Physical Sciences and Mathematics Commons^™

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser

Journal of Practitioner Research

Whole group math talks, or number talks, are a common practice to get students talking about their own understanding of mathematical concepts. The purpose of this study was to implement math talks in small group settings to see what would happen, specifically to students’ conceptual understanding as well their general perceptions of math talks. This study took place in a fourth-grade math classroom, and math talks were implemented with the whole class for a week and then moved to small groups for the remaining three weeks of the study. During the study, a pre-and post-assessment was given, field notes were …

Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma

Undergraduate Student Research Internships Conference

First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.

Developing Confidence And Interest In Teaching Relevant Mathematical Modeling Lessons, Jacy Beck

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

What is mathematical modeling and how can inservice and pre-service teachers develop the skills and competencies necessary to increase confidence and interest in teaching relevant mathematical modeling lessons? Mathematical modeling is “the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions” (CSSM, 2010, p. 72). By providing students with an opportunity to engage in relevant mathematical modeling prompts, we provide them with transferable skills and knowledge. The aim of this paper will be to provide insight into the relevance of teaching mathematical modeling, provide resources for integrating modeling …

Oer Ancient Egyptian Numerals And Arithmetic Activity, Cynthia Huffman Ph.D.

Faculty Submissions

Many people are fascinated with ancient Egypt. The amazing, unique culture influenced many other civilizations and cultures. If you study the history of math, you will see how this influence included mathematics. Ancient Egypt also lasted an incredibly long time – over 3000 years. According to Egyptologist Bob Brier, “No civilization lasted so long, contributed so much, or repeatedly amazed as did ancient Egypt.”

In this Open Educational Resource activity, students will have the opportunity to learn about ancient Egyptian numerals and basic arithmetic. For motivation, the setting is a scribal school with each student using a clipboard, paper, and …

For The Women Who Wear Pi Day Shirts, Jacqui Weaver

Honors College

This project, entitled To The Women Who Wear Pi Day Shirts, is a poetry manuscript that explores a journey of a women in STEM. While taking college English courses, I read about characters such as the creature in Frankenstein, by Mary Shelley, who had intelligence, yet was physically hideous, an outsider from the human population. The creature was an outsider to the normal human, much like how I feel as a woman in STEM, which gave me the idea to write about my own journey. The poetry in this manuscript is a reflection from being in elementary school learning mathematics …

Symmetric Presentations Of Finite Groups And Related Topics, Samar Mikhail Kasouha

Electronic Theses, Projects, and Dissertations

A progenitor is an infinite semi-direct product of the form m∗n : N, where N ≤ Sn and m∗n : N is a free product of n copies of a cyclic group of order m. A progenitor of this type, in particular 2∗n : N, gives finite non-abelian simple groups and groups involving these, including alternating groups, classical groups, and the sporadic group. We have conducted a systematic search of finite homomorphic images of numerous progenitors. In this thesis we have presented original symmetric presentations of the sporadic simple groups, M12, J1 as homomorphic images of the progenitor 2∗12 : …

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Meas: Exploring Links Between Implementation And Standards Mastery, Noah Silver

Honors Projects

In order to effectively enhance a student’s mathematical understanding and development in the field of mathematics, students need to engage in problem solving. Model eliciting activities, or MEAs, provide students with tasks that promote higher level thinking and the ability to utilize mathematics outside of the classroom; they also align and promote the utilization of the Common Core State Standards and Standards for Mathematical Practice. Research suggests that the language and motivation promoted by MEAs enriches engagement and increases student ability and performance of traditional and real-world mathematics. Use of technology further supports these goals. Through the analysis of checkpoint …

Program Review: Mathematics And Statistics Department, Katherine Kime, University Of Nebraska At Kearney Department Of Mathematics And Statistics Faculty & Staff

Academic Program Reviews

No abstract provided.

Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams

Honors Theses

Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …

An Integration Of Art And Mathematics, Henry Jaakola

Undergraduate Honors Theses

Mathematics and art are seemingly unrelated fields, requiring different skills and mindsets. Indeed, these disciplines may be difficult to understand for those not immersed in the field. Through art, math can be more relatable and understandable, and with math, art can be imbued with a different kind of order and structure. This project explores the intersection and integration of math and art, and culminates in a physical interdisciplinary product. Using the Padovan Sequence of numbers as a theoretical basis, two artworks are created with different media and designs, yielding unique results. Through these pieces, the order and beauty of number …