Other Mathematics Commons^™

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs

UNO Student Research and Creative Activity Fair

Communication networks tend to contain redundant devices and mediums of transmission, thus the need to locate, document, and optimize networks is increasingly becoming necessary. However, many people do not know where to start the optimization progress. What is network topology? What is this “Shortest Path Problem”, and how can it be used to better my network? These questions are presented, taught, and answered within this paper. To supplement the reader’s understanding there are thirty-eight figures in the paper that are used to help convey and compartmentalize the learning process needed to grasp the materials presented in the ending sections.

In …

Superoscillations And Analytic Extension In Schur Analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of Rfunctions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

New Representations For A Semi-Markov Chain And Related Filters, Robert J. Elliott, W. P. Malcolm

Journal of Stochastic Analysis

No abstract provided.

Math Escape Rooms: A Novel Approach For Engaging Learners In Math Circles, Janice F. Rech, Paula Jakopovic, Hannah Seidl, Greg Lawson, Rachel Pugh

Journal of Math Circles

Engaging middle and high school students in Math Circles requires time, planning and creativity. Finding novel approaches to maintain the interest of a variety of learners can be challenging. This paper outlines a model for developing and implementing math escape rooms as a unique structure for facilitating collaborative problem solving in a Math Circle. These escape rooms were designed and hosted by undergraduate secondary mathematics education majors. We provide possible structures for hosting escape rooms that could translate to a range of settings, as well as reflections and lessons learned through our experiences that could inform practitioners in other settings.

Wild Randomness And The Application Of Hyperbolic Diffusion In Financial Modelling, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Linear Decomposition And Anticipating Integral For Certain Random Variables, Ching-Tang Wu, Ju-Yi Yen

Journal of Stochastic Analysis

No abstract provided.

On Leibniz Cohomology, Jorg Feldvoss, Friedrich Wagemann

University Faculty and Staff Publications

In this paper we prove the Leibniz analogue of Whitehead's vanishing theorem for the Chevalley-Eilenberg cohomology of Lie algebras. As a consequence, we obtain the second Whitehead lemma for Leibniz algebras. Moreover, we compute the cohomology of several Leibniz algebras with ad joint or irreducible coefficients. Our main tool is a Leibniz analogue of the Hochschild-Serre spectral sequence, which is an extension of the dual of a spectral sequence of Pirashvili for Leibniz homology from symmetric bimodules to arbitrary bimodules.

The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Los conjuntos neutrosóficos, la lógica neutrosófica, la probabilidad neutrosófica, la estadística neutrosófica, el precálculo neutrosófico, el cálculo neutrosófico, la psicología neutrosófica, la sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, …

Group Theory Visualized Through The Rubik's Cube, Ashlyn Okamoto

University Honors Theses

In my thesis, I describe the work done to implement several Group Theory concepts in the context of the Rubik’s cube. A simulation of the cube was constructed using Processing-Java and with help from a YouTube series done by TheCodingTrain. I reflect on the struggles and difficulties that came with creating this program along with the inspiration behind the project. The concepts that are currently implemented at this time are: Identity, Associativity, Order, and Inverses. The functionality of the cube is described as it moves like a regular cube but has extra keypresses that demonstrate the concepts listed. Each concept …

First Exit-Time Analysis For An Approximate Barndorff-Nielsen And Shephard Model With Stationary Self-Decomposable Variance Process, Shantanu Awasthi, Indranil Sengupta

Journal of Stochastic Analysis

No abstract provided.

Quantum Theories Associated To Increasing Hilbert Space Filtrations And Generalized Jacobi 3–Diagonal Relation, Luigi Accardi, Yun Gang Lu

Journal of Stochastic Analysis

No abstract provided.

Rate Of Convergence In The Central Limit Theorem For Iid Pareto Variables, Claas Becker, Manuel Bohnet, Sarah Kummert

Journal of Stochastic Analysis

No abstract provided.

Noncentral Limit Theorem For Large Wishart Matrices With Hermite Entries, Charles-Philippe Diez, Ciprian A. Tudor

Journal of Stochastic Analysis

No abstract provided.

The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, Daniel J. Curtin

Euleriana

In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon's in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz's solution, which he corrected, after extending Varignon's solution in the case of circular base. Euler then used Leibniz's approach to solve …

Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, Nikos Mylonas, Basil K. Papadopoulos

Journal of Stochastic Analysis

No abstract provided.

Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Aims and Scope Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function �� into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to …

Once Upon A Party - An Anecdotal Investigation, Vijay Fafat

Journal of Humanistic Mathematics

Mathematicians and Physicists attending let-your-hair-down parties behave exactly like their own theories. They live by their theorems, they jive by their theorems. Life imitates their craft, and we must simply observe the deep truths hiding in their party-going behavior...

Mathematical Zendo: A Game Of Patterns And Logic, Philip Deorsey, Corey Pooler, Michael Ferrara

Journal of Math Circles

Mathematical Zendo is a logic game that actively engages participants in pattern recognition, problem solving, and critical thinking while providing a fun opportunity to explore all manner of mathematical objects. Based upon the popular game of Zendo, created by Looney Labs, Mathematical Zendo centers on a secret rule, chosen by the leader, that must be guessed by teams of players. In each round of the game, teams provide examples of the mathematical object of interest (e.g. functions, numbers, sets) and receive information about whether their guesses do or do not satisfy the secret rule. In this paper, we introduce Mathematical …

Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, I. Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

Boxes, Extended Boxes And Sets Of Positive Upper Density In The Euclidean Space, Polona Durcik, Vjekoslav Kovač

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove that sets with positive upper Banach density in sufficiently large dimensions contain congruent copies of all sufficiently large dilates of three specific higher-dimensional patterns. These patterns are: 2n vertices of a fixed n-dimensional rectangular box, the same vertices extended with n points completing three-term arithmetic progressions, and the same vertices extended with n points completing three-point corners. Our results provide common generalizations of several Euclidean density theorems from the literature.

Review Of Social Workers Count: Numbers And Social Issues By Michael Anthony Lewis, Michael T. Catalano

Numeracy

Lewis, Michael Anthony. 2017. Social Workers Count: Numbers and Social Issues. 2019. New York: Oxford University Press. 223 pp. ISBN 978-019046713-5

The numeracy movement, although largely birthed within the mathematics community, is an outside-the-box endeavor which has always sought to break down or at least transgress traditional disciplinary boundaries. Michael Anthony Lewis’s book is a testament that this effort is succeeding. Lewis is a social worker and sociologist with an impressive resume, author of Economics for Social Workers, co-editor of The Ethics and Economics of the Basic Income Guarantee, and member of the faculty at the Silberman School …

Green's Function For The Schrodinger Equation With A Generalized Point Interaction And Stability Of Superoscillations, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study the time dependent Schrödinger equation with all possible self-adjoint singular interactions located at the origin, which include the δ and δ'-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability …

Numerical Integration Through Concavity Analysis, Daniel J. Pietz

Rose-Hulman Undergraduate Mathematics Journal

We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.

Linear Combinations Of Harmonic Univalent Mappings, Dennis Nguyen

Rose-Hulman Undergraduate Mathematics Journal

Many properties are known about analytic functions, however the class of harmonic functions which are the sum of an analytic function and the conjugate of an analytic function is less understood. We wish to find conditions such that linear combinations of univalent harmonic functions are univalent. We focus on functions whose image is convex in one direction i.e. each line segment in that direction between points in the image is contained in the image. M. Dorff proved sufficient conditions such that the linear combination of univalent harmonic functions will be univalent on the unit disk. The conditions are: the mappings …

Mathematical Magic: A Study Of Number Puzzles, Nicasio M. Velez

Rose-Hulman Undergraduate Mathematics Journal

Within this paper, we will briefly review the history of a collection of number puzzles which take the shape of squares, polygons, and polyhedra in both modular and nonmodular arithmetic. Among other results, we develop construction techniques for solutions of both Modulo and regular Magic Squares. For other polygons in nonmodular arithmetic, specifically of order 3, we present a proof of why there are only four Magic Triangles using linear algebra, disprove the existence of the Magic Tetrahedron in two ways, and utilizing the infamous 3-SUM combinatorics problem we disprove the existence of the Magic Octahedron.

Floor Plan Assignment In Elementary Mathematics Education, Tunde Jakab

Open Educational Resources

In this upper elementary mathematics education assignment, the prospective teachers gain hands-on experience in measuring distances in feet and inches, calculating areas, and converting distance and area measurements. Moreover, they solve a real-life situation by choosing the most economical tiles for their kitchen. This last part (3) of the assignment develops critical thinking and expressing one's thought processes. Part 3 can be used as an in-class discussion, which further promotes reasoning skills.

Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole

Publications and Research

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.

A Relationship Built To Impact Instruction: Developing And Sustaining Productive Partnerships Between Mathematics Specialists And Principals, Nathan D. Potter, Hannah Adera Rooney, Melody Locher, Debra Kinsey

Journal of Mathematics and Science: Collaborative Explorations

How does the mathematics specialist provide a profound and lasting impact on instruction? We believe that a productive partnership between the principal and specialist, which we will call the principal-specialist relationship, is at the crux of the matter. When the principal-specialist relationship is built upon a foundation of a shared vision, clear roles, communication, and trust, both the teachers and students in the school benefit. We will explore the impact of the principal-specialist relationship on teacher success during the era of distance learning as necessitated by the COVID-19 pandemic. In order to explore how these ideas come alive in the …

Evolutionary Dynamics Of Bertrand Duopoly, Julian Killingback, Timothy Killingback

Computer Science Department Faculty Publication Series

Duopolies are one of the simplest economic situations where interactions between firms determine market behavior. The standard model of a price-setting duopoly is the Bertrand model, which has the unique solution that both firms set their prices equal to their costs-a paradoxical result where both firms obtain zero profit, which is generally not observed in real market duopolies. Here we propose a new game theory model for a price-setting duopoly, which we show resolves the paradoxical behavior of the Bertrand model and provides a consistent general model for duopolies.