Mathematics Commons^™

How The Perceived Value Of Education, Parental Influences, And Students' Perceived Success Affect Post-Graduate Decisions, Valerie Blanchard

Honors Projects in Mathematics

While technical education has been enhanced in many ways over the past few decades, college is still the preferred post-graduate path for many students and is the societal norm. This study will analyze the value that students view in their career path that leads them to make their post-graduate decisions. The goal of this research is to better understand why students pursue college and how these decisions come to be with specific attention paid to the impact of gender, interests, and self-efficacy. This understanding can educate others about the gravity of social norms and can start conversations about how to …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

Developing Awareness Around Language Practices In The Elementary Bilingual Mathematics Classroom, Gladys Krause, Melissa Adams Corral, Luz A. Maldonado Rodríguez

Teaching and Learning Faculty Publications and Presentations

This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-on-one interview and of the circulating portion of a mathematics class from a second grade classroom. We use these examples to foreground instructional practices, for researchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal …

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

Variety And Variation, Christopher Goff, Erik R. Tou

Euleriana

Welcome to Volume 2 of Issue 2 of Euleriana. While we occasionally discover themes that emerge from the articles and translations presented in a given issue, the wide range of Euler’s work more often results in a variety of topics for each issue. This is no less true for Issue 2.

Introduction To Mathematical Analysis I - 3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels …

Elegance Or Alchemy? An International Cross-Case Analysis Of Faculty And Graduate Student Perceptions Of Mathematical Proofs, Brooke Nicole Denney

Masters Theses

Artist Marcel Duchamp once said, ``The painter is a medium who doesn’t realize what he is doing. No translation can express the mystery of sensibility, a word, still unreliable, which is nonetheless the basis of painting or poetry, like a kind of alchemy" (Moffitt, 2012). Just as there is a puzzling aspect of creating art or writing poetry, the aesthetic quality of mathematical proofs is a mysterious and ill-defined concept. Like many other subjective terms, it can be difficult to reach a consensus on what elegance means in a mathematical context. In this thesis, I try to better understand faculty …

Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram

Journal of Humanistic Mathematics

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …

In Mathematics, As In Art, Andrew Granville

Journal of Humanistic Mathematics

The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes?

Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield

Journal of Humanistic Mathematics

Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics …

Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler

Journal of Humanistic Mathematics

Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …

Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel

Journal of Humanistic Mathematics

Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.

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 …

Temporal Sentiment Mapping System For Time-Synchronized Data, Jiachen Ma

Dissertations (1934 -)

Temporal sentiment labels are used in various multimedia studies. They are useful for numerous classification and detection tasks such as video tagging, segmentation, and labeling. However, generating a large-scale sentiment dataset through manual labeling is usually expensive and challenging. Some recent studies explored the possibility of using online Time-Sync Comments (TSCs) as the primary source of their sentiment maps. Although the approach has positive results, existing TSCs datasets are limited in scale and content categories. Guidelines for generating such data within a constrained budget are yet to be developed and discussed. This dissertation tries to address the above issues by …

The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many mathematics teachers are not prepared to design valid and usable measurements of their students’ mathematical achievements. There are relatively few opportunities for mathematics teachers to improve their assessment literacy. The purpose of this study is to (1) design a course on assessment for inservice mathematics teachers and (2) evaluate the effectiveness of the course. This paper recounts the development of the course and its influence on 16 teachers. Teachers who completed the course submitted a unit outline with learning objectives, a test blueprint, and a unit test. These artifacts influenced my evaluation on the effectiveness of the course. All …

Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …

Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Esther Rønn ’23, Majors: Physics and Mathematics
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Our research group used topological data analysis (TDA) to quantify the movement and behavior of ants in a colony.

We extracted higher dimensional networks from point cloud data collected from Dr. James Waters’ lab. Varying the proximity parameter in this construction gives a sequence of networks. We analyzed the enduring topological features of these networks, and how these features evolve over time as the ants move in the colony. Both the experimental and null model simulation data …

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 …

Classifications Of Transformations Of Km#Tn And Pm#Tn Via Symmetry Groups, Adam Banatwala, Jensen Barry, Mackenzie Maude

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Jensen Barry ’22, Majors: Biology and Mathematics
Mackenzie Maude ’22, Majors: Mathematics and Art History
Faculty Mentor: Dr. C. Joanna Su, Mathematics and Computer Science

One of the main topics in topology is the classification and comparison of shapes and surfaces. Since Spring 2020, our research group has been using symmetry groups to classify the 1- and 2-dimensional orientable and non-orientable closed surfaces.

First, the group worked on the symmetry groups of the 1- and 2-dimensional orientable closed surfaces; namely, the classification on V?? 1 (the one-point adjoint of n circles) …

Lines On A Smooth Projective Surface, Jordan Demoura

Mathematics & Computer Science Student Scholarship

Jordan DeMoura ’22
Major: Mathematics
Faculty Mentor: Dr. Su-Jeong Kang, Math

This research is to investigate lines on a smooth projective surface. A quadric surface contains two families of planes that provide a ruling of the surface. A cubic surface contains twenty-seven lines, and we provide a complete description of these lines for a Fermat cubic surface. Furthermore, under the Plucker embedding, we show that each family of the lines on a quadric surface corresponds to plane conic curves lying on complementary planes in the projective space of dimension five.

Reframing The Achievement Gap In Mathematics Education, Madeline Pavolovich '22

Posters

Much of math education research focuses on a so-called “achievement gap” measured by test scores and similar quantitative measures of “success.” By framing issues of equity in this way, methods to remedy the gap often require subordinated groups to become more like the “higher achieving” group. In other areas of study, we have been quicker to incorporate sociopolitical lenses into teaching and learning with an emphasis on identity and power. Such a sociopolitical turn could help us rethink what it means for math education to be truly equitable.

Bail Reform, Matthew Shang '22

Posters

The Public Safety Assessment (PSA) to assess the likelihood of pretrial risk. Then, the information is used to decide the conditions of release, including components like bail. The factors used are related only to age and criminal history. In short, the algorithm helps judges make more informed decisions.

Gender Discrimination In Ai, Nicole Papert '22

Posters

There are several studies revealing that AI tools used in job search applications and sites will promote different opportunities depending on the gender of the user. Specifically, men are typically shown more competitive job postings than women, given that the users have similar skills and qualifications. In this poster, I will closely examine why algorithms utilized for the job search process may present differently between men and women.

Tips For Success In Math Courses, Joshua Horowitz '22

Posters

Five steps in the development process for succeeding in mathematics.

Belonging In Math And How It’S Affected By Groupwork, Kara Mathes '22

Posters

Interactions in groups for class assignments are an important part of a student’s sense of belonging in mathematics and other academic disciplines. This sense of belonging has an impact on the student’s sense of self as well as their academic performance.

Cross-Sectoral Climate Change Modeling, Jeremy Gordon '22

Posters

Although climate data originates from various integrated sectors, it continues to be evaluated in isolation. By using cross-sectoral modeling, climate change modeling can more effectively represent data, and the possible consequences of misjudging future models.

Ranked Choice Voting: Who’S The Real Winner?, Brendan Magill '23

Posters

Ranked choice voting is a voting system in which voters rank candidates in order or preference. The winning candidate is determined by eliminating candidates and reassigning their votes until one has a majority. It provides solutions to some of the fundamental issues with traditional voting. But is it more fair? Should it be instituted in American democratic elections?

Racial Bias In Health Care Machine Learning Algorithms, Esther Akinpelu '22

Posters

Machine learning algorithms in healthcare are racially biased, especially when diagnosing patients and choosing candidates for care management programs.

Is U.S. News College Ranking A Weapon Of Math Destruction?, Zhipeng Kui '22

Posters

This poster presents Cathy O’Neil’s arguments from her book Weapons of Math Destruction and connects them with Columbia’s ongoing ranking scandal to show why we should view U.S. News college ranking as a WMD.

The Impossible Theorem Of Fairness, Man Nguyen '22

Posters

With the growth of machine learning, there has been an increase of machine biases that can cause wrongful discrimination. In the case of implementing “fairness,” several conceptions of bias were created to target a fair system. However, statisticians have found that these conceptions contradict one another. Thus, we run into an impossible conundrum of fairness in machine learning. In cases that high risk, we want to investigate the best fairness measures if one is possible. Moreover, we would like to determine when these fairness measures fail or what conditions must be met for them to succeed.