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Can We Preserve Physically Meaningful "Macro" Analyticity Without Requiring Physically Meaningless "Micro" Analyticity?, Olga Kosheleva, Vladik Kreinovich 2020 University of Texas at El Paso

Can We Preserve Physically Meaningful "Macro" Analyticity Without Requiring Physically Meaningless "Micro" Analyticity?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Physicists working on quantum field theory actively used "macro" analyticity -- e.g., that an integral of an analytical function over a large closed loop is 0 -- but they agree that "micro" analyticity -- the possibility to expand into Taylor series -- is not physically meaningful on the micro level. Many physicists prefer physical theories with physically meaningful mathematical foundations. So, a natural question is: can we preserve physically meaningful "macro" analyticity without requiring physically meaningless "micro" analyticity? In the 1970s, an attempt to do it was made by using constructive mathematics, in which only objects generated by algorithms are allowed. This did ...


Several Years Of Practice May Not Be As Good As Comprehensive Training: Zipf's Law Explains Why, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich 2020 University of Texas at El Paso

Several Years Of Practice May Not Be As Good As Comprehensive Training: Zipf's Law Explains Why, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many professions practice certifications as a way to establish that a person practicing this profession has reached a certain skills level. At first glance, it may sound like several years of practice should help a person pass the corresponding certification test, but in reality, even after several years of practice, most people are not able to pass the test, while after a few weeks of intensive training, most people pass it successfully. This sounds counterintuitive, since the overall number of problems that a person solves during several years of practice is much larger than the number of problems solved during ...


Explicit Ambient Metrics And Holonomy, Ian M. Anderson, Thomas Leistner, Pawel Nurowski 2020 Utah State University

Explicit Ambient Metrics And Holonomy, Ian M. Anderson, Thomas Leistner, Pawel Nurowski

Mathematics and Statistics Faculty Publications

We present three large classes of examples of conformal structures whose Fefferman-Graham ambient metrics can be found explicitly. Our method for constructing these examples rests upon a set of sufficiency conditions under which the Fefferman-Graham equations are assured to reduce to a system of inhomogeneous linear partial differential equations. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic co-rank 3 distributions in dimensions 5 and 6.Our examples illustrate various aspects of the ambient metric construction.

The holonomy algebras of our ambient metrics are studied in detail. In particular, we exhibit a large class ...


A (2+1)-Dimensional Sine-Gordon And Sinh-Gordon Equations With Symmetries And Kink Wave Solutions, Gangwei Wang, Kaitong Yang, Haicheng Gu, Fei Guan, A. H. Kara 2020 The University of Texas Rio Grande Valley

A (2+1)-Dimensional Sine-Gordon And Sinh-Gordon Equations With Symmetries And Kink Wave Solutions, Gangwei Wang, Kaitong Yang, Haicheng Gu, Fei Guan, A. H. Kara

Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and travelingwave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived.


Arithmetic Of Binary Cubic Forms, Gennady Yassiyevich 2020 The Graduate Center, City University of New York

Arithmetic Of Binary Cubic Forms, Gennady Yassiyevich

All 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.


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 2020 The Graduate Center, City University of New York

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

All 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 ...


Job Announcement: Guillford College Is Hiring A Chair For Its Mathematics Department, Mark Dixon 2020 Guillford College

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 2020 University of Leeds, U.K.

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 2020 Seton Hill University

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 2020 University of Strathclyde

The Master Oiler, Ernesto Estrada

Journal of Humanistic Mathematics

No abstract provided.


Sigint Signifier, Terry Trowbridge 2020 York University

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 2020 Saint Mary's University - Canada

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 2020 Student, Cal State Fullerton

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 2020 Indiana University South Bend

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 2020 The University of Texas at El Paso

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 2020 UC Berkeley

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 2020 Bar-Ilan University

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 ...


Simple Arithmetic: Heavy On Butter, Cream, Wine, Sarah Voss 2020 Claremont Colleges

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 2020 Pomona College

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 2020 The Catholic University of America

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.


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