Physical Sciences and Mathematics Commons^™

Student Perceptions Of Learning Introductory Mathematics In An Online Environment In Higher Education, Jamie Lynn Brooks

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study was to describe the essence of student perception of learning introductory mathematics courses in an online environment at the college level. The central research question was, “What are the lived experiences of students who have completed introductory college mathematics courses in the online learning environment?” The phenomenon described was that of the beliefs and attitudes of the students who participated in introductory mathematics courses on the college level. The ideas explored were if students believe they learn effectively in this environment and how they believe they can best learn. Student beliefs and attitudes …

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Mathematical Modeling (Fvsu), Samuel Cartwright, Bhavana Burell

Mathematics Grants Collections

This Grants Collection for Mathematical Modeling was created under a Round Thirteen 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.

Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Book Review: The Seduction Of Curves By Allan Mcrobie, Hans J. Rindisbacher

Journal of Humanistic Mathematics

This review emphasizes, as does the compelling and beautiful book, The Seduction of Curves by Allan McRobie, the “lines of beauty” that link art and mathematics. McRobie and his collaborator on the indispensable visuals of the volume, Helena Weightman, succeed admirably in connecting theoretically and visually the mathematical field of singularity or catastrophe theory and its graphical representations on the one hand and the seemingly intersecting lines around the volumes of the human body in the artistic representation of the nude. This book thus constitutes a creative and illuminating overlap of mathematics and art that lets the practitioners on both …

Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge

Journal of Humanistic Mathematics

Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.

Mathematics Versus Statistics, Mindy B. Capaldi

Journal of Humanistic Mathematics

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.

On Free-Type Rigid C*-Tensor Categories And Their Annular Representations., B. Madhav Reddy Dr.

Doctoral Theses

No abstract provided.

Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix

Masters Theses & Specialist Projects

This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set.

The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies …

Algebraic Topics In The Classroom – Gauss And Beyond, Lisa Krance

Masters Essays

No abstract provided.

Introduction Of Infinite Series In High School Level Calculus, Ericka Bella

Masters Essays

No abstract provided.

The Current State Of High School Female And Minority Self-Efficacy And Interest In Stem In Chatham County, Georgia, Sara Gremillion, Sarah Zingales, William Baird, Nia Hunter, Amy Durden, Sabrina Hessinger

Georgia Educational Researcher

With the growing demand for science, technology, engineering, and mathematics (STEM) jobs in the U.S., the attainment of college degrees in these areas is of paramount importance. Both federal and state governments have established initiatives to grow the number of STEM degrees earned by women and racial minorities, as these groups graduate in STEM disciplines and work in STEM fields at a lower rate than that of their majority counterparts. The factors that can deter women and underrepresented minorities from pursuing STEM careers have been identified with one of the most prominent being low self-efficacy, or a reduced belief in …

Data Mining And Machine Learning To Improve Northern Florida’S Foster Care System, Daniel Oldham, Nathan Foster, Mihhail Berezovski

Beyond: Undergraduate Research Journal

The purpose of this research project is to use statistical analysis, data mining, and machine learning techniques to determine identifiable factors in child welfare service records that could lead to a child entering the foster care system multiple times. This would allow us the capability of accurately predicting a case’s outcome based on these factors. We were provided with eight years of data in the form of multiple spreadsheets from Partnership for Strong Families (PSF), a child welfare services organization based in Gainesville, Florida, who is contracted by the Florida Department for Children and Families (DCF). This data contained a …

Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, Ty Stockham

Electronic Theses, Projects, and Dissertations

This study investigates the effects of implementing a remediation program in a high school Advanced Placement Calculus AB course on student class grades and success in passing the AP Calculus AB exam.

A voluntary remediation program was designed to help students understand the key concepts and big ideas in beginning Calculus. Over a period of eight years the program was put into practice and data on student participation and achievement was collected. Students who participated in this program were given individualized recitation activities targeting their specific misunderstandings, and then given an opportunity to retest on chapter exams that they had …

Theory Of Linear Models For Estimating Regression Parameters With Applications To Two-Factor Studies With Unequal Sample Sizes, Zenan Sun

Honors Program Theses and Projects

In this thesis we explored some topics in regression analysis. In particular, we studied what linear regression is from a matrix theory perspective, and applied analysis of variance in a setting with two factors and unbalanced sample sizes. In addition, we applied Box-Cox variable transformation as a solution when the regression model violated the normality and equal variance (also called homoscedasticity) assumption. Our main goal is to use these theories to construct models and investigate questions related to lifetime earnings of people living in America by using real data. In doing so, we used the statistical software R to perform …

Finite Field Dynamics: Exploring Isomorphic Graphs And Cycles Of Length P, Catlain Mccarthy

Honors Program Theses and Projects

For this project, we explore nite eld dynamics and the various patterns of cycles of elements that emerge from the manipulation of a function and eld. Given a function f : Fp ��! Fp, we can create a directed graph with an edge from c to f(c) for all c 2 Fp. We especially consider polynomials of the form f(x) = xd + c and investigate how varying the values of d and c affect the cycles in a given nite eld, Fp. We analyze data to look for graphs that result in cycles of length p. We also identify …

Bounding The Rates Of Convergence Towards The Extreme Value Distributions, James Palmer

Honors Program Theses and Projects

Extreme value theory is a branch of probability which examines the extreme outliers of probability distributions. Three extreme value distributions arise as the limits of the maxima of sequences of random variables with certain properties. In this paper, we will first give information about these three distributions and prove that they are the only limit distributions of maxima. After that, we switch to a discussion about Stein's method. Stein's method is commonly used to prove central limit theorems. Stein's method also develops bounds on the distance between probability distributions with regards to a probability metric. There are three essential steps …

Modified Ramsey Numbers, Meaghan Mahoney

Honors Program Theses and Projects

Ramsey theory is a eld of study named after the mathematician Frank P. Ramsey. In general, problems in Ramsey theory look for structure amid a collection of unstructured objects and are often solved using techniques of Graph Theory. For a typical question in Ramsey theory, we use two colors, say red and blue, to color the edges of a complete graph, and then look for either a complete subgraph of order n whose edges are all red or a complete subgraph of order m whose edges are all blue. The minimum number of vertices needed to guarantee one of these …

Firefighter Problem Played On Infinite Graphs, Sarah Days-Merrill

Honors Program Theses and Projects

The Firefighter Problem was introduced over 30 years ago and continues to be studied by researchers today. The problem consists of a graph of interest where a fire breaks out at time t = 0 on any given vertex of thegraph G. The player, then, gets to place a firefighter to “protect” a vertex from the fire. Each consecutive turn,the fire spreads to adjacent vertices. These vertices are then referred to as “burned”. The firefighter also gets tomove to protect an additional, unburned vertex, completing the first round. Each vertex that the firefighter “defends” stays protected for the remainder …

Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Nadia Kennedy, Armando Cosme

Publications and Research

As students we often wonder why some subjects are easy to understand and requires not much effort in terms of re-reading the material, for us to grasp what it entails. One subject seems to remain elusive and uneasy for a vast majority of learners at all levels of education; that subject is Mathematics, it is one subject that most learners finds difficult even after doubling the amount of time spent on studying the material. My intention is to explore ways to make Mathematics easier for other students using feedback from students enrolled in NSF mathematics peer leading workshops, and use …

Orbit Spaces Of Unimodular Rows Over Smooth Real Affine Algebras., Soumi Tikader Dr.

Doctoral Theses

Let R be a commutative, Noetherian ring of (Krull) dimension d. It is well known that the set of isomorphism classes of (oriented, if d is even) stably free R-modules of rank d carries the structure of an abelian group. This group can be identified with the orbit space of unimodular rows namely, Umd+1(R)/SLd+1(R). The prime objective of this thesis is to provide the complete computation of this group, when X = Spec(R) be a smooth real affine variety of dimension d ≥ 2 (with the assumption that the set of real points of X is non-empty and orientable). In …

Using Neural Networks To Classify Pdes, Julia Balukonis, Sabrina Fuller, Haley Rosso

Mathematics & Computer Science Student Scholarship

Major: Mathematics
Minor: Computer Science and Film

Faculty Mentor: Dr. Lynette Boos, Mathematics and Computer Science

We designed two neural networks that can learn how to classify three different types of partial differential equations (PDEs). Our data consists of numerical solutions to three categories of PDEs: Burger’s, Diffusion, and Transport equations. Using TensorFlow and the Keras library, we performed two tasks – the first a binary classification of Burger’s and Diffusion equation data, and the second a multi-label classification incorporating the Transport Equations as well. Our binary classification network requires vector labels to perform efficiently. Furthermore, our tertiary classification network …

Mathematical Analysis Of The Duck Migration To Louisiana, Brandon Garcia

Mathematics Senior Capstone Papers

The purpose of this project is to research the relationship between duck migration and weather patterns, more specifically trying to determine if the rainfall and temperature in a given year affects the migration patterns of ducks. Duck hunters and conservation- ists alike have observed an overall decrease in the duck population in Louisiana over the past 70 years. Though some years have seen an increase, the population has not recovered to the level from the 1950s. These observations have led to many questions about what have happened to the ducks or where have the ducks gone. Using differ- ent forms …

Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg

Computer Science: Faculty Publications and Other Works

This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics.

From Big Science To “Deep Science”, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The Standard Model of particle physics has accomplished a great deal including the discovery of Higgs boson in 2012. However, since the supersymmetric extension of the Standard Model has not been successful so far, some physicists are asking what alternative deeper theory could be beyond the Standard Model? This article discusses the relationship between mathematics and physical reality and explores the ways to go from Big Science to “Deep Science”.

Infinite Mode Quantum Gaussian States., Tiju Cherian John Dr.

Doctoral Theses

No abstract provided.

Estimating The Density Of The Abundant Numbers, Dominic Klyve, Melissa Pidde, Kathryn E. Temple

Mathematics Faculty Scholarship

Mathematicians have been interested in properties of abundant numbers – those which are smaller than the sum of their proper factors – for over 2,000 years. During the last century, one line of research has focused in particular on determining the density of abundant numbers in the integers. Current estimates have brought the upper and lower bounds on this density to within about 10−4, with a value of K ≈ 0.2476, but more precise values seem difficult to obtain. In this paper, we employ computational data and tools from inferential statistics to get more insight into this value. We also …

Sandor Szathmari's Kazohinia: Mathematics And The Platonic Idea, Susan J. Siggelakis

Journal of Humanistic Mathematics

In this article I analyse Sándor Szathmári’s utopian, satiric novel, The Voyage to Kazohinia, as an exercise in the portrayal of Platonist ideas. Through a discussion specifically of Szathmári’s portrayal of the way mathematics is conceived in two different, imaginary societies, I aim to reveal his preoccupation with exploring a solution to the essential political and moral problem of the alienation of interests between the individual and the group. This analysis locates Szathmari’s ideas within the Platonic tradition as well as within the context of 20^th century philosophical ideas, particularly those of Georg Lukács. Szathmári’s portrayal of two …

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_V on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and …

Efficient Numerical Methods For Chemotaxis And Plasma Modulation Instability Studies, Truong B. Nguyen

Browse all Theses and Dissertations

In this thesis, we develop efficient numerical solvers for nonlinear systems of partial differential equations (PDEs). These systems of PDEs concern two different sets of physical problems. The first set includes chemotaxis models such as Keller-Segel models and cancer cell invasion models. Solutions of these models are observed to experience the blow-up phenomenon or the development of sharp and spiky features. Therefore, efficient and accurate numerical techniques must be employed in order to capture the solutions' behaviors. For this research, we design efficient solvers for these systems in the one and two spatial dimensions. In particular, we plan to apply …

Applications Of Geometric And Spectral Methods In Graph Theory, Lauren Morey Nelsen

Electronic Theses and Dissertations

Networks, or graphs, are useful for studying many things in today’s world. Graphs can be used to represent connections on social media, transportation networks, or even the internet. Because of this, it’s helpful to study graphs and learn what we can say about the structure of a given graph or what properties it might have. This dissertation focuses on the use of the probabilistic method and spectral graph theory to understand the geometric structure of graphs and find structures in graphs. We will also discuss graph curvature and how curvature lower bounds can be used to give us information about …