Physical Sciences and Mathematics Commons^™

Tactivities: Fostering Creativity Through Tactile Learning Activities, Angie Hodge-Zickerman, Eric Stade, Cindy S. York, Janice Rech

Journal of Humanistic Mathematics

As mathematics teachers, we hope our students will approach problems with a spirit of creativity. One way to both model and encourage this spirit – and, at the same time, to keep ourselves from getting bored – is through creative approaches to problem design. In this paper, we discuss ``TACTivities'' – mathematical activities with a tactile component – as a creative outlet for those of us who teach mathematics, and as a resource for stimulating creative thinking in our students. We use examples, such as our ``derivative fridge magnets'' TACTivity, to illustrate the main ideas. We emphasize that TACTivities can …

Virtual Temari: Artistically Inspired Mathematics, Carl Giuffre, Lee Stemkoski

Journal of Humanistic Mathematics

Technology can be a significant aide in understanding and appreciating geometry, beyond theoretical considerations. Both fiber art and technology have been employed as a significant aide and an inspiring vessel in education to explore geometry. The Japanese craft known as temari, or "hand-balls", combines important artistic, spiritual, and familial values, and provides one such approach to exploring geometry. Mathematically, the artwork of temari may be classified based on whether they are inspired by polyhedra and discrete patterns or by periodic functional curves. The resulting designs of these categories provide an ancient vantage for displaying spherical patterns. We illustrate a …

Mathematical Modeling: Instructor And Student Resources, Marnie Phipps, Patty Wagner

Mathematics Ancillary Materials

This collection of student and instructor materials for Mathematical Modeling contains lesson plans, lecture slides, homework, learning goals, and student notes for the following major topics:

• Linear Functions
• Quadratic Functions
• Exponential Functions
• Logarithmic Functions

This is a materials update for a collection of materials created for a Round Nine ALG Textbook Transformation Grant.

College Algebra Notes And Exercises (Gcsu), Rabia Shahbaz, Janice Alves

Mathematics Ancillary Materials

Developed as part of a Round 13 Mini-Grant, these updated supplementary materials for Stitz-Zeager Open Source Mathematics and the LibGuides Open Course for College Algebra at GCSU include notes and exercises on equations, inequalities, functions, polynomial and rational functions, and exponential and logarithmic functions are included in one .zip file.

Studies On Polynomial Rings Through Locally Nilpotient Derivations., Nikhilesh Dasgupta Dr.

Doctoral Theses

No abstract provided.

The Perceptions And Experiences Of Math Anxiety, Bradley Baas

Education | Master's Theses

Math anxiety has the potential to negatively impact a student’s knowledge and awareness of themselves. This anxiety leaves students with feelings of incapability in learning math because of their existing beliefs they received in their early years in their educations. The purpose of this research was to better understand the development of middle school eighth grade students and their teachers’ math anxiety while also exploring the obstacles that anxiety creates preventing and/or inhibiting teachers from teaching the required standardized lessons. My research shows that without a trusting relationship between the teacher and student, students experience a decline in mathematics performance …

The Mathematics Behind Illusion, Kouassi Adou

All Zyzzogeton Presentations

Historically, research on optical, or visual illusions has belonged mainly to the field of psychology. However, in the 1980s, Professor Kokichi Sugihara, Meiji University, Japan, introduced a mathematical approach to design and classify 3-dimensional optical illusions. This presentation provides a sample of the mathematics behind some types of visual illusions.

Beginning Algebra Made Useful, Charlene E. Beckmann

Open Textbooks

Beginning Algebra Made Useful addresses the needs of learners to make sense of algebra by quantifying and generalizing everyday occurrences such as commuting to work, buying gas or pizza, and determining the better deal. It requires learners to actively engage with algebraic concepts through physical and thought experiments in ways that help them connect ideas, representations, and contexts, and solve problems that arise in their daily lives. The text helps learners grow their brains and develop growth mindsets as they learn algebra conceptually. Problem sets continue the process, extending work begun in each lesson, applying new understandings to new contexts, …

An Evolutionary Approach To Crowdsourcing Mathematics Education, Spencer Ward

Honors College

By combining ideas from evolutionary biology, epistemology, and philosophy of mind, this thesis attempts to derive a new kind of crowdsourcing that could better leverage people’s collective creativity. Following a theory of knowledge presented by David Deutsch, it is argued that knowledge develops through evolutionary competition that organically emerges from a creative dialogue of trial and error. It is also argued that this model of knowledge satisfies the properties of Douglas Hofstadter’s strange loops, implying that self-reflection is a core feature of knowledge evolution. This mix of theories then is used to analyze several existing strategies of crowdsourcing and knowledge …

Video Case Materials And The Development Of Collective Professional Knowledge, Victoria D. Bonaccorso

Theses, Dissertations and Culminating Projects

The dynamic nature of teaching means that teachers are making in-the-moment decisions on a daily basis. Video case study professional development can be used as a way to provide teachers an opportunity to analyze real teaching scenarios to prepare to make these decisions in practice. While work has been done to reveal the effectiveness of using case studies as a teaching tool, there has not been research conducted to determine if video case studies can be used to foster the development of collective professional knowledge. This study utilizes a particular professional development model using video case studies grounded in the …

College Of Liberal Arts And Sciences_Mt 101 & Wgs 101_Covid-19 Response, Kevin Roberge

College of Liberal Arts and Sciences

Email from Kevin Roberge, Adjunct Mathematics Faculty, University of Maine to the Provost Office regarding how he had incorporated the COVID-19 pandemic into his courses MAT 101 and WGS 101.

Self-Supervised Learning For Single-Molecule Localization Microscopy, Clare Minnerath

Mathematics & Computer Science Student Scholarship

Major: Mathematics and Computer Science

Faculty Mentor: Dr. Lynette Boos, Mathematics

We evaluate the ability of self-supervised deep learning for Poisson denoising of Single-Molecule Localization Microscopy (SMLM) in addition to the impact denoising can have on the ability to locate molecules within the Single-Molecule Localization Microscopy images. SMLM images are predominantly corrupted with Poisson noise. There is a need for a superior technique to provide accurate SMLM images in order for scientists to gain a better understanding of the functions of live cells at the nanoscale. By denoising SMLM images prior to the images undergoing the current state- of-the-art super-resolution …

Research In Sabermetrics: The Cape Cod Baseball League, Thomas Zinzarella

Mathematics & Computer Science Student Scholarship

Major: Sports Media

Faculty Mentor: Fr. Humbert Kilanowski O.P, Mathematics and Computer Science

We analyzed data from the Cape Cod Baseball League, a prestigious summer baseball league, where we looked at sabermetric statistics such as WAR (Wins above replacement). Stats like these can help evaluate a player and project whether they are a future MLB player or not. Especially on the Cape, where 1 in 7 current Major League Baseball players have played in the league.

Simplexity Of The N-Cube, Peter Graziano

Mathematics & Computer Science Student Scholarship

Major: Mathematics and Classics

Faculty Mentor: Dr. Su-Jeong Kang, Mathematics

The process of dividing shapes into triangles is called triangulation, and it is possible to abstract the idea of a triangle to higher dimensions, where it will be called a simplex in n-dimensions, or an n-simplex. I studied this process of generalized triangulation, or decomposition, in order to find an optimal decomposition of a 5-cube to help improve the bounds on the general case of an n-cube.

Application Of Black-Scholes-Merton Model In Option Pricing And Intangibles Assets, Giang Nguyen-Hoang

Mathematics & Computer Science Student Scholarship

Major: Finance and Mathematics

Faculty Mentor: Dr. Joseph Shomberg, Mathematics

The Black-Scholes model was developed by Fisher Black and Myron Scholes in the 1970s to price stock options. Since then the model has been suited to price so-called intangible assets such as trademarks and patents. In this paper, we investigate the related Black-Scholes-Merton model and the relevant characteristics of patents in order to associate patents as real options. After describing patents as options, we apply the Black-Scholes-Merton model to the valuation of the intangible assets. Special attention is given to modeling volatility and the cost of delay in order to …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Mat 116 Introduction To Calculus - Course Material, Ayesha Maliwal Bundy

Teaching, Learning & Research Documents

Updated addendum to MAT 116 (Introduction to Calculus) syllabus, updated course timeline (both before and after the storms since many students lost power) and a contingency plan for their course team.

Fern Or Fractal... Or Both?, Christina Babcock

Research and Scholarship Symposium Posters

Fractals are series of self similar sets and can be found in nature. After researching the Barnsley Fern and the iterated function systems using to create the fractal, I was able to apply what I learned to create a fractal shell. This was done using iterated function systems, matrices, random numbers, and Python coding.

Searching Games: A Bound For The Responder, Jose Garcia

Student Scholars Day Oral Presentations

A searching game with two unknowns and a lie involves two players, the responder and the questioner. Before the start of the game, the two parties predetermine an amount of numbers n to consider, and how many questions k the questioner can ask before the game ends with a victory (or loss) for the responder. The responder thinks of two secret numbers. The questioner asks questions of the form "How many of your two numbers are in the subset Q of the set {0,...,n-1}?", in an attempt to search and find what the two secret numbers are. If the questioner …

Knitting Math: Geometric Shapes, Cynthia Wright

WWU Honors College Senior Projects

When knitting 3-D objects such as hats or socks, the knitter is using geometry and mathematics to make the 2-dimensional string into 3-dimensional shapes. In this project, I will be creating mathematically accurate, geometric shapes, to directly show the relationship between the mathematical formulas, knitting patterns, and the knitted objects. There is more than one way to understand and perceive math, one of which is knitting. Past mathematical knitters have shown the relationship between algebra and complex shapes (such as a Klein bottle or Möbius strip) and knitting. In an effort to explore how more accessible mathematical shapes and concepts …

On The Mersenne Prime Numbers, Julia Vanlandingham

Undergraduate Honors Thesis Projects

The prime numbers have been an important field of research for thousands of years and are intertwined with most other fields of mathematics. One topic that has piqued the interest of mathematicians young and old is the Mersenne prime numbers, which have applications in many mathematics and computer science fields. The Mersenne primes get a lot of attention because there is not much known about them. However, we do have a very simple primality test for Mersenne numbers, which is why the largest currently known primes are Mersenne primes. These primes are also very closely related to another class of …

Mat 127 (Calculus Ii) - Course Syllabus, David Bradley

Teaching, Learning & Research Documents

Updated syllabus of MAT 127 (Calculus II) class. The update reflects the change in course format necessitated by the mandated transition to off-campus online instruction.

Higher Chow Cycles On The Jacobian Of Curves., Subham Sarkar Dr.

Doctoral Theses

The following formula, usually called Beilinson’s formula — though independently due to Deligne as well — describes the motivic cohomology group of a smooth projective variety X over a number field as the group of extensions in a conjectured abelian category of mixed motives, MMQ.The aim of this thesis is to describe this construction in the case of the motivic cohomology group of the Jacobian of a curve. The first work in this direction is due to Harris [Har83] and Pulte [Pul88], [Hai87]. They showed that the Abel-Jacobi image of the modified diagonal cycle on the triple product of a …

Mat 426 Real Analysis Ii - Course Syllabus, David Bradley

Teaching, Learning & Research Documents

Updated syllabus of MAT 426 (Introduction to Real Analysis II) class. The update reflects the change in course format necessitated by the mandated transition to off-campus online instruction.

A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez

Honors Theses

Crime is often regarded as nonsensical, impulsive, and irrational. These conjectures are pointed, though conversation about the pros and cons of crime does not happen often. People point to harsh fines, jail times, and life restrictions as their reason for judgement, stating that the trade-offs are far too unbalanced to participate in illicit activity. Yet, everyday people commit small crimes, sometimes based on hedonistic desires, other times based on a rational thought process.

Speeding seems to be one of those that almost all people commit at least once during their life. Our work hopes to make an incremental improvement on …

Characterization Of Eigenfunctions Of The Laplace-Beltrami Operator Through Radial Averages On Rank One Symmetric Spaces., Muna Naik Dr.

Doctoral Theses

Let X be a rank one Riemannian symmetric space of noncompact type and ∆ be the Laplace–Beltrami operator of X. The space X can be identified with the quotient space G/K where G is a connected noncompact semisimple Lie group of real rank one with finite centre and K is a maximal compact subgroup of G. Thus G acts naturally on X by left translations. Through this identification, a function or measure on X is radial (i.e. depends only on the distance from eK), when it is invariant under the left-action of K. We consider right-convolution operators Θ on functions …

Teaching A University Course On The Mathematics Of Gambling, Stewart N. Ethier, Fred M. Hoppe

UNLV Gaming Research & Review Journal

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a …

The User's Guide Project: Looking Back And Looking Forward, Don Larson, Kristen Mazur, David White, Carolyn Yarnall

Journal of Humanistic Mathematics

In 2014 Luke Wolcott created the User's Guide Project, in which a group of algebraic topologists came together to write user's guides to coincide with their research papers in hopes of making their research more accessible. We examine the role of this innovative project within the greater mathematics community. We discuss the structure and history of the project, its impact on the community, and its value to the participants of the project. We end by encouraging the math community to recognize the value of the project and expand the User's Guide Project to other subfields.

On Not Teaching Addition: A Homeschooling Parent Teaches And Researches Math, Marion D. Cohen

Journal of Humanistic Mathematics

Interactions with the humans in one’s life can have bearings on the way one interacts with one’s work – and vice versa. In particular, the ways in which a math person who is also a parent interacts with their children can correlate with the ways that person interacts with students, colleagues, and with math itself. This article describes some of that correlation in one mathmom’s life. In particular, this mathmom worked toward balancing, both as a mom and as a teacher, her beliefs and feelings with societal mindsets and practices.

A Study Of Operators On The Discrete Analogue Of Hardy Spaces On Homogeneous Trees And On Other Structures., P. Muthukumar Dr.

Doctoral Theses

In analytic function theory, the study of multiplication and composition operators has a rich structure for various analytic function spaces of the unit disk D = {z ∈ C : |z| < 1} such as the Hardy spaces Hp, the Bergman spaces Ap and the Bloch space B. This theory connects the operator theoretic properties such as boundedness, compactness, spectrum, invertibility, isometry with that of the function theoretic properties of the inducing map (symbol) such as bijectivity, boundary behaviour and vise versa In Chapter 2, we define discrete analogue of generalized Hardy spaces (Tp) and their separable subspaces (Tp,0) on a homogenous rooted tree and study some of their properties such as completeness, inclusion relations with other spaces, separability and growth estimate for functions in these spaces and their consequences. In Chapter 3, we obtain equivalent conditions for multiplication operators Mψ on Tp and Tp,0 to be bounded and compact. Furthermore, we discuss point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry. In Chapter 4, we give an equivalent conditions for the composition operator Cφ to be bounded on Tp and on Tp,0 spaces and compute their operator norms. We have considered the composition operators induced by special symbols such as univalent and multivalent maps and automorphism of a homogenous tree. We also characterize invertible composition operators and isometric composition operators on Tp and on Tp,0 spaces. Also, we discuss the compactness of Cφ on Tp spaces and finally we prove that there are no compact composition operators on Tp,0 spaces. In Chapter 5, we consider the composition operators on the Hardy-Dirichlet space H2, the space of Dirichlet series with square summable coefficients. By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on H2 , for the affine-like inducing symbol ϕ(s) = c1 + cqq −s , where q ≥ 2 is a fixed integer. We also give an estimate for approximation numbers of a composition operators in our H2 setting. In Chapter 6, we study the weighted composition operators preserving the class Pα. Some of its consequences and examples of certain special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.