Mathematics Commons^™

Mathematics In Contemporary Society Chapter 7, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Wright State University Math And Statistics Department History, Joanne Dombrowski, David Miller

Mathematics and Statistics Faculty Publications

No abstract provided.

Modern Crypto-Analysis Of Polyalphabetic Ciphers Using A Genetic Algorithm, Benjamin E. Heald

Student Publications

This project involved implementing a genetic algorithm to help automate the crypto-analysis of the Vigenere cipher.

The Kumaraswamy Marshal-Olkin Family Of Distributions, Morad Alizadeh, M. H. Tahir, Gauss M. Cordeiro, M. Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum …

Students’ Perceptions Of And Responses To Teaching Assistant And Peer Feedback, Kelsey Joy Rodgers, Aladar K. Horvath, Hyunyi Jung, Amanda S. Fry, Heidi A. Diefes-Dux, Monica E. Cardella

Mathematics, Statistics and Computer Science Faculty Research and Publications

Authentic open-ended problems are increasingly appearing in university classrooms at all levels. Formative feedback that leads to learning and improved student work products is a challenge, particularly in large enrollment courses. This is a case study of one first-year engineering student team’s experience with teaching assistant and peer feedback during a series of open-ended mathematical modeling problems called Model-Eliciting Activities. The goal of this study was to gain deep insight into the interactions between students, feedback providers, and written feedback by examining one team’s perceptions of the feedback they received and the changes they made to their solutions based on …

Sequencing Of 15 622 Gene-Bearing Bacs Clarifies The Gene-Dense Regions Of The Barley Genome, María Muñoz-Amatriaín, Stefano Lonardi, Mingcheng Luo, Kavitha Madishetty, Jan T. Svensson, Matthew J. Moscou, Steve Wanamaker, Tao Jiang, Andris Kleinhofs, Gary J. Muehlbauer, Roger P. Wise, Nils Stein, Shane Ma, Edmundo Rodriguez, Dave Kudrna, Prasanna R. Bhat, Shiaoman Chao, Pascal Condamine, Shane Heinen, Josh Resnik, Rod Wing, Heather N. Witt, Matthew Alpert, Marco Beccuti, Serdar Bozdag, Francesca Cordero, Hamid Mirebrahim, Rachid Ounit, Yonghui Wu, Frank You, Jie Zheng, Hana Simková, Jaroslav Dolezel, Jane Grimwood, Jeremy Schmutz, Denisa Duma, Lothar Altschmied, Tom Blake, Phil Bregitzer, Laurel Cooper, Muharrem Dilbirligi, Anders Falk, Leila Feiz, Andreas Graner, Perry Gustafson, Patrick M. Hayes, Peggy Lemaux, Jafar Mammadov, Timothy J. Close

Mathematics, Statistics and Computer Science Faculty Research and Publications

Barley (Hordeum vulgare L.) possesses a large and highly repetitive genome of 5.1 Gb that has hindered the development of a complete sequence. In 2012, the International Barley Sequencing Consortium released a resource integrating whole-genome shotgun sequences with a physical and genetic framework. However, because only 6278 bacterial artificial chromosome (BACs) in the physical map were sequenced, fine structure was limited. To gain access to the gene-containing portion of the barley genome at high resolution, we identified and sequenced 15 622 BACs representing the minimal tiling path of 72 052 physical-mapped gene-bearing BACs. This generated ~1.7 Gb of genomic …

Depression, Obesity, And Metabolic Syndrome: Prevalence And Risks Of Comorbidity In A Population-Based Study Of Mexican Americans, Rene L. Olvera, Douglas E. Williamson, Susan P. Fisher-Hoch, Kristina Vatcheva, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: We examined the prevalence of depression, obesity, and metabolic syndrome and associations between them in a population-based representative cohort of Mexican Americans living on the United States-Mexico border.

Method: The sample in this cross-sectional analysis consisted of 1,768 Mexican American adults (≥ 18 years of age) assessed between the years 2004 and 2010, with whom we tested our central hypothesis of a significant relationship between obesity and depression. Depression was measured using the Center for Epidemiologic Studies-Depression scale (CES-D) with a cutoff score of ≥ 16 for depression and a cutoff score of ≥ 27 for severe depression. We …

Mathematical Simulation Of Direct Glucose Fuel Cell, Jyothsna Jagannath Annepu

All Student Theses and Dissertations

Enzymatic glucose fuel cell and microbial fuel cell are limited by their extremely low power and short durability. Direct Glucose Fuel Cell (DGFC) appears to be a promising alternative power source in low power portable devices and medicinal implants. In this thesis, a one dimensional mathematical model is developed to simulate Direct Glucose Fuel Cell performance. The model accounts simultaneously for mass transport of reactants, products and intermediate species, together with reaction kinetics and ohmic resistance effects in a Direct Glucose Fuel Cell system. It resulted in two sets (for anode and cathode) of first order nonlinear differential equations (derived …

Age-Related Sexual Dimorphism In Temporal Discrimination And In Adult-Onset Dystonia Suggests Gabaergic Mechanisms, John Butler, Ines M. Beiser, Laura Williams, Eavan Mcgovern, Fiona Molloy, Timothy Lynch, Dan G. Healy, Helena Moore, Richard Walsh, Richard B. Reilly, Sean O'Riordan, Cathal Walsh, Michael Hutchinson

Articles

Background: Adult-onset isolated focal dystonia (AOIFD) presenting in early adult life is more frequent in men, whereas in middle age it is female predominant. Temporal discrimination, an endophenotype of adult-onset idiopathic isolated focal dystonia, shows evidence of sexual dimorphism in healthy participants. Objectives: We assessed the distinctive features of age-related sexual dimorphism of (i) sex ratios in dystonia phenotypes and (ii) sexual dimorphism in temporal discrimination in unaffected relatives of cervical dystonia patients. Methods: We performed (i) a meta-regression analysis of the proportion of men in published cohorts of phenotypes of adult-onset dystonia in relation to their mean age of …

Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor

Articles

Congruent audiovisual speech enhances our ability to comprehend a speaker, even in noise-free conditions. When incongruent auditory and visual information is presented concurrently, it can hinder a listener’s perception and even cause him or her to perceive information that was not presented in either modality. Efforts to investigate the neural basis of these effects have often focused on the special case of discrete audiovisual syllables that are spatially and temporally congruent, with less work done on the case of natural, continuous speech. Recent electrophysiological studies have demonstrated that cortical response measures to continuous auditory speech can be easily obtained using …

On String Topology Operations And Algebraic Structures On Hochschild Complexes, Manuel Rivera

Dissertations, Theses, and Capstone Projects

The field of string topology is concerned with the algebraic structure of spaces of paths and loops on a manifold. It was born with Chas and Sullivan's observation of the fact that the intersection product on the homology of a smooth manifold $M$ can be combined with the concatenation product on the homology of the based loop space on $M$ to obtain a new product on the homology of $LM$, the space of free loops on $M$. Since then, a vast family of operations on the homology of $LM$ have been discovered.

In this thesis we focus our attention on …

Equations Over Hyperbolic Groups, Alexander Kai-Chi Taam

Dissertations, Theses, and Capstone Projects

We show that the Diophantine problem, for quadratic equations over a non-elementary torsion-free hyperbolic group, is NP-complete. Furthermore, given a finite system of equations over a torsion-free hyperbolic group $\Gamma$, there is an algorithm which constructs a canonical $Hom$-diagram and a complete set of induced $\Gamma$-NTQ systems, for $\Gamma_{R(S)}$. Finally, the class of $\Gamma$-limit groups is the same as that of iterated generalized doubles over $\Gamma$.

The Moduli Space Of Rational Maps, Lloyd William West

Dissertations, Theses, and Capstone Projects

We construct the moduli space, M_d, of degree d rational maps on ℙ¹ in terms of invariants of binary forms. We apply this construction to give explicit invariants and equations for M₃.

Using this construction, we give a method for solving the following problems: (1) explicitly construct, from a moduli point P ∈ M_d(k), a rational map ∅ with the given moduli; (2) find the field of definition of a rational map ∅. We work out the method in detail for the case d = 3.

Some Bernstein Type Results Of Graphical Self-Shrinkers With High Codimension In Euclidean Space, Hengyu Zhou

Dissertations, Theses, and Capstone Projects

A self-shrinker characterizes the type I singularity of the mean curvature flow. In this thesis we concern about some Bernstein type results of graphical self-shrinkers with high codimension in Euclidean space.

There are two main tools in our work. The first one is structure equations of graphical self-shriners in terms of parallel forms (Theorem 2.3.6). This is motivated by M.T.Wang's work ([Wan02]) on graphical mean curvature flows with arbitrary codimension in product manifolds. The second one is an integration technique (Lemma 2.4.5) based on the fact that every graphical graphical self-shrinker has the polynomial volume growth (Corollary 2.4.4). Because of …

Counting Restricted Integer Partitions, David Dakota Blair

Dissertations, Theses, and Capstone Projects

The first chapter examines $p_b(n)$, the number of partitions of $n$ into powers of $b$, along with a family of identities which can be deduced by iterating a recurrence satisfied by $p_b(n)$ in a suitable way. These identities can then be used to calculate $p_b(n)$ for large values of $n$.

The second chapter restricts these types of partitions even further, limiting the multiplicity of each part. Its object of study is $p_{b,d}(n)$, that is, the number of partitions of $n$ into powers of $b$ repeating each power at most $d$ times. The methods of the first chapter are applied, and …

Algorithmic Properties Of Poly-Z Groups And Secret Sharing Using Non-Commutative Groups, Bren Cavallo

Dissertations, Theses, and Capstone Projects

Computational aspects of polycyclic groups have been used to study cryptography since 2004 when Eick and Kahrobaei proposed polycyclic groups as a platform for conjugacy based cryptographic protocols.

In the first chapter we study the conjugacy problem in polycyclic groups and construct a family of torsion-free polycyclic groups where the uniform conjugacy problem over the entire family is at least as hard as the subset sum problem. We further show that the conjugacy problem in these groups is in NP, implying that the uniform conjugacy problem is NP-complete over these groups. This is joint work with Delaram Kahrobaei. We also …

The Geometry And Combinatorics Of Closed Geodesics On Hyperbolic Surfaces, Chris Arettines

Dissertations, Theses, and Capstone Projects

In this thesis, we obtain combinatorial algorithms that determine the minimal number of self-intersections necessary for a free homotopy class $[\gamma]$ on an orientable surface, using algebraic input. Using this same input, we describe another algorithm which determines whether or not a minimally intersecting curve in $[\gamma]$ is \textit{filling}, that is, whether or not the complement is a disjoint union of disks or punctured disks. Next, we use these algorithms as inspiration for proving the existence of filling curves which self-intersect $2g-1$ times, which is the minimal number of intersections possible. The combinatorial viewpoint that is developed can then be …

Foliations With Geometric Structures: An Approach Through H-Principle., Sauvik Mukherjee Dr.

Doctoral Theses

A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures.The thesis consists of two parts. In the first part we classify foliations on open manifolds whose leaves are either locally conformal symplectic or contact manifolds. These foliations can be described by some higher geometric structures - namely the Poisson and the Jacobi structures. In the second part of the thesis, we consider foliations on open contact manifolds whose leaves are contact submanifolds of the ambient …

Life As An Nfl Statistician, Dennis Lock

Mathematics Colloquium Series

Over the last few years, the fields of statistics and mathematics have become more prevalent and popular in professional sports (with the help of mainstream books and movies like Moneyball). The use of advanced (and non-advanced) statistical methods is growing across the sporting landscape from the front office to the media, and even into business and ticket sales. This talk will discuss Lock’s experiences building an analytics department with the Miami Dolphins as well as the general role of statistics in sports today. It will also including the recent analytics boom in the front office framework, the coinciding need for …

A Nonlinear Filter For Markov Chains And Its Effect On Diffusion Maps, Stefan Steinerberger

Yale Day of Data

Diffusion maps are a modern mathematical tool that helps to find structure in large data sets - we present a new filtering technique that is based on the assumption that errors in the data are intrinsically random to isolate and filter errors and thus boost the efficiency of diffusion maps. Applications include data sets from medicine (the Cleveland Heart Disease Data set and the Wisconsin Breast Cancer Data set) and engineering (the Ionosphere data set).