Digital Commons Network^™

Pension Building, Washington Dc, E Laura Golberg

Journal of Humanistic Mathematics

No abstract provided.

Select Poems From Sizes Only Slightly Distinct And From Truth And Beauty, Marion D. Cohen

Journal of Humanistic Mathematics

No abstract provided.

The Allure Of Mathematics Or Book Review: Seduced By Logic: Émilie Du Châtelet, Mary Somerville, And The Newtonian Revolution, By Robyn Arianrhod, Elizabeth A. Lamprecht

Journal of Humanistic Mathematics

Today, there is a tendency to overlook the contributions of women such as Émilie du Châtelet and Mary Somerville; yet, despite numerous obstacles, they were able to make meaningful contributions to science. This review of Robyn Arianrhod’s book provides brief biographical summaries of the lives of these extraordinary women. It also considers some of the ramifications of Isaac Newton’s theory.

Throughout history, various factors have impeded women from full participation in scientific research; nevertheless, Émilie du Châtelet and Mary Somerville found and took advantage of opportunities to engage in scientific activities. This raises the question: had these women been born …

Teaching Calculus With Infinitesimals, Rebecca Vinsonhaler

Journal of Humanistic Mathematics

This article argues that first semester calculus courses for non-mathematics majors should be taught using infinitesimals. This applies to both high school and undergraduate calculus courses. The use of infinitesimals in calculus, though more intuitive than the approach developed in the 19^th Century, has been controversial for over two millennia. However, in the 20^th Century their use was shown to be equa-consistent with the approach developed in the 19^th Century. Here I first provide a brief history of infinitesimals, why they were controversial, and how they were finally put on a firm footing. Next I illustrate the …

Jay Leno And Abstract Algebra, Adam Glesser, Martin Bonsangue

Journal of Humanistic Mathematics

The Jay Leno skit Jaywalking, showing ordinary people struggling to answer basic questions, is both entertaining and applicable to teaching. This article describes how an instructor can strengthen students' conceptual understanding by creating an element of confusion, or "cognitive dissonance," in the students' minds using Jaywalking-style interactions in the classroom.

Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.

A Meeting Of Minds: An Alternate Humor For Teaching Mathematics To Non-Stem Majors, Paul H. Grawe

Journal of Humanistic Mathematics

John Allen Paulos argued essentially for three forms of humor dear to mathematics: Incongruity, Gotcha, and Word Play. Unfortunately, these three are often combative forms and easily drive non-STEM majors out of mathematics and statistics.

William Dunham in The Mathematical Universe shows how a fine mathematician can use humor to draw non-specialists in. Central to Dunham’s success is his use of Sympathetic Pain humor, which creates softer synthetic Reconciler, Consoler, or Bridgebuilder humor styles.

What If?: Mathematics, Creative Writing, And Play, Emily Clader

Journal of Humanistic Mathematics

Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.

The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam

Journal of Humanistic Mathematics

Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed …

Wabi-Sabi Mathematics, Jean-Francois Maheux

Journal of Humanistic Mathematics

Mathematics and aesthetics have a long history in common. In this relation however, the aesthetic dimension of mathematics largely refers to concepts such as purity, absoluteness, symmetry, and so on. In stark contrast to such a nexus of ideas, the Japanese aesthetic of wabi-sabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabi-sabi mathematics” by showing (1) how wabi-sabi mathematics is conceivable; (2) how wabi-sabi mathematics is observable; and (3) why we should bother about wabi-sabi mathematics

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

Surprise And The Aesthetic Experience Of University Students: A Design Experiment, Ofer Marmur, Boris Koichu

Journal of Humanistic Mathematics

Little is known about instructional means by which the aesthetic experience of mathematics can be enhanced for undergraduate learners. This paper presents and discusses an iterative lesson design process towards creating an opportunity for students to appreciate the beauty of an unexpected solution to a challenging calculus problem. The lesson design draws on insights from both mathematics education research on aesthetics and research on aesthetic appreciation in music. The data were collected over the course of five lessons with different groups of calculus students in which the intended problem was presented in two different ways. In addition, stimulated-recall interviews were …

Kaleidoscopes, Chessboards, And Symmetry, Tricia M. Brown

Journal of Humanistic Mathematics

This paper describes the n-queens problem on an n by n chessboard. We discuss the possible symmetries of n-queens solutions and show how solutions to this classical chess question can be used to create examples of colorful artwork.

A Short Walk Can Be Beautiful, Jonathan M. Borwein

Journal of Humanistic Mathematics

The story I tell is of research undertaken, with students and colleagues, in the last six or so years on short random walks. As the research progressed, my criteria for `beauty' changed. Things seemingly remarkable became `simple' and other seemingly simple things became more remarkable as our analytic and computational tools were refined, and understanding improved. I intentionally display some rather advanced mathematics as it is my contention -- as with classical music -- that one can learn to appreciate and enjoy complex formulas without needing to understand them deeply.

A Beautiful Proof By Induction, Lars-Daniel Öhman

Journal of Humanistic Mathematics

The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

Mathematical Proofs: The Beautiful And The Explanatory, Marcus Giaquinto

Journal of Humanistic Mathematics

Mathematicians sometimes judge a mathematical proof to be beautiful and in doing so seem to be making a judgement of the same kind as aesthetic judgements of works of visual art, music or literature. Mathematical proofs are also appraised for explanatoriness: some proofs merely establish their conclusions as true, while others also show why their conclusions are true. This paper will focus on the prima facie plausible assumption that, for mathematical proofs, beauty and explanatoriness tend to go together.

To make headway we need to have some grip on what it is for a proof to be beautiful, and for …

Explanatory Proofs And Beautiful Proofs, Marc Lange

Journal of Humanistic Mathematics

This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples …

The Nature And Experience Of Mathematical Beauty, Manya Raman-Sundström, Lars-Daniel Öhman, Nathalie Sinclair

Journal of Humanistic Mathematics

No abstract provided.

Editorial: Not Just In The Eye Of The Beholder, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Verification Of Emotion Recognition From Facial Expression, Yanjia Sun

Dissertations

Analysis of facial expressions is an active topic of research with many potential applications, since the human face plays a significant role in conveying a person’s mental state. Due to the practical values it brings, scientists and researchers from different fields such as psychology, finance, marketing, and engineering have developed significant interest in this area. Hence, there are more of a need than ever for the intelligent tool to be employed in the emotional Human-Computer Interface (HCI) by analyzing facial expressions as a better alternative to the traditional devices such as the keyboard and mouse.

The face is a window …

Semantics And Result Disambiguation For Keyword Search On Tree Data, Cem Aksoy

Dissertations

Keyword search is a popular technique for searching tree-structured data (e.g., XML, JSON) on the web because it frees the user from learning a complex query language and the structure of the data sources. However, the convenience of keyword search comes with drawbacks. The imprecision of the keyword queries usually results in a very large number of results of which only very few are relevant to the query. Multiple previous approaches have tried to address this problem. Some of them exploit structural and semantic properties of the tree data in order to filter out irrelevant results while others use a …

Generalized Dft: Extensions In Communications, Yuewen Wang

Dissertations

Discrete Fourier Transform (DFT) is a restricted version of Generalized DFT (GDFT) which offers a very limited number of sets to be used in a multicarrier communication system. In contrast, as an extension on Discrete Fourier Transform (DFT) from the linear phase to non-linear phase, the proposed GDFT provides many possible carrier sets of various lengths with comparable or better performance than DFT. The availability of the rich library of orthogonal constant amplitude transforms with good performance allows people to design adaptive systems where user code allocations are made dynamically to exploit the current channel conditions in order to deliver …

Normal-Strength And High-Strength Concrete Columns Under Cyclic Axial Load And Biaxial Moment, Mehdi Zarei

Dissertations

The technique of using Carbon Fiber Reinforced Polymer (CFRP) materials to repair and strengthen various concrete members has become popular in the structural retrofitting field as an effective way to enhance the strength and ductility of concrete members due to its superior mechanical properties. In this study a method was introduced to study the behavior of concrete columns with and without CFRP jackets under constant axial load and variable lateral load. The lateral load was applied monotonically and cyclically. To predict the behavior of concrete columns under monotonic and cyclic compressive loadings, a computer code was developed to produce the …

Terahertz Wireless Communication Through Atmospheric Atmospheric Turbulence And Rain, Jianjun Ma

Dissertations

This dissertation focusses on terahertz (THz) wireless communication technology in different weather conditions. The performance of the communication links is mainly studied under propagation through atmospheric turbulence and rain. However, as real outdoor weather conditions are temporally and spatially varying, it is difficult to obtain reproducible atmospheric conditions to verify results of independent measurements making it a challenge to measure and analyze the impact of outdoor atmospheric weather on communication links. Consequently, dedicated indoor weather chambers are designed to produce controllable weather conditions to emulate the real outdoor weather as closely as possible. To emulate turbulent air conditions, an enclosed …

Task-Based User Profiling For Query Refinement (Toque), Chao Xu

Dissertations

The information needs of search engine users vary in complexity. Some simple needs can be satisfied by using a single query, while complicated ones require a series of queries spanning a period of time. A search task, consisting of a sequence of search queries serving the same information need, can be treated as an atomic unit for modeling user’s search preferences and has been applied in improving the accuracy of search results. However, existing studies on user search tasks mainly focus on applying user’s interests in re-ranking search results. Only few studies have examined the effects of utilizing search tasks …

The University Of San Francisco Fact Book And Almanac 2016, Alan Ziajka

USF Fact Book and Almanac

No abstract provided.

Plasticity Of The Cortical Representation Of Finger Extensors Induced By Paired Associative Stimulation, Ian Anthony Gerard Lafond

Dissertations

This dissertation first explored associative plasticity of the human motor cortical representation with the use of noninvasive transcranial magnetic stimulation (TMS) paired with peripheral electrical stimulation. Paired Associative Stimulation (PAS) has grown in popularity because of its potential clinical applications. PAS techniques are used in combination with electromyography (EMG) measurements to study cortical excitability and features of hand movement. This work focuses on a cohesive approach to answer central questions about: the ideal mechanism to facilitate cortical plasticity via PAS, the interaction between the behavior performed and type of stimulation delivered to the targeted cortical network and the effects of …

Admissions Report - Summary Data - January 2016, Office Of Institutional Research & Effectiveness, Wright State University

Admissions Reports

Summary report of applicants to Wright State including data on ethnicity, region, intended college, transfer, and direct admit from high school for Fall Semester 2016.

Admissions Report - Detailed Data - January 2016, Office Of Institutional Research & Effectiveness, Wright State University

Admissions Reports

Detailed report of applicants to Wright State including data on county of residency, intended major, and ethnicity for Fall Semester 2015.