Mathematics Commons^™

Forecasting Crashes, Credit Card Default, And Imputation Analysis On Missing Values By The Use Of Neural Networks, Jazmin Quezada

Open Access Theses & Dissertations

A neural network is a system of hardware and/or software patterned after the operation of neurons in the human brain. Neural networks,- also called Artificial Neural Networks - are a variety of deep learning technology, which also falls under the umbrella of artificial intelligence, or AI. Recent studies shows that Artificial Neural Network has the highest coefficient of determination (i.e. measure to assess how well a model explains and predicts future outcomes.) in comparison to the K-nearest neighbor classifiers, logistic regression, discriminant analysis, naive Bayesian classifier, and classification trees. In this work, the theoretical description of the neural network methodology …

Predictive Factors Of Student Mathematics Achievement Decline Between Third And Fifth Grade, Jean E. Salters

Walden Dissertations and Doctoral Studies

Low math achievement among elementary school students is a concern because students who lack a strong early foundation in mathematics may experience difficulty learning in future mathematics classes. Students in 2 rural southeastern school districts demonstrated low math achievement in 5th grade and their scores declined from 3rd to 5th grade. In this quantitative study, teacher-related factors that research has shown to predict student achievement were examined using Bandura's theory of self-efficacy and Ball and McDiarmid's emerging theory of subject matter content knowledge. The research question asked whether the teacher factors, years of teaching experience, hours of professional development in …

The Near-Peer Mathematical Mentoring Cycle: Studying The Impact Of Outreach On High School Students’ Attitudes Toward Mathematics, Aaron T. Wilson, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

College students may be seen as near-peers to high school students and high school students are often able to see themselves in the college students who are but one step ahead. This nearness in maturity and educational level may place college students in a particularly powerful position when it comes to reaching out to high school students to promote higher education in math and science. In this study college students gave dynamic mathematics outreach presentations, MathShows, to minority and low-income high school students in a mid-sized public school district on the U.S. border with Mexico. The study investigated the impacts …

Blocks In The Category Of Finite-Dimensional Representations Of Principal W-Algebra For Q(2), Elena Poletaeva

School of Mathematical & Statistical Sciences Faculty Publications

We describe the blocks in the category of finite-dimensional representations of the principal finite W-algebra for the Lie superalgebra Q(2).

An Uncommon Textbook: Review Of Common Sense Mathematics By Ethan Bolker And Maura Mast, Bernard Madison

Numeracy

Ethan D. Bolker and Maura B. Mast. 2016. Common Sense Mathematics.(Washington DC.: Mathematics Association of America) ISBN-13: 978-1-93951-210-9.

Common Sense Mathematics is an integrative quantitative reasoning (QR) textbook that is built around scores of exercises derived from authentic circumstances from public media and other public sources. The exercises elicit responses from students requiring extensive communication and analyses and distinguish the book from ones typically encountered in a mathematics or science course. Responses to exercises often require one-half page or more of writing and can occupy considerable class time in discussion. The book has material for a one- or two-semester …

The Second Decade Of Numeracy: Entering The Seas Of Literacy, H. L. Vacher

Numeracy

This multipurpose editorial explores and tries to count the many types of literacy that are referred to by name in Wikipedia and Numeracy. Wikipedia’s Category:Literacy page identifies 44 kinds of literacy that are the subject of articles, ranging from numeracy and graphicacy to braille literacy and diaspora literacy. In addition, searching Google finds more than 30 adjective-literacy or noun-literacy collocations, including quantitative literacy, adult literacy, and document literacy, that do not have Wikipedia pages of their own but are mentioned on other Wikipedia pages. The sum puts this modest literacy count in line with the more than 70 bodies …

K -Isocoronal Tilings, Eduard C. Taganap, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s k. A tiling T is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of T is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k- transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then …

Positive Subreducts In Finitely Generated Varieties Of Mv-Algebras, Leonardo M. Cabrer, Peter Jipsen, Tomáš Kroupa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Positive MV-algebras are negation-free and implication-free subreducts of MV-algebras. In this contribution we show that a finite axiomatic basis exists for the quasivariety of positive MV-algebras coming from any finitely generated variety of MV-algebras.

Remarks On Suzuki's Epimorphism Number, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

A partial order on prime knots can be defined by declaring ��≥��, if there exists an epimorphism from the knot group of �� onto the knot group of ��. Suppose that �� is a 2-bridge knot that is strictly greater than �� distinct, nontrivial knots. In this paper, we determine a lower bound on the crossing number of �� in terms of ��. Using this bound, we answer a question of Suzuki regarding the 2-bridge epimorphism number EK(��) which is the maximum number of nontrivial knots which are strictly smaller than some 2-bridge knot with crossing number ��. We establish …

Finite N-Quandles Of Torus And Two-Bridge Links, Alissa Crans, Blake Mellor, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

We compute Cayley graphs and automorphism groups for all finite n-quandles of two-bridge and torus knots and links, as well as torus links with an axis.

On The Structure Of Hom Quandles, Alissa Crans

Mathematics, Statistics and Data Science Faculty Works

We continue the study of the quandle of homomorphisms into a medial quandle begun in [2]. We show that it suffices to consider only medial source quandles, and therefore the structure theorem of [11] provides a characterization of the Hom quandle. In the particular case when the target is 2-reductive this characterization takes on a simple form that makes it easy to count and determine the structure of the Hom quandle

Improved Prediction Of Periodicity Using Quartet Approximation In A Lattice Model Of Intracellular Calcium Release, Robert J. Rovetti

Mathematics, Statistics and Data Science Faculty Works

This study uses a probabilistic cellular automata (PCA) to model the spatial and temporal dynamics of calcium release units (CRUs) within cardiac myocytes. The CRUs are subject to random activation, nearest-neighbor recruitment, and temporal refractoriness, and their interactions produce a physiologically-important condition called calcium alternans, a beat-to-beat oscillation in the amount of calcium released. In the PCA this manifests as a transition to period-2 behavior in the fraction of activated lattice sites. We investigate this phenomenon using PCA simulations and moment-closure approximation methods of zero order (mean-field), first order (pair), and second order (quartet). We show that only the quartet …

Kings In The Direct Product Of Digraphs, Morgan Norge

Theses and Dissertations

A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.

Block-Avoiding Sequencings Of Points In Steiner Triple Systems, Donald L. Kreher, Douglas R. Stinson

Michigan Tech Publications, Part 1

Given an STS(v), we ask if there is a permutation of the points of the design such that no l consecutive points in this permutation contain a block of the design. Such a permutation is called an l-good sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v>3 and 4-good sequencings exist for any STS(v) with v>71. Similar re-sults also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v =7, 9, 13 and 15.

Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis

Michigan Tech Publications, Part 1

Certain excess versions of the Minkowski and Hölder inequalities are given.

Proceedings Of Thirteenth Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Front Matter

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 13th Annual GAMTE Proceedings Front Matter:

• Officers of GAMTE
• Reviewers
• Copyright & Licensing Terms
• Purposes and Goals of GAMTE
• Conference Schedule
• Dedication
• Table of Contents

An Alternative Approach To The Traditional Internship, Basil M. Conway, David Erikson, Christopher Parrish, Marilyn Strutchens, Jennifer Whitfield

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

This paper reports the benefits and challenges of incorporating a paired-placement model at four different post-secondary teacher preparation programs in secondary mathematics education. The paired-placement model places two secondary mathematics clinical teachers with one mentor (or cooperating) teacher during their internship experience. Benefits exhibited were increased collaboration, more knowledgeable cooperating teachers, increased sense of community, teaming, pedagogical risk-taking, increased reflective practice, established natural professional learning communities, Plan-Do-Study-Act Cycle (PDSA), and increased accountability. Challenges found through the PDSA cycle include personnel issues, number of days teaching, perceived classroom management preparation, preparing university supervisors, mentors, and teacher candidates, and support for collaboration …

K-2 Mathematicians & Writers: Professional Learning Communities For Developing Conceptual Understanding, Doris Santarone, Angel R. Abney, Sandra M. Webb

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

National Council of Teachers of Mathematics (NCTM) has long supported the use of children’s literature, writing, and manipulatives to improve conceptual understanding of mathematics (2000). In a professional learning community for K-2 teachers, professional development was designed and implemented on ways to incorporate literacy and manipulatives into a mathematics lesson. The teachers were charged with collaboratively planning lessons that included multiple components: the standard(s), a mathematics activity, manipulatives, a writing task, and children’s literature. As the data were analyzed, it became apparent that while most of the lessons were well connected, this did not happen for all of the lessons. …

Creative Writing In The Mathematics Classroom, William Lacefield, Laura Markert

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Creative writing in the mathematics classroom promotes mathematical applications in the real world, constructivist learning, embodied learning, transfer of mathematical ideas, and student engagement. When students are allowed to write about mathematical concepts creatively, they are able to take concepts that they have learned and put them into their world or even create a situation where the mathematical concept applies. Applying mathematical concepts to other environments helps learners transfer mathematical concepts. Learners are able to take the mathematics content and contextualize it outside of the classroom. Writing in mathematics also is a way for students to embody learning. Because writing …

On Burr Iii Marshal Olkin Family: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the …

The Exponentiated Generalized Topp Leone-G Family Of Distributions: Properties And Applications, Hesham Mohammed Reyad, Morad Alizadeh, Farrukh Jamal, Soha Othman, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics, extreme values and characterizations. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of …

Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

We approach student presentations of solutions to modeling tasks as occasions for whole-class reflection on the rich conceptual work that small-group teams have done in parallel. Analyzing and interpreting these interactions can offer insights into how a classroom group negotiates a shared sense of what they have learned and what they collectively view as “newsworthy” across groups from their recent (and ongoing) model-building. We describe analytical tools to interpret a classroom’s work during presentations, and we illustrate their use in a single case. This work offers a foothold for design-based research to harness presentations to improve learning, drive instructional decisions, …

Conceptualizing And Interpreting Mean And Median With Future Teachers, Eryn Stehr Maher, Ha Nguyen, Gregory Chamblee, Sharon Taylor

Mathematical Sciences: Faculty Publications

Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of …

Developing Mathematics Teachers’ Attention To Quantitative Reasoning In Task Design: A Modeling Approach, David Glassmeyer

Numeracy

This study examines how a models-and-modeling perspective affected teachers' attention to quantitative reasoning in task design. A Model-Eliciting Activity (MEA) was implemented with 21 teachers over four weeks, challenging teachers to design a quantitative reasoning task for their students. Teachers’ initial quantitative reasoning tasks did not incorporate quantities or quantitative relationships, two essential components of quantitative reasoning. As teachers revised their tasks through the MEA, most teachers began attending to these components. This article details how a modeling approach to teacher education provided a method to describe and support teachers to incorporate quantitative reasoning in their classroom tasks, though attending …

The Sons Report (1989-1994, Mathematical Association Of America): The Way It Was, Linda R. Sons

Numeracy

Recollections and commentary by Linda R. Sons on a 1994 national report entitled Quantitative Reasoning for College Graduates: A Complement to the Standards. Professor Sons chaired the committee which wrote the report and championed its use.

This paper traces the development of the 1994 MAA report Quantitative Reasoning for College Graduates: A Complement to the Standards--a report which is still surprisingly relevant. The paper highlights some major parts of the report, describing the context in which its conclusions were made. Additionally, it challenges and encourages those continuing the quest for QL in the nation by noting progress made …

Three Formative Questions In The Quantitative Literacy Movement, Dorothy Wallace

Numeracy

In this essay we remember early discussions attempting to answer three questions that played a formative role in our understanding of and approach to numeracy, quantitative literacy, and quantitative reasoning: (1) What is numeracy? (2) Should the QL movement promote any specific kind of pedagogy? (3) What organizational structure will best support QL?

As the QL movement has progressed, these three questions continue to be difficult to answer. As a result, they have been useful formative guides for institutions and organizations seeking to improve the quantitative reasoning of students. Now that the quantitative literacy movement has a firmer standing in …

Finite Integration Method With Chebyshev Expansion For Finding Numerical Solution Of Nonlinear And Fractional Order Differential Equations, Ampol Duangpan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we develop the finite integration method by using Chebyshev polynomial expansion (FIM-CPE) for solving one- and two-dimensional nonlinear differential equations. The developed FIM-CPE can be used on any domains. Then, we utilize our FIM-CPE to deal with the spatial variable and the forward difference quotient to handle the derivative involving temporal variable. Thus, the numerical algorithms based on this idea are devised to overcome three nonlinear problems including one-dimensional Burgers' equation with shock wave, time-fractional Benjamin-Bona-Mahony-Burgers' equation and two-dimensional nonlinear Poisson equation over irregular domains. Moreover, we examine our algorithms with several experimental examples by comparing the …

Automatic Model Identification For Time Series Analysis Using Deep Learning, Paisit Khanarsa

Chulalongkorn University Theses and Dissertations (Chula ETD)

Most time series data can be characterized by a linear process via the autoregressive integrated moving average model requiring a three-component vector which are the autoregressive, differencing, and moving average orders before fitting coefficients. A model identification which determines those orders is analyzed via the partial autocorrelation function to identify the autoregressive order, the autocorrelation function to identify the moving average order and an extended sample autocorrelation function to identify both orders which is a challenging problem for statisticians. Accordingly, the auto-ARIMA model was proposed to automatically vary those orders and estimates their corresponding coefficients. This thesis proposes three architectures …

Stochastic Differential Equation With Jumps For Tilapia Population, Kanitin Sukchum

Chulalongkorn University Theses and Dissertations (Chula ETD)

Tilapia population with harvesting in the tilapia farm can be modeled by an ordinary differential equation (ODE). In real life, tilapia population can be affected by many factors. To make the model for tilapia population more realistic, we develop the ODE into the stochastic differential equation (SDE) together with jumps that represent the epidemic occuring for tilapia. Furthermore, we study the effect of some important parameters in the model to the number of tilapia in the tilapia farm via simulation. Both SDEs for tilapia population with and without jumps are simulated by using Euler-Maruyama and jump-adapted Euler methods.

Graph Representation For Room Layout Matching Using Spectral Embedding, Thamonwan Sa-Ngawong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Graph matching is efficient to search similar layout when the architectural floor plan data size is increasing. Because the computational time of floor plan matching using spectral embedding is only in seconds, so it is one of the popular methods. However, the isomorphism of each floor plan leads to low accuracy in the matching process and it becomes the weakness of this method. Therefore, we propose a graph representation for room layout matching using spectral embedding. Normally, graph representations of the floor plan define nodes as rooms and edges as connections between rooms. Besides, the graph spectral embedding is to …