Mathematics Commons^™

Balancing Entertainment And Learning In The Popularization Of Mathematics: The Seven Light Bulbs Problem, Man Keung Siu

Journal of Humanistic Mathematics

Popularization of mathematics plays a significant role in drawing more “friends of mathematics” from the public, which is important for the healthy and prosperous development of the discipline. The issue of a suitable balance between entertainment and learning is constantly on the minds of those who put effort into this task. This article discusses this issue in the context of mathematical museums and describes a simple problem involving seven light bulbs to illustrate its main points.

To Fall In Love With Math, Do This, Susan D'Agostino

Journal of Humanistic Mathematics

In the viral New York Times essay, “To Fall in Love with Anyone, Do This,” Mandy Len Catron details an experience she and an acquaintance had as they shared responses to psychologist Arthur Aron’s thirty-six questions intended to make participants fall in love. She notes that, “we all have a narrative of ourselves that we offer up to strangers and acquaintances, but Dr. Aron’s questions make it impossible to rely on that narrative.” In this paper, we claim that we also have narratives of our relationship to mathematics that we offer up to ourselves and others. Following, we offer a …

The Humanistic Mathematics Network Journal: A Bibliographic Report, Nurullah E. Goren, Tiffany Zhu

Journal of Humanistic Mathematics

The content of the Humanistic Mathematics Network Newsletter was reviewed by Claire Skrivanos and Qingcheng Zhang in [1]. This report reviews the content of the Humanistic Mathematics Network Journal (1992-2004).

A Survey Of The Math Blogosphere, Katherine Thompson

Journal of Humanistic Mathematics

This article provides an overview of different types of mathematical blogs currently available. There are over twenty blogs highlighted, ranging from the technical to the recreational, from those sponsored by national mathematical organizations to those run by individuals--including students.

Rolling Dice On A Date, Francesca Raphael, Jennifer Switkes

Journal of Humanistic Mathematics

When a young mathematician faces the prospect of a date, all kinds of mathematics ensue. Here we explore her innovative way to keep the conversation going through rolling dice to decide which conversation starter to utilize. In the course of our exploration, we solve an interesting generating function problem.

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann

Journal of Humanistic Mathematics

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Journal of Humanistic Mathematics

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Mathematics, Writing, And Rhetoric: Deep Thinking In First-Year Learning Communities, Christine Von Renesse, Jennifer Digrazia

Journal of Humanistic Mathematics

Through the process of combining two seemingly unlikely bedfellows, mathematics and composition, two instructors explain how rhetoric connects the art of writing and the art of doing mathematics in an inquiry-based learning community. Combining these two courses in a learning community enables students and instructors to practice the deep thinking valued by each instructor and by a traditional liberal arts education while challenging both our and our students’ individual, disciplinary, and rhetorical conventions and beliefs. Using student writing from our course, our assignments from mathematics and composition, and survey evaluation results, we demonstrate how engaging in inquiry-based education provides unconventional …

Ways Of Relating To The Mathematics Of The Past, Michael N. Fried

Journal of Humanistic Mathematics

Historians of mathematics, by definition, look at mathematics of the past. But mathematicians, too, often look at mathematics of the past; mathematicians of the past themselves often looked very closely at mathematics of their own past. Is their relationship to the past the same as that of the historians? Is every view of the past an historical view? Indeed, is every historical view historical in the same way? Or is it possible that there are different kinds of relationships to the mathematics of the past? This paper will suggest that there are in fact a variety of such relationships. It …

Communicating Mathematics Across Time, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Fully Discrete Second-Order Linear Schemes For Hydrodynamic Phase Field Models Of Binary Viscous Fluid Flows With Variable Densities, Yuezheng Gong, Jia Zhao, Xiaogang Yang, Qi Wang

Mathematics and Statistics Faculty Publications

We develop spatial-temporally second-order, energy stable numerical schemes for two classes of hydrodynamic phase field models of binary viscous fluid mixtures of different densities. One is quasi-incompressible while the other is incompressible. We introduce a novel energy quadratization technique to arrive at fully discrete linear schemes, where in each time step only a linear system needs to be solved. These schemes are then shown to be unconditionally energy stable rigorously subject to periodic boundary conditions so that a large time step is plausible. Both spatial and temporal mesh refinements are conducted to illustrate the second-order accuracy of the schemes. The …

An Iteratively Reweighted Least Square Implementation For Face Recognition, Jie Liang

The Pegasus Review: UCF Undergraduate Research Journal

We propose, as an alternative to current face recognition paradigms, an algorithm using reweighted l₂ minimization, whose recognition rates are not only comparable to the random projection using l₁ minimization compressive sensing method of Yang et al [5], but also robust to occlusion. Through numerical experiments, reweighted l₂mirrors the l₁solution [1] even with occlusion. Moreover, we present a theoretical analysis on the convergence of the proposed l₂approach.

College Algebra Through Problem Solving (2018 Edition), Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Dabkowska

Open Educational Resources

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

Traveling In Networks With Blinking Nodes, Braxton Carrigan, James Hammer

Theory & Applications of Graphs

We say that a blinking node system modulo n is an ordered pair (G,L) where G is a graph and L is an on-labelling which indicates when vertices can be visited. An On-Hamiltonian walk is a sequence of all the vertices of G such that the position of each vertex modulo n is an integer of the label of that vertex. This paper will primarily investigate finding the shortest On-Hamiltonian walks in a blinking node system on complete graphs and complete bipartite graphs but also establishes the terminology and initial observations for working with blinking node systems on other graphs.

The Graphs And Matroids Whose Only Odd Circuits Are Small, Kristen Nicole Wetzler

LSU Doctoral Dissertations

This thesis is motivated by a graph-theoretical result of Maffray, which states that a 2-connected graph with no odd cycles exceeding length 3 is bipartite, is isomorphic to K_4, or is a collection of triangles glued together along a common edge. We first prove that a connected simple binary matroid M has no odd circuits other than triangles if and only if M is affine, M is M(K_4) or F_7, or M is the cycle matroid of a graph consisting of a collection of triangles glued together along a common edge. This result implies that a 2-connected loopless graph G …

Comparison Of Inter And Intra-Operator Differences For Cephalometric Landmark Identification On Three-Dimensional Cbct Images Using Pro Plan Cmf, Timothy P. Levine, Gregory J. Matthews, Hugo F. Calero, Victor M. Badner

Mathematics and Statistics: Faculty Publications and Other Works

Objective: To establish reliability of cephalometric landmark identification in threedimensions using ProPlan CMF software.

Methods: Two orthodontist identified a series of 33 cephalometric landmarks on 20 CBCT scans of Class I, pre-orthodontic patients and repeated the landmark identification about two months later. Intraclass correlations (ICC) were calculated by landmark in the X, Y, and Z dimensions and F-test were used to assess difference in landmark location in the X, Y, and Z dimensions.

Results: The majority of landmarks had good to excellent ICC for both inter- and intraobserver reliability. F-test also showed the majority of landmarks had no significant difference …

A Patient-Specific Treatment Model For Graves’ Hyperthyroidism, Balamurugan Pandiyan, Stephen J. Merrill, Flavia Di Bari, Alessandro Antonelli, Salvatore Benvenga

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Graves’ is disease an autoimmune disorder of the thyroid gland caused by circulating anti-thyroid receptor antibodies (TRAb) in the serum. TRAb mimics the action of thyroid stimulating hormone (TSH) and stimulates the thyroid hormone receptor (TSHR), which results in hyperthyroidism (overactive thyroid gland) and goiter. Methimazole (MMI) is used for hyperthyroidism treatment for patients with Graves’ disease.

Methods: We have developed a model using a system of ordinary differential equations for hyperthyroidism treatment with MMI. The model has four state variables, namely concentration of MMI (in mg/L), concentration of free thyroxine - FT4 (in pg/mL), and concentration of TRAb …

Wulff Shapes And A Characterization Of Simplices Via A Bezout Type Inequality, Christos Saroglou, Ivan Soprunov, Artem Zvavitch

Mathematics and Statistics Faculty Publications

Inspired by a fundamental theorem of Bernstein, Kushnirenko, and Khovanskii we study the following Bezout type inequality for mixed volumes V(L₁,...,L_n)V_n(K) ≤ V(L₁,K[n-1])V(L₂,..., L_{n},K). We show that the above inequality characterizes simplices, i.e. if K is a convex body satisfying the inequality for all convex bodies L₁, ..., L_n ⊂ Rⁿ, then K must be an n-dimensional simplex. The main idea of the proof is to …

Regrets, I'Ve Had A Few: When Regretful Experiences Do (And Don't) Compel Users To Leave Facebook, Shion Guha, Eric P.S. Baumer, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Previous work has explored regretful experiences on social media. In parallel, scholars have examined how people do not use social media. This paper aims to synthesize these two research areas and asks: Do regretful experiences on social media influence people to (consider) not using social media? How might this influence differ for different sorts of regretful experiences? We adopted a mixed methods approach, combining topic modeling, logistic regressions, and contingency analysis to analyze data from a web survey with a demographically representative sample of US internet users (n=515) focusing on their Facebook use. We found that experiences that arise because …

Review Of Painting By Numbers By Jason Makansi, Thomas J. Pfaff

Numeracy

Makansi, Jason. 2016. Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the "Experts." (Tucson, AZ: Layla Dog Press, 2016). 196 pp. ISBN 978-0-9984259-0-0.

In Painting by Numbers Jason Makansi adds another book to the quantitative literacy bookshelf, with a book focusing on models. The book offers twelve commandments to aid the reader in assess quantitative models. The second section of the book offers examples to apply the models. Increasing quantitative literacy is crucial and generally, the more books the better. Unfortunately, this book is too superficial, often misses key ideas, and can easily lead a person …

Life, The Universe, And Numeracy: Review Of A Numerate Life By John Allen Paulos (2015), Kira H. Hamman

Numeracy

John Allen Paulos. 2015. A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours (Buffalo, NY: Prometheus Books) 200 pp. ISBN: 978-1633881181

John Allen Paulos, author of Innumeracy and many other books addressing quantitative literacy and numeracy in society, tackles autobiography in this quirky "anti-memoir."

A Few Reflections On A Numerate Life, John Allen Paulos

Numeracy

John Allen Paulos. 2015. A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours (Amherst, NY: Prometheus Books). 200 pp. ISBN 978-1633881181.

This piece briefly introduces and excerpts A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours, written by John Allen Paulos and published by Prometheus Books. The book shares observations on life—many biographical—from the perspective of a numerate mathematician. The excerpt uses basic statistical reasoning to explore why we should expect that being odd is a most normal experience.

Math Course For Liberal Arts Majors: A Pilot With Embedded Remediation, Eileen B. Perez, Hansun To, Mary Fowler, Linda Larrivee

Numeracy

This study was designed to determine if embedded remediation is significant in accelerating the pathway to completion of a college-level math course for students needing remediation. The project studied the impact on student success in a quantitative literacy course at a Massachusetts four-year state university with remedial material embedded. The course satisfies the university’s general education math requirement for students with liberal arts majors who are not required to complete college algebra or calculus-based courses. The paper begins with a presentation of the issues with remedial mathematics and its impact on students’ graduation and persistence. Next, the paper covers the …

Thinking Out Loud On Early Creation Through The Lens Of Hermeneutics Of Sherlock Holmes (Towards A Model Of Universe Based On Turbulence-Generated Sound Theory), Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In recent years, apparently the Big Bang as described by the Lambda CDM-Standard Model Cosmology has become widely accepted by majority of physics and cosmology communities. Even some people have concluded that it has no serious alternative in horizon. Is that true? First, as we argued elsewhere, Big Bang story relies on singularity. In other words, when we are able to describe the observed data without invoking singularity, then Big Bang model is no longer required. Therefore, here we explore a few alternative stories other than Big Bang story, which most cosmologists believe it is the nearest to Biblical account …

Theoretical Open-Loop Model Of Respiratory Mechanics In The Extremely Preterm Infant, Laura Ellwein Fix, Joseph Khoury, Russell R. Moores Jr., Lauren Linkous, Matthew Brandes, Henry J. Rozycki

Mathematics and Applied Mathematics Publications

Non-invasive ventilation is increasingly used for respiratory support in preterm infants, and is associated with a lower risk of chronic lung disease. However, this mode is often not successful in the extremely preterm infant in part due to their markedly increased chest wall compliance that does not provide enough structure against which the forces of inhalation can generate sufficient pressure. To address the continued challenge of studying treatments in this fragile population, we developed a nonlinear lumped-parameter respiratory system mechanics model of the extremely preterm infant that incorporates nonlinear lung and chest wall compliances and lung volume parameters tuned to …

Limiting Absorption Principle And Strichartz Estimates For Dirac Operators In Two And Higher Dimensions, William Green, M Erdogan, Michael Goldberg

Faculty Publications - Mathematics

No abstract provided.

Mini Review: A Note On Nonoscillatory Solutions For Higher Dimensional Time Scale Systems, Elvan Akin, Ozkan Ozturk, Ismail Ugur Tiryaki, Gulsah Yeni

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we focus on nonoscillatory solutions of two (2D) and three (3D) dimensional time scale systems and discuss nonexistence of such solutions.

The Generalized Hypergeometric Difference Equation, Martin Bohner, Tom Cuchta

Mathematics and Statistics Faculty Research & Creative Works

A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special functions are demonstrated.