Mathematics Commons^™

Abstraction And Epistemic Economy, Marco Panza

MPP Published Research

Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning …

Records Of The Brooklyn College Mathematics Department, Brooklyn College

Finding Aids

This collection consists largely of handwritten grade books from Brooklyn College’s earliest years. Much of it also relates to the Math Department’s extracurricular activities such as contests. There are only two Subgroups in the collection: Notebooks: Records of Classes in Mathematics 1926 – 1976, and Department of Mathematics General Information.

Pandey's Method Of Cube Root Extraction: Is It Better Than Aryabhata’S Method?, Deepak Basyal

Mathematics and Statistics

We compare two methods of cube root extraction: one proposed by the Nepali mathematician Gopal Pandey in the 19th century, which uses proportionality, and another one provided by the Indian mathematician and astronomer Aryabhata.

Exploring Consciousness Through The Qualitative Content Of Equations, Ashok Narasimhan, Menas C. Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

The majority of the focus on equations in physics has been on the mathematical and computational aspects. Here we focus on the qualitative content of what the relationships expressed in equations imply. In some sense, we are asking foundational questions about the ontology of equations.

Mathematical Frameworks For Consciousness, Menas C. Kafatos, Ashok Narasimhan

Mathematics, Physics, and Computer Science Faculty Articles and Research

If Awareness is fundamental in the universe, mathematical frameworks are better suited to reveal its fundamental aspects than physical models. Awareness operates through three fundamental laws which apply at all levels of reality and is characterized by three universal powers. We explore and summarize in general terms mathematical formalisms that may take us as close as possible to conscious awareness, beginning with the primary relationships between the observer with the observed, using a Hilbert space approach. We also examine insights from category theory, and the calculus of indications or laws of forms. Mathematical frameworks as fundamental languages of our interaction …

The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni

MPP Published Research

The indispensability argument (IA) comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and …

The Mathematics And Applications Behind Image Warping And Morphing, Tanvir Prince, Maria Malik, Ildefonso Salva, Ariel Mazor, Sakhr Aldaylam

Publications and Research

This research is conducted in the summer of 2015 and is possible by the support of various agency, in particular, by the grant of Prof. Angulo Nieves and the New York City Research Initiative.

The purpose of this research is to reveal the mathematics and applications of the computer animation techniques of warping and morphing. A warp is a twist or distortion in the form of an object in an image while a morph is the smooth and gradual transformation of an object in one image into the object in another image. Linear algebra makes these computer animation techniques possible; …

Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Learn about our experiences co-teaching a K–8 methods course using 1:1 tablets in a high-tech lab. This innovative course included a move away from a textbook to a dynamic research-based curriculum supported by NCTM resources and CCSSM as well as integral utilization of apps, web 2.0 tools, and professional learning networks.

Manzanar Murakami As Radical Mathematician, Logan Bishop-Van Horn

Scholarly Undergraduate Research Journal at Clark (SURJ)

In Karen Tei Yamashita’s Tropic of Orange, characters attempt to make meaning of the many complex structures in which they are situated. In his unique meaning-making process, Manzanar Murakami, a homeless Sansei, “conducts” the Los Angeles traffic with a silver baton from atop a highway overpass. In conducting his music, Murakami per- forms complex mathematics, finding meaning in connection by mapping the rhythmic flow of humans, machines, and goods. Through his baton, to the sounds of a beautiful orchestra, he translates precisely the relationships he sees before him. Murakami’s music and Yamashita’s fantastic images constitute a “mathematical realism,” a lens …

The Topology Of Absence, Nora E. Culik

Journal of Humanistic Mathematics

“The Topology of Absence” literalizes triangulations, hyperbeloids, and the concept of the limit in the story of “locating” a lost mother. This story, like “The Physicist’s Basement” in the July 2014 issue, is part of a series that worries about competing notions of mathematics, i.e., mathematics as some sort of disembodied configuration or as emergent in the material reality of human life.

Mathematical Double Dactyls, Tristan Miller

Journal of Humanistic Mathematics

No abstract provided.

A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look

Journal of Humanistic Mathematics

The aim of this paper is to showcase a handful of mathematical challenges found in classical literature and to offer possible ways of integrating classical literature in mathematics lessons. We analyze works from a range of authors such as Jules Verne, Anton Chekhov, and others. We also propose ideas for further tasks. Most of the problems can be restated in terms of simple mathematical equations, and they can often be solved without a computer. Nevertheless, we use the computer program Mathcad to solve the problems and to illustrate the solutions to enhance the reader’s mathematical experience.

Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, Hourya Benis Sinaceur, Marco Panza, Gabriel Sandu

MPP Published Research

This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive …

Review Of Developing Quantitative Literacy Skills In History And The Social Sciences: A Web-Based Common Core Approach By Kathleen W. Craver, Victor J. Ricchezza, H L. Vacher

Numeracy

Kathleen W. Craver. Developing Quantitative Literacy Skills in History and Social Sciences: A Web-Based Common Core Standards Approach (Lantham MD: Rowman & Littlefield Publishing Group, Inc., 2014). 191 pp.
ISBN 978-1-4758-1050-9 (cloth); ISBN …-1051-6 (pbk); ISBN…-1052-3 (electronic).

This book could be a breakthrough for teachers in the trenches who are interested in or need to know about quantitative literacy (QL). It is a resource providing 85 topical pieces, averaging 1.5 pages, in which a featured Web site is presented, described, and accompanied by 2-4 critical-thinking questions purposefully drawing on data from the Web site. The featured Web sites range from …

Mathematics And Humor: John Allen Paulos And The Numeracy Crusade, Paul H. Grawe

Numeracy

John Allen Paulos at minimum gave the Numeracy movement a name through his book Innumeracy: Mathematical Illiteracy and Its Consequences. What may not be so obvious was Paulos’ strong interest in the relationship between mathematics and mathematicians on the one hand and humor and stand-up-comedian joke structures on the other. Innumeracy itself could be seen as a typically mathematical Gotcha joke on American culture generally. In this perspective, a Minnesotan acculturated to Minnesota-Nice Humor of Self-Immolation Proclivities (SImP) looks at the more raw-boned, take-no-prisoners humor style Paulos outlined in Mathematics and Humor and implemented in Innumeracy.

Despite the …

What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin

Publications and Research

For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies …

Wallis On Indivisibles, Antoni Malet, Marco Panza

MPP Published Research

The present chapter is devoted, first, to discuss in detail the structure and results of Wallis’s major and most influential mathematical work, the Arithmetica Infinitorum (Wallis 1656). Next we will revise Wallis’s views on indivisibles as articulated in his answer to Hobbes’s criticism in the early 1670s. Finally, we will turn to his discussion of the proper way to understand the angle of contingence in the first half of the 1680s. As we shall see, there are marked differences in the status that indivisibles seem to enjoy in Wallis’s thought along his mathematical career. These differences correlate with the changing …

Newton On Indivisibles, Antoni Malet, Marco Panza

MPP Published Research

Though Wallis’s Arithmetica infinitorum was one of Newton’s major sources of inspiration during the first years of his mathematical education, indivisibles were not a central feature of his mathematical production.

Practical Applications Of An Integrally Christian Approach To Teaching Mathematics, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Descriptions of various frameworks and approaches to integrating Christian faith in the mathematics classroom are explored, as well as examples and techniques. In particular, a subject-centered approach is advocated in contrast to the traditional teacher-centered approach or, more recently, the student-centered approach.

Designing For Mistrust, Eric Gossett

ACMS Conference Proceedings 2015

The 2014 ACM North Central Region programming contest contained a problem about a group of v bandits who want to use multiple locks to seal their treasure and distribute keys in such a way that no group of less than m bandits can open all the locks. The problem asks for an algorithm that will determine the number of locks needed for any set of parameters (v, m). I will present an analytic solution that produces a minimum number of locks, a recurrence relation solution, and a constructive algorithm that can print out a table showing the …

The Mathematics Of Evolution, Steven R. Lay

ACMS Conference Proceedings 2015

Like many universities, Lee University has a non-major’s course for liberal arts students. The course typically includes a potpourri of topics: logical thinking, scientific notation, linear functions, estimation, and probability. At Lee, we have found a way to conclude the course that applies these varied topics to an issue designed to engage student interest and promote critical thinking. We have developed a series of three lessons on “The Mathematics of Evolution.” The first lesson is on radiometric dating. The second lesson is on the origin and progression of life. And the third lesson deals with the nature of the DNA …

A Triune Philosophy Of Mathematics, Dusty Wilson

ACMS Conference Proceedings 2015

What is mathematics and is it discovered or invented? The Humanist, Platonist, and Foundationalist each provide answers. But are the options within the philosophy of mathematics so limited? Rather than viewing and describing mathematics in a mutually exclusive manner, each of these approaches includes components of truth from a greater triune philosophy of mathematics. This talk will introduce this inclusive triune paradigm through which to explore fundamental questions about mathematics.

Software Engineering I: Teaching Challenges, Paul C. Grabow

ACMS Conference Proceedings 2015

The term software engineering can be traced to the late 1960s in response to large-scale, software development problems. Since then it has evolved as a discipline, both within industry and the academy. There have been distinct educational successes: “Standard practice” has matured (and found its way into more textbooks),the ACM and IEEE Computer Society have published curriculum guidelines, computer science programs commonly offer at least one software engineering course, and software engineering degrees (undergraduate or graduate) are more common. However, software engineering still presents a challenge. The term itself has become contorted by companies (and society in general); software has …

Mystery Of The Infinite: Developing A Mathematically Based Summer Scholars Program, Christopher Micklewright

ACMS Conference Proceedings 2015

For the past two years, the Templeton Honors College, at Eastern University, has been conducting a Summer Scholars Program for high school students. The program, which has offered courses in a variety of topics, brings students to campus for an intensive residential program, coupled with pre-program and post-program work, for which students can earn college credit. In summer 2014, I helped to develop a mathematically based course, to include rigorous study of discrete mathematics, as well as a variety of lectures and extracurricular activities integrating faith and philosophy with mathematics. In this presentation, I will give an overview of the …

The Best Religious Calendar, Andrew Simoson

ACMS Conference Proceedings 2015

Many religions have deep roots in the rhythms of the moon. And ever since at least the fifth century BC man has known that the moon repeats itself every n = 19 years. Is this integer valuen the best of all choices?Easter follows such a calendar. We briefly show that 19 is second best. And then we run time backwards, and give a rationale as to why a certain species of cicada has a life cycle of 17 years. The answer involves the moon, the Farey series, and Kepler’s laws of motion.

Math, God And Politics—A Fight Over Geometry In 19th Century Italy, Donna Pierce

ACMS Conference Proceedings 2015

In 1839 a polemic, reminiscent of the Renaissance public challenges over mathematical problems, was issued by the leader of the synthetic school of geometry, Vincent Flauti, to the analytical school, headed by Fortunato Padula. Three geometric problems were proposed, all carefully chosen to guarantee a victory for the synthetic school. The judges were from the Royal Academy of Sciences, men also favorable to the synthetic method. Why then did the analytics take up this challenge, and who were the real victors? This was not just a fight over the ‘correct’ way to do geometry, it was a fight over politics, …

Experiencing A Paradigm Shift: Teaching Statistics Through Simulation-Based Inference, Dave Klanderman, Mandi Maxwell, Nathan Tintle

ACMS Conference Proceedings 2015

For decades, statistics has been taught as an application of formulas, making use of normal and other distributions, and relying heavily on algebraic skills of students, in short, emphasizing mathematical thinking. More recently, several textbook author teams have published statistics books that place an increased emphasis on simulation and randomization methods, and a corresponding decreased emphasis on the algebraic manipulation in formulas (e.g., Lock et al., 2012; Tintle et al., 2015) as a way to encourage better statistical thinking.This session describes simulation-based inference curricula more fully, reports on the necessary steps towards implementation of such an approach, and provides both …

On Random Numbers And God’S Nature, James Bradley

ACMS Conference Proceedings 2015

I start with mathematical Platonism, an ancient stream of thought that views numbers as transcending physical reality. I join this to recent insights into mathematical randomness from theoretical computer science. Joining these streams – one ancient, one recent – yields the surprising conclusion that randomness, defined in a particular way, is part of the nature of God. I then explore some of the implications of this conclusion for our understanding of the doctrine of God’s infinitude.

Parables To A Mathematician, Melvin Royer

ACMS Conference Proceedings 2015

Jesus frequently used parables in His ministry, usually short narratives illustrating the outcomes of people’s choices. In John 3:12 and Matthew 13:10-15, He explained that one reason was to be sure that people who genuinely wanted to understand His message would be able to do so. Since most of His audience was familiar with an agrarian economy, Jesus spoke extensively of wheat, fish, trees, wine, debt, tenants, lamps, etc. Many people have speculated on parables Jesus might have used had He lived in a different society. This non-scholarly (but hopefully thought-provoking) talk will propose parables targeted toward groups of mathematicians …

God: One, Daniel Kiteck

ACMS Conference Proceedings 2015

I see the most mathematically significant verse as Deut. 6:4 where God says He is ONE. (And I don’t believe that it is an accident that the greatest commandment to love God with all we are immediately follows.) What is the concept of “one” in relationship to God? Is God dependent on the concept of “one?” What if “one” is ultimately always a comparison going back to God? God is also commonly viewed as infinite. How is this connected to our understanding of the mathematical continuum? Could this help us see how God is foundational both to discrete and continuous …