Mathematics Commons^™

Using Chatgpt As A Thought Partner In Writing Relevant Proportional Reasoning Word Problems, Andrea Berryhill, Lendon Chandler, Liza Bondurant, Bima Sapkota

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we, two preservice mathematics teachers (PSTs) and two mathematics teacher educators (MTEs), explore the potential of using ChatGPT, a large language model (LLM), as a thought partner to create relevant proportional reasoning word problems. We detail our iterative process of refining our inputs and critically evaluating ChatGPT's outputs. Our takeaways from this journey offer valuable insights for educators seeking to leverage the capabilities of LLMs in their lesson-planning endeavors.

Mathematical Methods For Economics And Business Syllabus, Marian Melnyk

Open Educational Resources

This syllabus outlines an online asynchronous course introducing essential mathematical tools and techniques in economics. It spans 24 sessions covering Functions, Differentiation, Limits, Integration, and Multivariable Functions, grounded in college algebra and calculus. The course utilizes Open Educational Resources (OER) for all materials, available in text and video formats on Blackboard. Continuous assessment, including quizzes, homework, two 1-hour tests, and a final exam, ensures consistent progress. Weekly online office hours provide additional support. The primary objective is to equip students with the mathematical skills necessary for economic analysis and problem-solving.

Mega-Influencers And Brand Dynamics: Shaping Attitudes Toward Leading And Challenger Brandsthrough Electronic Word Of Mouth, Riccardo Rialto, Lamberto Zollo, Kacy Kim, Sukki Yoon

Mathematics and Economics Faculty Journal Articles

The aim of this paper is to explore how mega‐influencers' electronic word of mouth (eWOM) messages on social media influence consumers' brand attitudes in duopolistic markets. Through three experimental studies, we observe that when mega‐ influencers send positive (vs. negative) eWOM messages about a leading brand, followers form positive (vs. negative) brand attitudes, but these effects fail to occur when influencers back challenger brands. The findings are consistent across three duopolistic market rivals (Apple vs. Samsung; UPS vs. FedEx; Nike vs. Adidas), three social media platforms (Facebook, Instagram, and X), and four mega‐influencers (Marques Brownlee, Gary Vaynerchuk, Kanye West, and …

Parallel-In-Time Implicit Schemes For Nonlinear Pdes, Subhash Paudel

Mathematics & Statistics Theses & Dissertations

An accurate prediction of unsteady physical phenomena arising in various applications (e.g., rotorcraft and turbomachinery flows, fluid-structure interaction, maneuvering flight conditions, etc.) requires a very large number of time steps, thus considerably increasing the total computational time, because conventional time integrators are inherently sequential. Parallel-in-time methods offer a promising direction for drastically reducing the computational time and achieving such scalability that is required for solving these unsteady problems on modern supercomputers with hundreds of thousands of computing cores. The parallel performance of existing parallel-in-time algorithms for nonlinear equations especially of the hyperbolic or mixed type is far from being satisfactory. …

Torus Surgery, Fibrations, Multisections, And Spun 4-Manifolds, Nicholas Paul Meyer

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A compact n-manifold X is fibered if it is a fiber bundle where the fiber F and base space B are manifolds. Fibered manifolds are particularly nice, as they are essentially classified by their monodromy maps. Two common examples of 4-dimensional fibered manifolds are surface bundles over surfaces and 3-manifold bundles over the circle.

The main focus of this dissertation is to investigate fibered 4-manifolds whose boundaries are the 3-torus and how these manifolds glue together to give new closed, fibered 4-manifolds. In particular, suppose W is diffeomorphic to S¹ × E_Y (K) where Y …

Differentiated Instruction In Geometry Using Low Floor, High Ceiling Mathematical Tasks, Franklin R. Falculan, Maria Alva Q. Aberin

Mathematics Faculty Publications

This study investigated the effects of using Low Floor High Ceiling (LFHC) mathematical tasks on students’ conceptual understanding and procedural fluency in seventh-grade Geometry by closely examining pre-test and posttest results. Two intact classes composed of thirty-two grade 7 students in each class participated in the study. The control group was taught and had practice using conventional, algorithmic tasks while the experimental group was taught and had practice using LFHC mathematical tasks. Data analysis revealed that, as compared to students exposed to algorithmic problems, students exposed to LFHC activities were much more mathematically proficient in Geometry, at the very least …

Nonlocal Frameworks For Nonlinear Conservation Laws And Advection-Diffusion Processes, Anh Thuong Vo

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Conservation laws are fundamental principles that play an important role in modeling various phenomena in physics, chemistry, and biology. However, their limitations, such as the development of shocks despite smooth initial conditions, are well known. The nonlocal model framework can be used to overcome these challenges. Nonlocal frameworks utilize integral operators that mimic differential operators but also incorporate long-range interactions within a finite horizon. This approach not only allows for non-smooth solutions, but also provides flexibility in modeling different phenomena. This study investigates the convergence of nonlocal divergence operators, defined with a general flux density function, to their classical counterparts. …

Conditional Optimal Sets And The Quantization Coefficients For Some Uniform Distributions, Evans Nyanney

Theses and Dissertations

Bucklew and Wise (1982) established that the quantization dimension of an absolutely continuous probability measure on a Euclidean space equals the Euclidean dimension of the space, and that the quantization coefficient is finite and positive. This thesis explores the variability of quantization coefficients for uniform distributions on various geometric structures, including line segments, circles, and regular polygons. We derive the conditional optimal sets of n-points and calculate the n-th conditional quantization errors for uniform distributions under different conditions. On line segments, we identify optimal point distributions as either equally spaced or geometrically spaced towards fixed end-points. For circles, we analyze …

Application And Analysis Of Machine Learning And Deep Learning Algorithms In Detection Of Ddos Cyberattacks, Dipok Deb

Theses and Dissertations

A Distributed Denial-of-Service (DDoS) attack involves overwhelming a target system's data bandwidth or computational resources, often using multiple attack systems, aiming to slow down or disable the targeted system. Detecting and mitigating DDoS attacks effectively remains challenging due to their varying characteristics. One of the promising approaches involves developing an AI based Intrusion Detection System (IDS) against cyberattacks. In this study, we aim to develop an AI based Intrusion Detection System (IDS) for DDoS threat detection using Machine Learning, Deep Learning, or hybrid techniques. Different Machine Learning (ML) and Deep Learning (DL) algorithms like Random Forest (RF), Naïve Bayes (NB), …

On Angles In Higher Order Brillouin Tessellations And Related Tilings In The Plane, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian

School of Mathematical & Statistical Sciences Faculty Publications

For a locally finite set in R 2 , the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R 2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in …

A Portable Numerical Library For The Calculation Of Multi-Dimensional Integrals, Ioannis Sakiotis

Computer Science Theses & Dissertations

Multi-dimensional numerical integration is a prevalent task in physics and other scientific fields, e.g., in the simulation of particle-beam dynamics and Bayesian parameter estimation. Scientific computing applications that simulate complex phenomena may require the solution to numerous multi-variate integrals. However, functions that have features such as sharp peaks or oscillations in high dimensional spaces, can result in an exorbitant number of computations. For many cases, convergence to accurate results in a reasonable amount of time is infeasible with existing numerical libraries. One approach towards making multi-dimensional integration viable is to parallelize existing algorithms. No commonly available algorithms or libraries exist …

Bivariate Polynomials Of Low Degree And Small Mahler Measure, Souad El Otmani

BAU Journal - Science and Technology

In this work, we highlight that many of the known limit points of the Mahler measure of univariate polynomials can be obtained as the Mahler measure of low-degree bivariate polynomials. To this end, we provide for each relevant measure the corresponding original bivariate polynomial found in the literature, along with the corresponding low-degree polynomial with an analogous measure.

On The Size Of Maximal Binary Codes With 2, 3, And 4 Distances, Alexander Barg, Alexey Glazyrin, Wei-Jiun Kao, Ching-Yi Lai, Pin-Chieh Tseng, Wei-Hsuan Yu

School of Mathematical & Statistical Sciences Faculty Publications

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n≥6 as well as the exact size of maximal binary constant weight codes with 2, 3, and 4 distances for several values of the weight and for all but small lengths.

Enhancing Tumor Classification Through Machine Learning Algorithms For Breast Cancer Diagnosis, Lawrence Agbota, Edmund F. Agyemang, Priscilla Kissi-Appiah, Lateef Moshood, Akua Osei- Nkwantabisa, Vincent Agbenyeavu, Abraham Nsiah, Augustina Adjei

School of Mathematical & Statistical Sciences Faculty Publications

In cancer diagnosis, machine learning helps improve cancer detection by providing doctors with a second perspective and allowing for faster and more accurate determination and decisions. Numerous studies have used both classic machine learning approaches and deep learning to address cancer classification. In this study, we examine the efficacy of five commonly used machine learning algorithms; both traditional and deep learning models namely, Logistic Regression, Support Vector Machines (SVM), Random Forest (RF), Decision Tree and Deep Neural Networks (DNN). We analyze their ability to properly classify tumors as Benign or Malignant using the Wisconsin breast cancer dataset (WBCD). Random Forest …

Some Problems In Harmonic Analysis, Anastasios Fragkos

Arts & Sciences Graduate Student Theses and Dissertations

One the most central questions in harmonic analysis of whether the Fourier series of a square integrable function on the torus $\mathbb T$ converges Lebesgue a.e.\ $ x\in\mathbb T$ was answered positively by L.\ Carleson in 1966 \cite{C}, by means of a weak-$L^2$ inequality for the maximal operator \begin{equation} \label{carleson0} \mathcal C f(x) =\sup_{N\in \mathbb Z} \Bigg| \sum_{|\xi|\leq N} \widehat f(\xi) \exp(ix\xi) \Bigg|, \qquad x\in \mathbb T. \end{equation} The argument of \cite{C} estimates $\mathcal C $ pointwise as a maximal modulated Hilbert transform, outside appropriately constructed exceptional sets whose mass is controlled by almost-orthogonality. The implicit distributional estimate in \cite{C} …

Post-Baccalaureate Research Experiences For Students At Two Hispanic-Serving Institutions (Experience), Dessaray Monique Gorbett, Benjamin C. Flores, Cristina Villalobos, Sara E. Rodriguez, Ariana (Ari) Arciero, Josef A. Sifuentes

School of Mathematical & Statistical Sciences Faculty Publications

This study examines the implementation of a one-year program that offered post-baccalaureate research experiences to a cohort of recent STEM graduates from two large Hispanic-serving institutions. Both institutions are collaborators in an NSF Louis Stokes Alliance for Minority Participation (LSAMP) grant, which is dedicated to enhancing the academic experience of historically underrepresented minorities. Applicants were either self-nominated or were nominated by faculty to participate in the post-baccalaureate program. Following an application process that included an interview, selected participants were matched to research faculty and committed to engage in a high-impact research project for at least one semester and for up …

Laboratories In Mathematical Experimentation: A Bridge To Higher Mathematics, 2nd Edition, J. William Bruce, George Cobb, Giuliana Davidoff, Christopher Dugaw, Alan Durfee, Art M. Duval, Janice Gifford, Helmut Knaust, Donal O’Shea, Mark Peterson, Harriet Pollatsek, Margaret Robinson, Lester Senechal, Robert Weaver

Textbooks and Manuals Series

This second edition is composed of a set of sixteen laboratory investigations which allow the student to explore rich and diverse ideas and concepts in mathematics. The approach is hands-on and experimental, an approach that is very much in the spirit of modern pedagogy. The course is typically offered in one semester, at the sophomore (second year) level of college. It requires prior exposure to calculus and provides a transition to the study of higher, abstract mathematics. Most of the laboratories require the use of a computer for experimentation, but the text is written independent of any particular software.

Note …

A Note On Surfaces In ℂℙ² And ℂℙ²#ℂℙ², M. Marengon, Allison N. Miller, A. Ray, A. I. Stipsicz

Mathematics & Statistics Faculty Works

In this brief note, we investigate the ℂℙ²-genus of knots, i.e., the least genus of a smooth, compact, orientable surface in ℂℙ² \ \mathringB⁴ bounded by a knot in 𝑆³. We show that this quantity is unbounded, unlike its topological counterpart. We also investigate the ℂℙ²-genus of torus knots. We apply these results to improve the minimal genus bound for some homology classes in ℂℙ²#ℂℙ².

Bounds For The Regularity Radius Of Delone Sets, Nikolay Dolbilin, Alexey Garber, Egon Schulte, Marjorie Senechal

School of Mathematical & Statistical Sciences Faculty Publications

Delone sets are discrete point sets X in Rd characterized by parameters (r, R), where (usually) 2r is the smallest inter-point distance of X, and R is the radius of a largest “empty ball” that can be inserted into the interstices of X. The regularity radius ρ^d is defined as the smallest positive number ρ such that each Delone set with congruent clusters of radius ρ is a regular system, that is, a point orbit under a crystallographic group. We discuss two conjectures on the growth behavior of the regularity radius. Our “Weak Conjecture” states that ρ^d=O(d2log2d)R as d→∞ , …

Optimal Selection Of Good Polynomials And Constructions Of Locally Recoverable Codes Via Galois Theory, Austin Dukes

USF Tampa Graduate Theses and Dissertations

To keep up with the ever-growing demand for reliable and efficient availability of data,locally recoverable codes (LRCs) have been the focus of much study due to their applications in cloud and distributed storage systems. A fundamental construction of LRCs was given in [36] based on polynomials which relied on the existence of r-good polynomials. In the same paper some constructions of good polynomials were given, but these constructions did not cover every configuration of parameters. Naturally this led to research into constructing good polynomials for what was not addressed in [36], but new ponderings were also posed, such as the …

Supplementary Files For "Using Digitized Building And Weather Records To Improve The Accuracy Of Ground To Roof Snow Load Ratio Estimations", Gideon Parry, Brennan Bean

Browse all Datasets

Reliability targeted snow loads (RTLs) measure the weight in accumulated snow (i.e. snow load) that a roof is required to support to ensure the probability of failure is suf- ficiently low. This calculation has historically relied upon a probability distribution that characterizes the ratio between the annual maximum ground snow load to the annual max- imum roof snow load, a quantity referred to as Gr. The best available data for estimating Gr comes from Canadian case studies from the 1950s and 1960s. However, much of the data was never digitized, with only approximations of data being made available in scanned …

Numerical Issues For A Non-Autonomous Logistic Model, Marina Mancuso, Kaitlyn M. Martinez, Carrie Manore, Fabio Milner

CODEE Journal

The user-friendly aspects of standardized, built-in numerical solvers in
computational software aid in the simulations of many problems solved using
differential equations. The tendency to trust output from built-in numerical
solvers may stem from their ease-of-use or the user’s unfamiliarity with the
inner workings of the numerical methods. Here, we show a case where the
most frequently used and trusted built-in numerical methods in Python’s
SciPy library produce incorrect, inconsistent, and even unstable approxima-
tions for a the non-autonomous logistic equation, which is used to model
biological phenomena across a variety of disciplines. Some of the most com-
monly used …

Cellular Automata Modeling Approach Of Addiction, Ruba Hameed

Thesis/ Dissertation Defenses

This thesis develops a mathematical model and cellular automata simulations to study the spread of drug addiction in populations, incorporating key factors like peer influence, substance availability, support networks, and awareness campaigns. The model describes transitions between non-use, experimental use, recreational use, and addiction states. Mathematical analysis establishes model properties, while an irregular graph cellular automata framework analyzes emerging spatial patterns and behaviors. Extensive scenario simulations explore peer influence, isolation, substance availability, support networks, and awareness campaign impacts, enabling visualization of model evolution over time and determining thresholds, tipping points, and intervention effectiveness. The findings provide an actionable understanding of …

Mixed Uncertainty Analysis On Pumping By Peristaltic Hearts Using Dempster-Shafer Theory, Yanyan He, Nicholas A. Battista, Lindsay D. Waldrop

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster–Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief …

Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser

Electronic Theses and Dissertations

This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.

We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets of {1, 2, . . . , n} whose least common multiple is small, we improved a result of Brown and Rödl on the smallest integer n such that every 2-coloring of {1, 2, . . . , n} has a monochromatic solution to equations with unit fractions. Using a recent result of Boza, …

Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk

Electronic Theses and Dissertations

The universal 2-parameter vertex algebra W_∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W_∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in …

Circling The Square: Computing Radical Two, Isaiah Mellace, Joshua Kroeker

NEXUS: The Liberty Journal of Interdisciplinary Studies

Discoveries of equations for irrational numbers are not new. From Newton’s Method to Taylor Series,there are many ways to calculate the square root of two to arbitrary precision. The following method is similar in this way, but it is also a fascinating derivation from geometry that has applications to other irrationals. Additionally, the equation derived has some properties that may lead to fast computation. The first part of this paper is dedicated to deriving the equation, and the second is focused on computer science implementations and optimizations.

Mathematical Modeling Of An Epidemic In Scale-Free Network With Imperfect Vaccination, Heba Hameed

Thesis/ Dissertation Defenses

In light of the recent COVID-19 pandemic, the mathematical epidemiological model has proven to be essential for understanding the disease dynamic and finding the best control tool to help contain the disease and minimize its impact. This thesis investigates the dynamics of an infectious disease spread with latent infection and vaccination. The aim is to study this model's dynamic in a network that reflects the heterogeneity of the environment where the disease spreads. The vaccination is assumed to be not perfect, which means that vaccinated persons are likely to be infected and that the vaccinated person could lose their immunity, …

The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.

Instructional Strategies That Support Student Achievement With The Eureka Algebra 1 Curriculum, Honnalora Hill

Walden Dissertations and Doctoral Studies

Numerous states use research-based mathematics curricula as a teaching tool to enhance mathematics performance outcomes on state assessment scores. Despite implementation of the Eureka curriculum, students at the study site were still struggling to master Algebra 1 skills sufficiently to pass the Louisiana state exam. The aim of this basic qualitative study was to explore strategies teachers employed while implementing the Eureka curriculum to increase student achievement. The study was guided by Vygotsky’s zone of proximal development (ZPD) theoretical framework and involved semi-structured interviews with 12 participants who had been teaching Algebra 1 with the Eureka curriculum for at least …