programs to transition to more student-centered learning environments. To ensure that TAs are able to support these types of learning environments, their perspectives of training, their abilities, and other work related aspects must be understood. In this paper a survey that was created based on interviews conducted with eight TAs is discussed. The survey has four primary categories of content that are critical for understanding TAs' perspectives: (1) background, (2) motivation, (3) training, …

The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour

Senior Independent Study Theses

Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …

Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman

Senior Independent Study Theses

This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …

Selected Research In Covering Systems Of The Integers And The Factorization Of Polynomials, Joshua Harrington

Theses and Dissertations

In 1960, Sierpi\'{n}ski proved that there exist infinitely many odd positive integers $k$ such that $k\cdot 2^n+1$ is composite for all positive integers $n$. Such integers are known as Sierpi\'{n}ski numbers. Letting $f(x)=ax^r+bx+c\in\mathbb{Z}[x]$, Chapter 2 of this document explores the existence of integers $k$ such that $f(k)2^n+d$ is composite for all positive integers $n$. Chapter 3 then looks into a polynomial variation of a similar question. In particular, Chapter~\ref{CH:FH} addresses the question, for what integers $d$ does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ with $f(1)\neq -d$ such that $f(x)x^n+d$ is reducible for all positive integers $n$. The last two chapters of …

Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda

Department of Math & Statistics Faculty Publications

We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identifiedwith the …

Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.

Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann

Department of Math & Statistics Faculty Publications

In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces H(b), mainly when b is a non-extreme point of the unit ball of H^∞.

On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin

Department of Math & Statistics Faculty Publications

The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic functions such as model subspaces of Hardy spaces, deBranges-Rovnyak spaces and Herglotz spaces, ordinary differential operators (including Schrodinger operators from quantum mechanics), Toeplitz operators, and infinite Jacobi matrices.

In this paper we develop a general representation theory of simple symmetric operators with equal deficiency indices, and …

Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati

Electronic Theses and Dissertations

In this thesis we compare various potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang Splitting) is justied. Numerical simulations provide graphical evidence of properties of both focusing and nonfocusing cases.

Metacognition And Its Effect On Learning High School Calculus, Bonnie Sue Bergstresser

LSU Master's Theses

The following paper discusses the effect of metacognitive training sessions on students’ calculus retention. Students in two high school classes participated. The students in both classes were then given lessons on a chapter without metacognitive training and lessons on a subsequent chapter with training in a set of metacognitive skills. After the latter chapter students scored higher on a post-test and expressed desire to incorporate the skills they learned into their other classes.

Exploring Student Perseverance In Problem Solving, Angelique Renee (Treadway) Duncker

LSU Master's Theses

ABSTRACT Many high school Geometry students lack the perseverance required to complete complex and time-consuming problems. This project tests the hypothesis that if students were provided with a means of organizing their problem solving work they will be less apt to quit when faced with complex and time-consuming mathematical problems. This study involved students enrolled in 10th grade Geometry and 10th grade Honors Geometry in two similar high schools. After trying unsuccessfully to implement methods adapted from an engineering workshop, I designed a graphic organizer that was simple to use and acceptable to the students. Ultimately, I did not detect …

Coloring Pythagorean Triples And A Problem Concerning Cyclotomic Polynomials, Daniel White

Theses and Dissertations

One may easily show that there exist $O( \log n)$-colorings of $\{1,2, \ldots, n\}$ such that no Pythagorean triple with elements $\le n$ is monochromatic. In Chapter~\ref{CH:triples}, we investigate two analogous ideas. First, we find an asymptotic bound for the number of colors required to color $\{1,2,\ldots ,n\}$ so that every Pythagorean triple with elements $\le n$ is $3$-colored. Afterwards, we examine the case where we allow a vanishing proportion of Pythagorean triples with elements $\le n$ to fail to have this property.

Unrelated, in 1908, Schur raised the question of the irreducibility over $\Q$ of polynomials of the form …