Mathematics Commons^™

An Event- And Network-Level Analysis Of College Students’ Maximum Drinking Day, Matthew K. Meisel, Angelo M. Dibello, Sara G. Balestrieri, Miles Q. Ott, Graham T. Diguiseppi, Melissa A. Clark, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

Background—Heavy episodic drinking is common among college students and remains a serious public health issue. Previous event-level research among college students has examined behaviors and individual-level characteristics that drive consumption and related consequences but often ignores the social network of people with whom these heavy drinking episodes occur. The main aim of the current study was to investigate the network of social connections between drinkers on their heaviest drinking occasions.

Methods—Sociocentric network methods were used to collect information from individuals in the first-year class (N=1342) at one university. Past-month drinkers (N=972) reported on the characteristics of their heaviest drinking occasion …

Calculus I (Fvsu), Samuel Cartwright, Bhavana Burell, Patcharin Marion, Jianmin Zhu

Mathematics Grants Collections

This Grants Collection for Calculus I was created under a Round Six ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Differential Equations (Ung), Hashim Saber, Beata Hebda, Piotr Hebda, Benkam Bobga

Mathematics Grants Collections

This Grants Collection for Differential Equations was created under a Round Seven ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Dalton State College Apex Calculus, Thomas Gonzalez, Michael Hilgemann, Jason Schmurr

Mathematics Open Textbooks

This text for Analytic Geometry and Calculus I, II, and III is a Dalton State College remix of APEX Calculus 3.0. The text was created through a Round Six ALG Textbook Transformation Grant.

Topics covered in this text include:

• Limits
• Derivatives
• Integration
• Antidifferentiation
• Sequences
• Vectors

Files can also be downloaded on the Dalton State College GitHub:

https://github.com/DaltonStateCollege/calculus-text/blob/master/Calculus.pdf

Accessible files with optical character recognition (OCR) and auto-tagging provided by the Center for Inclusive Design and Innovation.

Calculus I (Ga Southern), Scott Kersey, Stephen Carden

Mathematics Grants Collections

This Grants Collection for Calculus I was created under a Round Eight ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Calculus Iii (Ung), Hashim Saber, Beata Hebda, Piotr Hebda, Benkam Bobga

Mathematics Grants Collections

This Grants Collection for Calculus III was created under a Round Seven ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Direct Error Driven Learning For Deep Neural Networks With Applications To Bigdata, R. Krishnan, Jagannathan Sarangapani, V. A. Samaranayake

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, generalization error for traditional learning regimes-based classification is demonstrated to increase in the presence of bigdata challenges such as noise and heterogeneity. To reduce this error while mitigating vanishing gradients, a deep neural network (NN)-based framework with a direct error-driven learning scheme is proposed. To reduce the impact of heterogeneity, an overall cost comprised of the learning error and approximate generalization error is defined where two NNs are utilized to estimate the costs respectively. To mitigate the issue of vanishing gradients, a direct error-driven learning regime is proposed where the error is directly utilized for learning. It …

Dynamics For A Random Differential Equation: Invariant Manifolds, Foliations, And Smooth Conjugacy Between Center Manifolds, Junyilang Zhao

Theses and Dissertations

In this dissertation, we first prove that for a random differential equation with the multiplicative driving noise constructed from a Q-Wiener process and the Wiener shift, which is an approximation to a stochastic evolution equation, there exists a unique solution that generates a local dynamical system. There also exist a local center, unstable, stable, centerunstable, center-stable manifold, and a local stable foliation, an unstable foliation on the center-unstable manifold, and a stable foliation on the center-stable manifold, the smoothness of which depend on the vector fields of the equation. In the second half of the dissertation, we show that any …

A New Family Of Topological Invariants, Nicholas Guy Larsen

Theses and Dissertations

We define an extension of the nth homotopy group which can distinguish a larger class of spaces. (E.g., a converging sequence of disjoint circles and the disjoint union of countably many circles, which have isomorphic fundamental groups, regardless of choice of basepoint.) We do this by introducing a generalization of homotopies, called component-homotopies, and defining the nth extended homotopy group to be the set of component-homotopy classes of maps from compact subsets of (0,1)ⁿ into a space, with a concatenation operation. We also introduce a method of tree-adjoinment for "connecting" disconnected metric spaces and show how this method can …

Subtraction Games: Range And Strict Periodicity, Bryce Emerson Blackham

Theses and Dissertations

In this paper I introduce some background for subtraction games and explore the Sprague-Grundy functions defined on them. I exhibit some subtraction games where the functions are guaranteed to be strictly periodic. I also exhibit a class of subtraction games which have bounded range, and show there are uncountably many of these.

Number Theory: Niven Numbers, Factorial Triangle, And Erdos' Conjecture, Sarah Riccio

Mathematics Undergraduate Publications

In this paper, three topics in number theory will be explored: Niven Numbers, the Factorial Triangle, and Erdos's Conjecture . For each of these topics, the goal is for us to find patterns within the numbers which help us determine all possible values in each category. We will look at two digit Niven Numbers and the set that they belong to, the alternating summation of the rows of the Factorial Triangle, and the unit fractions whose sum is the basis of Erdos' Conjecture.

Understanding Natural Keyboard Typing Using Convolutional Neural Networks On Mobile Sensor Data, Travis Siems

Computer Science and Engineering Theses and Dissertations

Mobile phones and other devices with embedded sensors are becoming increasingly ubiquitous. Audio and motion sensor data may be able to detect information that we did not think possible. Some researchers have created models that can predict computer keyboard typing from a nearby mobile device; however, certain limitations to their experiment setup and methods compelled us to be skeptical of the models’ realistic prediction capability. We investigate the possibility of understanding natural keyboard typing from mobile phones by performing a well-designed data collection experiment that encourages natural typing and interactions. This data collection helps capture realistic vulnerabilities of the security …

Probabilistic Modeling Of Student Interactions During A Passing Period At The University Of Dayton, Allyson Pacifico

Honors Theses

The University of Dayton is composed of five colleges and schools: College of Arts and Sciences, School of Law, School of Business Administration, School of Education and Health Sciences, and School of Engineering. The University of Dayton is composed of about 11,000 students on campus who all have distinct class schedules and paths they take between their classes. In this study, I wanted to know the probability of meeting my friends with a different class schedule as I walk between classes. The data consisted of one to two students from each college, except for the School of Law, who documented …

A Computational Method For Solving A Class Of Fractional-Order Non-Linear Singularly Perturbed Volterra Integro-Differential Boundary-Value Problems, Mohammed M. A. Abuomar

Mathematical Sciences Theses

In this thesis, we present a computational method for solving a class of fractional singularly perturbed Volterra integro-differential boundary-value problems with a boundary layer at one end. The implemented technique consists of solving two problems which are a reduced problem and a boundary layer correction problem. The reproducing kernel method is used to the second problem. Pade’ approximation technique is used to satisfy the conditions at infinity. Existence and uniformly convergence for the approximate solution are also investigated. Numerical results provided to show the efficiency of the proposed method.

Mathematics In Contemporary Society - Chapter 1 (Spring 2018), 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.

Mathematics In Contemporary Society - Chapter 2 (Spring 2018), 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.

Crystallographic Patterns In Philippine Indigenous Textiles, Ma. Louise Antonette N. De Las Peñas, Agnes Garciano, Debbie Marie Verzosa, Eduard C. Taganap

Mathematics Faculty Publications

The aim of this study was to analyze a representative sample of Philippine indigenous textiles in order to capture the range of symmetries and color symmetries present. This paper examines the existence of symmetries in finite designs, and classifies the plane-group and frieze-group symmetry types of the repeated patterns in woven textiles. The tendency of a particular symmetry to be more or less common than another can indicate relationships between the symmetries and the weaving technique or the culture that produced them. This paper will also examine designs and patterns with color symmetry found in these textiles. The sample consisted …

Optimal Quantizers For Some Absolutely Continuous Probability Measures, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of n-means and the nth quantization errors are calculated for some positive integers n.

Symplectic Structures On The Integration Of Exact Courant Algebroids, Rajan Amit Mehta, Xiang Tang

Mathematics Sciences: Faculty Publications

We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a “Lagrangian” sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn-Crainic-Weinstein-Zhu that every integrable Dirac structure integrates to a presymplectic groupoid.

A Mathematical Analysis Of The Game Of Chess, John C. White

Selected Honors Theses

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first …

Webwork Problems For Openstax Introductory Statistics, Scott Kersey, Stephen Carden

Mathematics Ancillary Materials

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Introductory Statistics. They were created through a Round Eight Textbook Transformation Grant.

Webwork Problems For Openstax Calculus Volume I, Scott Kersey, Stephen Carden

Mathematics Ancillary Materials

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Calculus Volume I. They were created through a Round Eight Textbook Transformation Grant.

A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, a multi-step dimension-reduction approach is proposed for addressing nonlinear relationships within attributes. In this work, the attributes in the data are first organized into groups. In each group, the dimensions are reduced via a parametric mapping that takes into account nonlinear relationships. Mapping parameters are estimated using a low rank singular value decomposition (SVD) of distance covariance. Subsequently, the attributes are reorganized into groups based on the magnitude of their respective singular values. The group-wise organization and the subsequent reduction process is performed for multiple steps until a singular value-based user-defined criterion is satisfied. Simulation analysis is …

The Impact Of Khan Academy Math Remediation On Ninth Grade Student Achievement, Sandra Kelly

Doctoral Dissertations and Projects

The purpose of this quasi-experimental study was to determine if using Khan Academy as math remediation for fifteen minutes per day during a ninth grade Math I class would significantly affect student math achievement as measured by the North Carolina READY Math I End-of-Course Assessment. This quantitative study conducted at two rural high schools in West Virginia used remediation theory to make a comparison against a control population with the independent variable being grade level instruction only or grade level instruction plus math remediation using Khan Academy. The participants in the study included 131 ninth grade high school students taking …

Some Studies On Algebraic Integers In Q(I,√3) By Using Coset Diagram, Florentin Smarandache, Saima Anis, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we studied the action of Picard modular group PSL(2,Z[i])

Remark On Vacuum Fluctuation As The Cause Of Universe Creation: Or How Neutrosophic Logic And Material Point Method May Resolve Dispute On The Origin Of The Universe Through Re-Reading Gen. 1:1-2, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

Questions regarding the formation of the Universe and what was there before the existence of Early Universe have been great interest to mankind of all times. In recent decades, the Big Bang as described by the Lambda CDMStandard Model Cosmology has become widely accepted by majority of physics and cosmology communities. Among other things, we can cite A.A. Grib Pavlov who pointed out some problems of heavy particles creation out of vacuum and also other proposal of Creatio ex nihilo theory (CET). But the philosophical problems remain, as Vaas pointed out: Did the universe have a beginning or does it …

Strong Degrees In Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Seema Mehra, Mohamed Talea, Manjeet Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of single valued neutrosophic graphs (SVNGs) generalizes the concept of fuzzy graphs and intuitionistic fuzzy graphs. The purpose of this research paper is to define different types of strong degrees in SVNGs and introduce novel concepts, such as the vertex truth-membership, vertex indeterminacy-membership and falsity-membership sequence in SVNG with proof and numerical illustrations.

Algorithms For Numerical Implementation Of The Shooting Method Of The Boundary Solution Problems For Ordinary Second-Order Differential Equations, A. Otarov Professor, Kh. Umarova, S. Karabekov

Karakalpak Scientific Journal

In the article algorithms of numerical realization of a shooting method decisions of marginal problems for nonlinear ordinary differential equations of the second order are under construction.

On Lattices Of Z-Ideals Of Function Rings, Themba Dube, Oghenetega Ighedo

Mathematics, Physics, and Computer Science Faculty Articles and Research

An ideal I of a ring A is a z-ideal if whenever a, b ∈ A belong to the same maximal ideals of A and a ∈ I, then b ∈ I as well. On the other hand, an ideal J of A is a d-ideal if Ann²(a) ⊆ J for every a ∈ J. It is known that the lattices Z(L) and D(L) of the ring 𝓡L of continuous real-valued functions on a frame L, consisting of z-ideals and d-ideals of 𝓡 …

Rook Placements And Jordan Forms Of Upper-Triangular Nilpotent Matrices, Martha Yip

Mathematics Faculty Publications

The set of n by n upper-triangular nilpotent matrices with entries in a finite field 𝔽_q has Jordan canonical forms indexed by partitions λ ⊢ n. We present a combinatorial formula for computing the number F_λ(q) of matrices of Jordan type λ as a weighted sum over standard Young tableaux. We construct a bijection between paths in a modified version of Young's lattice and non-attacking rook placements, which leads to a refinement of the formula for F_λ(q).