Mathematics Commons^™

Delaunay Surfaces Expressed In Terms Of A Cartan Moving Frame, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Delaunay surfaces are investigated by using a moving frame approach. These surfaces correspond to surfaces of revolution in the Euclidean three-space. A set of basic one-forms is defined. Moving frame equations can be formulated and studied. Related differential equation which depend on variables relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case in which the mean curvature is constant, these functions can be expressed in terms of Jacobi elliptic functions.

Arithmetic Of Binary Cubic Forms, Gennady Yassiyevich

Dissertations, Theses, and Capstone Projects

The goal of the thesis is to establish composition laws for binary cubic forms. We will describe both the rational law and the integral law. The rational law of composition is easier to describe. Under certain conditions, which will be stated in the thesis, the integral law of composition will follow from the rational law. The end result is a new way of looking at the law of composition for integral binary cubic forms.

Quasinormality Of Powers Of Commuting Pairs Of Bounded Operators, Raul E. Curto, Sang H. Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We study jointly quasinormal and spherically quasinormal pairs of commuting operators on Hilbert space, as well as their powers. We first prove that, up to a constant multiple, the only jointly quasinormal 2-variable weighted shift is the Helton-Howe shift. Second, we show that a left invertible subnormal operator T whose square T2 is quasinormal must be quasinormal. Third, we generalize a characterization of quasinormality for subnormal operators in terms of their normal extensions to the case of commuting subnormal n-tuples. Fourth, we show that if a 2-variable weighted shift W(α,β) and its powers W(α,β)(2,1) and W(α,β)(1,2) are all spherically quasinormal, …

Black And Brown Students’ Mathematics Anxiety In Elementary School: The Use Of Restorative Justice Circles And Critical Concepts Of Care, Hope, And Love, Mariana E. Winnik

Dissertations, Theses, and Capstone Projects

Children navigate their world and are constantly making meaning of their experiences. Through this meaning making, children are also constructing their identities. Black and Brown children have an added layer of identity construction compared to their White peers. Black and Brown students develop their racial identity in conjunction with multiple other identities. This paper focuses specifically on how Black and Brown students construct a "mathematics identity" that is meaningful to their racial identity in order to help lessen their mathematics anxiety. I argue that the use of Restorative Justice Circles (RJC) in classrooms will allow for students to bring their …

Classification Of Radial Solutions To Equations Related To Caffarelli–Kohn–Nirenberg Inequalities, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

This article studies the qualitative and quantitative properties of radial solutions to an elliptic equation related to the Euler–Lagrange equations for certain sharp Caffarelli–Kohn–Nirenberg inequalities. Namely, we examine the equation

−div(|x|aDu)=|x|bup, u>0, in RN, where p>1, N≥2, N−2+a≥0 and b>−N. The main results establish the properties of radially symmetric solutions including existence, uniqueness, and classification results as well as results on the asymptotic and intersecting behaviour of such solutions.

The Role Of The Asymmetric Ekman Dissipation Term On The Energetics Of The Two-Layer Quasi-Geostrophic Model, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

In the two-layer quasi-geostrophic model, the friction between the flow at the lower layer and the surface boundary layer, placed beneath the lower layer, is modeled by the Ekman term, which is a linear dissipation term with respect to the horizontal velocity at the lower layer. The Ekman term appears in the governing equations asymmetrically; it is placed at the lower layer, but does not appear at the upper layer. A variation, proposed by Phillips and Salmon, uses extrapolation to place the Ekman term between the lower layer and the surface boundary layer, or at the surface boundary layer. We …

Job Announcement: Guillford College Is Hiring A Chair For Its Mathematics Department, Mark Dixon

Journal of Humanistic Mathematics

Guilford College is looking to hire a leader and educator of vision to chair its mathematics department. The chair will have the opportunity to build a revolutionary mathematics program that invites all students into the joy, beauty, creativity, and vitality of mathematics.

Verba Volant, Scripta Manent, Tom Ward

Journal of Humanistic Mathematics

``Most people think typography is about fonts. Most designers think typography is about fonts. Typography is more than that, it's expressing language through type. Placement, composition, typechoice.'' (Mark Boulton)

What The Revolution Requires, Timons Esaias

Journal of Humanistic Mathematics

A flash fiction which addresses the coming revolution in the genre of Mathematical Fiction.

The Master Oiler, Ernesto Estrada

Journal of Humanistic Mathematics

No abstract provided.

Sigint Signifier, Terry Trowbridge

Journal of Humanistic Mathematics

This poem is a meditation on the concept of signal-to-noise ratios. What is the most minimal signal that can be decoded, regardless of the amount of noise?

The Empress's Nose: A Parable, After Feynman, Robert Dawson

Journal of Humanistic Mathematics

No abstract provided.

A Letter To Niccolò Fontana De Brescia, Jessica Huey

Journal of Humanistic Mathematics

A letter to Niccolò Fontana de Brescia from an undergraduate student.

Perfect (A Poem), Joseph Chaney

Journal of Humanistic Mathematics

This sonnet-length, unrhymed syllabic poem speaks of the way the concept of perfection engages the imagination of mathematicians, an experience it compares to the mysterious, complex attraction we may feel toward a lover.

Statistical Poetry, Lawrence M. Lesser

Journal of Humanistic Mathematics

This poetry folder consists of author reflection followed by his eight new poems related to statistics.

Book Review: Prime Suspects: The Anatomy Of Integers And Permutations By Andrew Granville And Jennifer Granville, Paolo Mancosu

Journal of Humanistic Mathematics

Prime Suspects is a delightful graphic novel that performs what might, prima facie, seem almost like an impossible feat. Apart from the aesthetic pleasure it provides by being a well-illustrated and well thought out graphic novel, I would describe its major conceptual goal to be that of conveying to its reader a taste of the exciting nature of mathematical discovery. This is accomplished by focusing on a set of results connecting the study of prime numbers, the study of cycles of permutations, irreducible polynomials in finite fields and more.

Mathematical Conquerors, Unguru Polarity, And The Task Of History, Mikhail Katz

Journal of Humanistic Mathematics

I compare several approaches to the history of mathematics recently proposed by Blåsjö, Fraser–Schroter, Fried, and others. I argue that tools from both mathematics and history are essential for a meaningful history of the discipline.

In an extension of the Unguru–Weil controversy over the concept of geometric algebra, Michael Fried presents a case against both Andr ́e Weil the “privileged observer” and Pierre de Fermat the “mathematical conqueror.” Here I analyze Fried’s version of Unguru’s alleged polarity between a historian’s and a mathematician’s history. I identify some axioms of Friedian historiographic ideology, and propose a thought experiment to gauge its …

Simple Arithmetic: Heavy On Butter, Cream, Wine, Sarah Voss

Journal of Humanistic Mathematics

The language of poetry is one way to offer perspective on ethical issues and social behavior. The language of mathematics is another. The piece herein combines both these ways.

On "Animals", Ql Converts, And Transfer - An Interview, Gizem Karaali, H. L. Vacher

Journal of Humanistic Mathematics

In March 2017, Gizem Karaali interviewed Len Vacher, the editor in chief of Numeracy, the flagship journal of the National Numeracy Network. This is the extended transcript of this conversation, which ranges from quantitative literacy to computational geology, from transfer of learned content and skills to interdisciplinary collaboration.

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.

My Last Fermat’S Last Theorem Talk, Richard Delaware

Journal of Humanistic Mathematics

From the dangerous snowfall preceding and nearly ending it, to the pleasant years-long fallout afterward, I tell the story of the events surrounding my final presentation of an expository talk on Fermat’s Last Theorem in the same year but months before Andrew Wiles announced his proof.

My Sets Are My Foundation, Andres Sanchez

Journal of Humanistic Mathematics

You might be wondering, what the hell does set theory have to do with writing? I’ll tell you a secret:\ everything is built on sets. Sets are things of beauty. They are great ways to conceptualize, compartmentalize, and classify the world and everything it encompasses. And now I know I’ve danced around the question of what sets have to do with my writing. So, here is my answer: I use set theory as the foundation for all of my writing.

Tired: A Reflection On Asceticism And The Value Of Quantitative Assessment, Frances Dean

Journal of Humanistic Mathematics

I have spent a lot of time thinking this past year and a half about the relationship between asceticism and success. As a mathematics student and a collegiate athlete, I have far too often gotten caught up in the pursuit of objective standards. This chase has left me burnt out and broken. Existential philosophy has been my greatest asset in discerning the true purpose of asceticism. I reflect on this journey and the nature of assessment in this short reflection.

Surviving Mathematics, Nathalie M. Luna

Journal of Humanistic Mathematics

In this essay written in an informal voice, the author shares the ups and downs of her experience in academia. She shares her motivation to study mathematics, her undergraduate experience in Puerto Rico, and her graduate experience in South Texas.

The Healing Powers Of Mathematics In The Age Of #Metoo, Veronica G. Sine

Journal of Humanistic Mathematics

The ideas of mathematics can provide metaphors to help people handle traumatic situations, or to better understand life experiences. In this short note, the author describes three ways in which the study of mathematics has given her ways to cope with her own difficult experiences.

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.

Tips For Undergraduate Research Supervisors, Stephan Ramon Garcia

Journal of Humanistic Mathematics

I was recently asked to contribute a paper to a forthcoming Foundations for Undergraduate Research in Mathematics (FURM) volume [1]. The article contained, in addition to several lengthy case studies, a list of brief recommendations for undergraduate research supervisors. Several colleagues suggested developing these general principles into a separate, self-contained article. This is that article.

Mathematical Cognition And The Arts, Marcel Danesi

Journal of Humanistic Mathematics

This article revisits the study of mathematics in the arts, and vice versa, the arts in mathematics, with a view to connecting mathematical and artistic creativity to the same neural circuits—a proposition put forward for mathematics and language in a critical 2000 book by Lakoff and Núñez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. This expanded perspective would open up suggestive avenues for connecting mathematics, language, and the arts as part of an imaginative blend that comes out in different forms but having the same underlying neural source. Whether or not this can be …

Mathematical Possibilities In Modernism: Can Literature Be A System?, Arka Chattopadhyay

Journal of Humanistic Mathematics

From Aristotle’s Poetics, literature and logic have been companions in approaching the hypothetical realm of the ‘what if.’ In this paper, I focus on the combinatorial possibilities of logic to see how mathematics becomes an important tool for the Modernist text’s aesthetic appeal to anti-representational and self-enclosed systemic autonomy. Is mathematical discourse autonomous vis-à-vis external reality? Can literary Modernism achieve textual autonomy that goes against realistic verisimilitude by following mathematical discourse? Though literary texts often negotiate formal systems with sophisticated governing logics, can literature itself become a logico-mathematical system? I trace the dialectic of form and system in the …

Why Our Hand Is Not The Whole Deck: Embrace, Acceptance, Or Use Of Limitations, Robert S.D. Thomas

Journal of Humanistic Mathematics

I investigate with examples limitations that mathematicians accept in research: aesthetic, scientific, and practical, in particular, on what bases such choices are made. Discussion is partly in terms of the ideal agents that Philip Kitcher and Brian Rotman used to analyse mathematical writing.