Mathematics Commons^™

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.

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 …

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 …

Decidability For Residuated Lattices And Substructural Logics, Gavin St. John

Electronic Theses and Dissertations

We present a number of results related to the decidability and undecidability of various varieties of residuated lattices and their corresponding substructural logics. The context of this analysis is the extension of residuated lattices by various simple equations, dually, the extension of substructural logics by simple structural rules, with the aim of classifying simple equations by the decidability properties shared by their extensions. We also prove a number of relationships among simple extensions by showing the equational theory of their idempotent semiring reducts coincides with simple extensions of idempotent semirings. On the decidability front, we develop both semantical and syntactical …

Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan

Electronic Theses and Dissertations

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …

Teachers' Perceptions About Instructing Underachieving K-5 Students On Mathematical Word Problem-Solving, Crystal Yvette Baldwindouglas

Walden Dissertations and Doctoral Studies

The state of Maryland has implemented the Common Core State Standards for Mathematics (CCSSM) operations & algebraic thinking and number & operations-fractions with emphasis on students in Grades K-5 acquiring the ability to solve word problems for state and curriculum math assessments. However, since the implementation of CCSSM, 30% of elementary students in a Maryland school district have demonstrated underachievement (basic or below basic level) on problem-solving sections of the state and school standardized tests. This qualitative case study, guided by Polya's model of the four phases of mathematical problem-solving, was conducted to address this problem. The research questions addressed …

A First-Year Teacher’S Implementation Of Short-Cycle Formative Assessment Through The Use Of A Classroom Response System And Flexible Grouping, Adrienne Irving Dumas

Electronic Theses and Dissertations

As teachers we are tasked with ensuring that our students are equipped with the skills necessary to not only perform with proficiency on local state and national assessments but also to provide our students with opportunities to develop confidence and competence as learners of mathematics through meaningful challenging and worthwhile activities. As such many teachers have turned to technology and cooperative groups as staples in the classroom. The purpose of this study was to understand how one first-year teacher implemented what she was taught in her undergraduate coursework in teaching two specific units of instruction in two sections of high …

Beta Invariant And Variations Of Chain Theorems For Matroids, Sooyeon Lee

Electronic Theses and Dissertations

The beta invariant of a matroid was introduced by Crapo in 1967. We first find the lower bound of the beta invariant of 3-connected matroids with rank r and the matroids which attain the lower bound. Second we characterize the matroids with beta invariant 5 and 6. For binary matroids we characterize matroids with beta invariant 7. These results extend earlier work of Oxley. Lastly we partially answer an open question of chromatic uniqueness of wheels and prove a splitting formula for the beta invariant of generalized parallel connection of two matroids. Tutte's Wheel-and-Whirl theorem and Seymour's Splitter theorem give …