Physical Sciences and Mathematics Commons^™

On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.

Doctoral Theses

This thesis concerns problems related to the ramification behaviour of the branched Galois covers of smooth projective connected curves defined over an algebraically closed field of positive characteristic. Our first main problem is the Inertia Conjecture proposed by Abhyankar in 2001. We will show several new evidence for this conjecture. We also formulate a certain generalization of it which is our second problem, and we provide evidence for it. We give a brief overview of these problems in this introduction and reserve the details for Chapter 4.Let k be an algebraically closed field, and U be a smooth connected affine …

Perron Theorem For Delay Differential Equations, William Barker

Theses and Dissertations

This note discusses results furthering the study of bounded solutions of non-homogeneous second-order differential equations with delay. The equation of interest has already been shown to possess unique bounded solutions in accordance to Perron's Theorem. We will determine the negativity of the solutions given a positive forcing term by establishing a uniform bound regarding small time delay.

Expansion Of The Department Of Mathematics At Princeton University And The Founding Of The School Of Mathematics At The Institute For Advanced Study: 1900-1950, Andrew Beman-Cavallaro

Great Plains Graduate Review

From 1900 to 1950 Princeton, New Jersey, hosted two of the most prestigious institutions and provided a location for the expansive mathematical investigations taking place just before, during, and immediately after the Second World War. Princeton University and the Institute for Advanced Study housed, fed, and provided workspaces for an array of Mathematicians uncovering new research methodologies (resulting in the defeat of both the Nazi Party and the Empire of Nippon), the foundation for modern experimental Mathematics, and expansions of Theoretical and Applied Physics.

Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.

Doctoral Theses

A very general and fundamental problem in the theory of bounded linear operators on Hilbert spaces is to find invariants and representations of commuting families of isometries.In the case of single isometries this question has a complete and explicit answer: If V is an isometry on a Hilbert space â„‹, then there exists a Hilbert space Hu and a unitary operator U on â„‹u such that V on â„‹u and[ S ⊗ IW 0 0 U] ∈ B((l 2 (ℤ+) ⊗ W) ⊕ â„‹u),are unitarily equivalent, whereW = ker V∗ ,is the wandering subspace for V and S is the …

College Algebra Through Problem Solving (2021 Edition), Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Stelmach

Open Educational Resources

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

For The Love Of Mathematical Research: A Conversation With Undergraduate Research Students, Mike Janssen

Faculty Work Comprehensive List

"One of my passions as a professor is creating opportunities for students to ask questions about mathematics."

Posting about students' perspectives on mathematics research from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

https://inallthings.org/for-the-love-of-mathematical-research-a-conversation-with-undergraduate-research-students/

Partial Representations For Ternary Matroids, Ebony Perez

Electronic Theses, Projects, and Dissertations

In combinatorics, a matroid is a discrete object that generalizes various notions of dependence that arise throughout mathematics. All of the information about some matroids can be encoded (or represented) by a matrix whose entries come from a particular field, while other matroids cannot be represented in this way. However, for any matroid, there exists a matrix, called a partial representation of the matroid, that encodes some of the information about the matroid. In fact, a given matroid usually has many different partial representations, each providing different pieces of information about the matroid. In this thesis, we investigate when a …

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions.

As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …

Fantasy At The Service Of Mathematics, Clara Ziskin, Esther Williams, Alla Shmukler

Journal of Humanistic Mathematics

This article aims to introduce the reader to a book published in 2016 under the title “Amazing Tales from the Magic Wood and Famous Problems of Mathematics” by Elli Shor and Clara Ziskin. The book offers an original method of presenting mathematical facts and history through a fantasy narrative. The book’s two authors, Clara Ziskin and Alla Shmukler (Elli Shor), together with consultant psychologist Esther Williams, share here several excerpts taken from the first part of the book as well as related illustrations and mathematical riddles, so that the reader can form an informed impression of the book, its structure, …

Crocheting Mathematics Through Covid-19, Beyza C. Aslan

Journal of Humanistic Mathematics

As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.

An Interdisciplinary Rendezvous Between Mathematics And Literature: Reflections On Beauty As A Perspective In Comparative Disciplinary Didactics And A Thematic Approach To Interdisciplinary Work In Upper Secondary School, Uffe Thomas Jankvist, Helle Rørbech, Jesper Bremholm

Journal of Humanistic Mathematics

In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of literacy can potentially strengthen students’ understanding of ways of thinking particular to specific (academic) disciplines; ways of thinking that are otherwise often hidden when teaching focuses on more pragmatic aspects. G. H. Hardy’s A Mathematician’s Apology from 1940 serves as the recurring illustrative example in our discussions of the pedagogical …

Mathematics And Magic Realism: A Study Of "The Raven Legend", Veselin Jungic

Journal of Humanistic Mathematics

This article demonstrates that “The Raven Legend”, a Haida myth transcribed by Franz Boas in 1888, is full of (ethno)mathematical concepts that Haida society used to make sense of the natural, real world. Calculus can be used to model several segments of the story since the narrative relied heavily on ideas that a mathematician would identify as the concepts of infinity and mathematical limits.

Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.

Doctoral Theses

This thesis comprises four essays on social choice theory. The first three essays/chapters consider models where voters follow “non-standard” rules for decision making. The last chapter considers the binary social choice model and analyzes the consequences of a new axiom. The first chapter introduces a new axiom for manipulability when voters incur a cost if they misreport their true preference ordering. The second chapter considers the random voting model with strategic voters where standard stochastic dominance strategy-proofness is replaced by strategy-proofness under two lexicographic criteria. The third chapter also considers the random voting model but from a non-strategic perspective. It …

N-Th Order Functional Problems With Resonance Of Dimension One., Erin Benham

Theses and Dissertations

We consider a nonlinear n-th order boundary value problem given arbitrary bounded linear functional conditions and develop a method that allows us to study all such resonance problems of order one, as well as implementing a more general constructive method for deriving existence criteria in the framework of the coincidence degree method of Mawhin. We demonstrate applicability of the formalism by giving an example for when n is 4.

Developing An Inquiry-Based Laboratory Project For Chem 142l Course At Bsu, Manuel Pina

Honors Program Theses and Projects

In addition to content knowledge, critical and independent thinking, scientific reasoning, and problem-solving skills are essential in preparing next generation of successful workforce. Since one of the biggest advantages of STEM disciplines is a “must-have” hands-on laboratory experience, it is intuitive to exploit this learning space to reinforce afore-mentioned skills. In this context, project-based (PBL) or inquiry-based (IBL) laboratory experiences are rapidly becoming mainstream pedagogical choice for many STEM instructors across United States.^[1-4] PBL, and IBL are learning experiences that offer students an opportunity to experience realistic scientific process of discovery through carefully designed inquiry-driven and/or open-ended investigative laboratory …

An Exploration Of Manipulatives In Math Education, Jade Monte

Honors Program Theses and Projects

Pre-existing literature has shown that the education system needs to re-evaluate mathematical teaching practices in a manner that can boost students’ confidence in mathematics. Thus, the research is to investigate the use of manipulatives in reducing students’ anxiety by increasing their learning experience and engagement in mathematics. Furthermore, the purpose of this thesis is to explain the interconnectedness of math manipulatives, student engagement, and problem-solving. An in-depth literature review is conducted, which contains definitions, important benefits and methodologies of manipulatives, as well as the teacher’s role regarding these three terms. When manipulatives, student engagement, and problem-solving are in harmony, students …

We’Re Here To Get You There: A Statistical Analysis Of Bridgewater State University’S Transit System, Abigail Adams

Honors Program Theses and Projects

Bridgewater State University first established its on-campus transportation service in January of 1984. While it began only running as an on-campus service for students throughout the day, the service grew to expand by offering an off-campus connection to the neighboring city of Brockton and absorbed the night service system from the campus safety team. As BSU Transit continues to grow, the organization is seeking ways to improve their overall service and better prepare their fleet and driver pool to accommodate this growth. The purpose of this research is to analyze trends among the data collected by BSU Transit and assist …

Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, Zachary Beamer

Inquiry: The Journal of the Virginia Community Colleges

In corequisite models of instruction, marginally prepared students are placed directly into college-level coursework, taught with a paired support course. Initial research suggests that such models yield significant improvements in the number of students passing credit-level mathematics when compared to previous models of prerequisite remediation. The present study employs qualitative methods to investigate methods of instruction at one community colleges to understand how instructors identify and respond to student needs. It concludes with recommendations for practice and highlights advantages of small format corequisite classes taught by the same instructor.

The Impact Of Decriminalizing Marijuana In Rhode Island On The Number Of Narcotic Related Arrests And Quantities Seized, Abigail Kojoian

Mathematics & Computer Science Student Scholarship

Major: Mathematics
Minor: Classics
Faculty Mentor: Dr. Asta Shomberg, Mathematics

An Exploratory Analysis Of The Bgsu Learning Commons Student Usage Data, Emily Eskuri

Honors Projects

The purpose of this study was to explore past student usage data in individualized tutoring sessions from the Learning Commons from two academic years. The Bowling Green State University (BGSU) Learning Commons is a learning assistance center that offers various services, such as individualized tutoring, math assistance, writing assistance, study hours, and academic coaching. There have been limited research studies into how big data and analytics can have an impact in higher education, especially research utilizing predictive analytics.

This project applied analytics to individualized tutoring data in the Learning Commons to create a better understanding of why those trends happen …

On Tests Of Independence Among Multiplerandom Vectors Of Arbitrary Dimensions., Angshuman Roy Dr.

Doctoral Theses

Measures of dependence among several random vectors and associated tests of independence play a major role in different statistical applications. Blind source separation or independent component analysis (see, e.g., Hyv¨arinen et al., 2001; Shen et al., 2009), feature selection and feature extraction (see, e.g., Li et al., 2012), detection of serial correlation in time series (see, e.g., Ghoudi et al., 2001) and finding the causal relationships among the variables (see, e.g., Chakraborty and Zhang, 2019) are some examples of their wide-spread applications. Tests of independence has vast applications in other areas of sciences as well. For instance, to characterize the …

Factoring: Difference Of Squares, Thomas Lauria

Open Educational Resources

This lesson plan will explain how to factor basic difference of squares problems

Matrix Product Structure Of A Permuted Quasi Cyclic Code And Its Dual, Perian Perdhiku

Dissertations

In my Dissertation I will work mostly with Permuted Quasi Cyclic Codes. They are a generalization of Cyclic Codes, one of the most important families of Linear Codes in Coding Theory. Linear Codes are very useful in error detection and correction. Error Detection and Correction is a technique that first detects the corrupted data sent from some transmitter over unreliable communication channels and then corrects the errors and reconstructs the original data. Unlike linear codes, cyclic codes are used to correct errors where the pattern is not clear and the error occurs in a short segment of …

Examining Middle School Students' Methods Of Justification, Leslie Reyes- Hernandez

Mathematics

Researching students’ thinking is imperative to improving the education system throughout the world. From extensive research, it is noted that students are unaccustomed and struggle with providing valid mathematical justifications (e.g. Inglis & Alcock 2012). The National Council of Teachers of Mathematics (NCTM, 2000) and Common Core State Standards of Mathematics (CCSSM, 2010) suggest that students should have several opportunities to construct mathematical arguments across all grade levels. To take a closer look at this educational phenomenon, we prompt fifth to eighth-grade students with nine mathematical tasks. Within our research, we focus on tasks based on number properties, algebraic thinking, …

Quantifying Eco-Friendliness Of Plastic, Paper, And Reusable Bags, Leah Ryan

Honors Projects in Science and Technology

The plight of the consumer in regards to making eco-conscious decisions is growing as concerns regarding the environment increase. This study was conducted in an effort to give consumers a tool to combat some of this issue and compare the types of shopping bags they use in terms of eco-friendliness. Research conducted in this avenue thus far contains convoluted conclusions, all made with consideration of some variables, but not all. This purpose of this study therefore lay in trying to give consumers a standardized tool to compare bag types that considered variables across all stages of a bags’ life (pre-use, …

Prediction Of Individual Income: A Machine Learning Approach, Michael Matkowski

Honors Projects in Economics

The use of machine learning models to improve prediction problems and handle increasingly large datasets is a rising trend in economics. Prediction plays a particularly important role in applied economics because it provides critical insights to assess market outcomes. This study builds on previous literature to showcase the relative power of these modelling methodologies in economics through the prediction of income. This research utilizes data from the Current Population Survey from 2017 – 2020, containing 467,811 observations and 264 variables. 2017-2018 data served as training data for the models and 2019-2020 served as data for the two testing sets. The …

Millennials' Retirement Struggle: The Interaction Between Student Loans, Financial Decisions, And Financial Literacy., Rebecca Michaud

Honors Projects in Finance

As millennials grow older and begin their careers in the workforce, saving for retirement begins to become an important part of spending. This paper analyzes a variety of factors and challenges that impact an individual’s retirement savings. This thesis ultimately looks to determine whether the driving force for the general inadequacy of retirement savings is student loan debt, financial decision making, or both. Through both research and survey responses, this thesis will also look at whether a public policy that removes a certain percentage of student loan repayment obligations will have any impact on the amount that young workers are …

Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden

Mathematics

Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.

Innovative Approach To Solving Combinatic Elements And Some Problems Of Newton Binomy In School Mathematics Course, Nilufar Okbayeva

Central Asian Problems of Modern Science and Education

This article provides information on the elements of combinatorics in the school mathematics course and solutions to some problems related to the Newtonian binomial. This article is also aimed at solving problems related to the indepth study of the elements of combinatorics in the school course, the creation of a sufficient basis for the study of probability theory and mathematical statistics in the future.

Quantum Symmetries In Noncommutative Geometry., Suvrajit Bhattacharjee Dr.

Doctoral Theses

No abstract provided.