Physical Sciences and Mathematics Commons^™

Discovering And Demonstrating Patterns, Maria Klawe

The STEAM Journal

Harvey Mudd College's President Maria Klawe shares her personal journey in combining a love of mathematics and art.

Gödel’S Incompleteness Theorem, Emma Buntrock

Essential Studies UNDergraduate Showcase

In 1931 Gödel released his Incompleteness Theorem. His theorem was the opposite of what other mathematicians at the time wanted, but it was very influential to realize there is no perfectly complete formal systems. The incompleteness theorem is based of the idea that in a consistent system there are pieces that can not be proved or disproved, causing for incompleteness. The second part of that idea is that such a system can not prove that itself is consistent, which also makes it incomplete. I will verify theses proofs using a series of logic problems that show how a system is …

The Most Important Statistics In Football, Jacob Holmen

Essential Studies UNDergraduate Showcase

This research is based on the Five Factors that were devised by Bill Connelly of SBNation. The Five Factors of football include Explosiveness, Efficiency, Field Position, Finishing Drives, and Turnovers. Each factor is composed of associated statistics that when put together make up the most important statistics in football. This research includes the analysis of all 857 FBS (the highest level of NCAA Division I football) games from the 2016 season. Data was analyzed through the use of an Excel spreadsheet. Five different statistics were looked at, each associated with one of the Five Factors. The statistics include Yards per …

Tangled Up: Women’S Experiences In Mathematics, Lori Loftin

Honors College

This thesis is a bridge between two disciplines: Women's, Gender, and Sexuality Studies, and Mathematics. The first portion of the work synthesizes both theory and previously done studies to describe the state of women in mathematics as a whole, as well as historicizing the role of women in mathematics. Obstacles to the full and equal participation of women in mathematics are examined through a feminist lens. The second part of the thesis is a feminist biography crafted from an interview with a professor of mathematics, Dr. Erica Flapan. This provides information about her personal experiences as a woman in mathematics …

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Essays On Economic Behaviour And Regulation., Subrato Banerjee Dr.

Doctoral Theses

To sum up, this thesis looks at agent behaviour in the laboratory, in the field, and in the market. Firstly, we impose a requirement in the laboratory (Chapter 2) that mimics a regulatory environment (similar to the introduction of a maximum retail price, or a legal fare subject to which an economic transaction must take place), and study individual behaviour subject to our (imposed) requirements. We then study the effect of real-life regulation on the behaviour of economic agents in the field. While the effect of regulation is seen in the field (that is, we see that many auto drivers …

Special Issue Call For Papers: Mathematics And Motherhood, Pamela E. Harris, Becky Hall, Carrie Diaz Eaton, Emille Davie Lawrence

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Mathematics and Motherhood. Please send your abstract submissions via email to the guest editors by October 1, 2017. Initial submission of complete manuscripts is due January 1, 2018. The issue is currently scheduled to appear in July 2018.

Descartes Comes Out Of The Closet, Nora E. Culik

Journal of Humanistic Mathematics

While “Descartes Comes Out of the Closet” is ostensibly about a young woman’s journey to Paris, the descriptive detail borrows language and images from Cartesian coordinate geometry, dualistic philosophy, neuroanatomy (the pineal), and projections of three dimensions onto planes. This mathematical universe is counterpointed in the natural language of the suppressed love story that locates the real in the human. Thus, at the heart of the story is the tension between competing notions of mathematics, i.e., as either an independent realm apart from history or as a culturally produced and historical set of practices. Of course, the central character proves …

Disciple, Jessica K. Sklar

Journal of Humanistic Mathematics

This is a love poem for mathematics.

They Say She Was Good -- For A Woman: Poetry And Musings, Joanne Growney

Journal of Humanistic Mathematics

These pages contain ideas and verses that consider the roles of women in mathematics. Details of the life of Amalie “Emmy” Noether inspired a poem and the poem, in turn, led to the poet’s growth and awareness of her self and her voice.

Inquiry Based Learning From The Learner’S Point Of View: A Teacher Candidate’S Success Story, Caroline Johnson Caswell, Derek J. Labrie

Journal of Humanistic Mathematics

The goal of this paper is to review current research on Inquiry Based Learning (IBL) and shed some light, from a student's perspective, on the challenges and rewards of this pedagogy. The first part of the article provides an extensive review of the literature on IBL. The second part focuses on one student's experiences in an IBL classroom.

In particular, a graduate secondary mathematics student reflects upon his experiences in a college mathematics class where the instructor implemented an Inquiry Based Learning model. His experience is validated by current research on IBL educational methodology which structures the classroom environment for …

Ready, Set, Learn, Michael G. Wright

Masters Essays

No abstract provided.

An Introduction To Topology For The High School Student, Nathaniel Ferron

Masters Essays

No abstract provided.

How The Use Of Subjectivist Instructional Strategies In Teaching Multiple Sections Of An Eighth Grade Algebra Class In Guyana Relates To Algebra Achievement And Attitude Changes Toward Mathematics, Jennifer Hoyte

FIU Electronic Theses and Dissertations

In Guyana, South America, the Ministry of Education seeks to provide universal, inclusive education that prepares its citizens to take their productive places in society and to creatively solve complex, real-world problems. However, with frequent national assessments that are used to place students in high school, college or into jobs, teachers resort to using familiar strategies such as lecture, recitation and test drilling. Despite their efforts, over 56% of students are failing the Grade 6 assessments, 43% failing 10th grade Mathematics and over 60% failing college algebra courses. Such performance has been linked to students’ lower academic self-concept and their …

Finding Fibonacci: The Quest To Rediscover The Forgotten Mathematical Genius Who Changed The World (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World by Keith Devlin. Princeton, NJ: Princeton University Press, 2017. 256 pp. ISBN: 9780691174860.

Mathematical Competencies Of Third Level Students: A Review, Colm Mcguinness

The ITB Journal

Many lecturers of mathematics and related disciplines in Ireland and internationally believe there has been a gradual decline in mathematical competencies of students presenting for first year at third level educational establishments. Some of the evidence to support this view is reviewed, along with the types of solutions being applied in Ireland and the UK. Attention is drawn to the explicit and implicit decline in standards potentially associated with some of the solutions, particularly for short courses involving mathematics.

Student-Created Test Sheets, Samuel Laderach

Honors Projects

Assessment plays a necessary role in the high school mathematics classroom, and testing is a major part of assessment. Students often struggle with mathematics tests and examinations due to math and test anxiety, a lack of student learning, and insufficient and inefficient student preparation. Practice tests, teacher-created review sheets, and student-created test sheets are ways in which teachers can help increase student performance, while ridding these detrimental factors. Student-created test sheets appear to be the most efficient strategy, and this research study examines the effects of their use in a high school mathematics classroom.

Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay

Zea E-Books Collection

Scholars of all stripes are turning their attention to materials that represent enormous opportunities for the future of humanistic inquiry. The purpose of this book is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. This book is a primer for developing the skills to enable humanist scholars to address complicated technical material with confidence. This book, to put it plainly, is concerned with the things that the author of a technical article knows, but isn’t saying. Like any field, mathematics operates …

The Value Of A Win: Analysis Of Playoff Structures, Matthew Orsi

Honors Projects in Mathematics

The purpose of this Senior Capstone project is to analyze the distinctions between existing playoff systems. In particular, we are looking to analyze the differences between the standard single-elimination tournament (which the NCAA has used since the inception of the tournament) and other potential options: double-elimination and multiple game series. Popular sports such as Major League Baseball and the National Basketball Association all use multiple game series for their playoffs. This project will use probability theory and simulation to determine the likelihood of different seeds winning a championship as well as the expected number of victories by seed in each …

A Study Of Perceptions Of Math Mindset, Math Anxiety, And View Of Math By Young Adults, Tami L. Hocker

Doctor of Education (Ed.D)

This study’s purpose was to determine whether instruction in growth math mindset led to change in perceptions of 18-22-year-old at-risk students in math mindset, math anxiety, and view of math. The experimental curriculum was created by the researcher with the guidance of experts in mathematics and education and focused on the impact of brain growth and learning supported by positive math mindset. Young adult public charter high school at-risk students were surveyed before and after completion of the experimental intervention to measure their perceptions in the domains of Math Mindset, Math Anxiety, and View of Math. The results revealed significant …

Application Of Inverse Problems In Imaging, Xiaoyue Luo

Post-Grant Reports

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield …

2017: "From Sea To Shining Sea: Looking Ahead With The National Park Service", Abhay Gupta '18, James Wei '18, Istvan Kovach '18, Shyam Sai '18, Darius Hong '18

Distinguished Student Work

There is a natural inclination for humanity to view the Earth as our steadfast, never-changing home. After all, it seems as permanent as the ground beneath our feet. However, nothing could be further from the truth, especially in today’s rapidly changing climes. Global temperatures are on the rise, and with them comes an increase in sea levels, wildfires, and hurricanes, three serious, expensive issues. Unfortunately for the National Park Service (NPS), who guard ninety-seven coastal units, coastlines are especially vulnerable to such problems. Thus, the NPS must take extra precautions and expenditures to maintain and protect them. With limited budget, …

2017: "Park2vec: A Vector Representation Of Our National Parks’ Climate Change Susceptibility", William Tong '17, Ankit Agarwal '17, George Moe '17, Aakash Lakshmanan '17

Distinguished Student Work

With over 400 units, between them covering almost 850 million acres of carefully preserved land, the National Park Service (NPS) acts as steward to the nation’s natural treasures. In the move to the Twenty-First century, the NPS faces numerous looming challenges, particularly those related to a rapidly changing climate. It was our task to strategize with the Service in addressing three such issues, leveraging our experience in mathematical modelling and data analysis to aid them in the quest to protect and to preserve.

The first problem under consideration was determining the risk associated with sea-level change for five different coastal …

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Libraries' Newsletters

No abstract provided.

Badiou’S Logics: Math, Metaphor, And (Almost) Everything, Vladimir Tasic

Journal of Humanistic Mathematics

Mathematics plays a central role in the philosophical system of Alain Badiou. The aim of this essay is to situate this appeal to mathematics in the broader context of his work, including its literary and political elements.

On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao

Senior Independent Study Theses

Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.

Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

In the history of the Missouri Section of the MAA, some of the more interesting people who influenced the growth and development of the section through the years were and are women. In this chapter, we discuss the contributions of a few (certainly not all) of these women to the Missouri Section and mathematics as a whole, including Emily Kathryn Wyant (founder of KME), Margaret F. Willerding (who dealt with sexism in the 1940s), Maria Castellani (an official in Mussolini’s Italy before coming to America), and T. Christine Stevens (co-founder of Project NExT). Without them, and others like them, both …

Spectrally Similar Incommensurable 3-Manifolds, David Futer, Christian Millichap

Faculty Publications

Reid has asked whether hyperbolic manifolds with the same geodesic length spectrum must be commensurable. Building toward a negative answer to this question, we construct examples of hyperbolic 3–manifolds that share an arbitrarily large portion of the length spectrum but are not commensurable. More precisely, for every n ≫ 0, we construct a pair of incommensurable hyperbolic 3–manifolds N_n and N^µ_n whose volume is approximately n and whose length spectra agree up to length n.

Both N_n and N^µ_n are built by gluing two standard submanifolds along a complicated pseudo-Anosov map, ensuring that …

Mutations And Short Geodesics In Hyperbolic 3-Manifolds, Christian Millichap

Faculty Publications

In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in their respective commensurability classes by analyzing their cusp shapes.

The knot complements in each class differ by a topological cut-and-paste operation known as mutation. Ruberman has shown that mutations of hyperelliptic surfaces inside hyperbolic 3-manifolds preserve volume. Here, we provide geometric and topological conditions under which such mutations also preserve the initial (complex) length spectrum. This work requires us to analyze when least …

Math And Physics Activities, Maureen Miller, Hope Bragg, Christy Keefer

Integrated Math & Social Studies Lessons

Mathematics is at the core of the Hidden Figures story. These women were united by their passion for the field of mathematics. Society often portrays that there are “bad” math students, those that struggle with calculations and applications. The structure of these activities, pairing of students, permits students to support each other in working through the problems. The video clip allows students to establish connections between mathematical calculations and scientific concepts. The physics problems that students complete are motion problems that beginning rocket engineers would have solved to determine how high their rocket flew.