Mathematics Commons^™

The Log-Exponential Smoothing Technique And Nesterov’S Accelerated Gradient Method For Generalized Sylvester Problems, N. T. An, Daniel J. Giles, Nguyen Mau Nam, R. Blake Rector

Mathematics and Statistics Faculty Publications and Presentations

The Sylvester or smallest enclosing circle problem involves finding the smallest circle enclosing a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov’s accelerated gradient method, we present an effective numerical algorithm for solving these problems.

Unions Of Lebesgue Spaces And A1 Majorants, Greg Knese, John E. Mccarthy, Kabe Moen

Mathematics Faculty Research

We study two questions. When does a function belong to the union of Lebesgue spaces, and when does a function have an A1 majorant? We provide a systematic study of these questions and show that they are fundamentally related. We show that the union ofLwp(ℝn)spaces withw∈Apis equal to the union of all Banach function spaces for which the Hardy–Littlewood maximal function is bounded on the space itself and its associate space.

Pythagoras Plays His Lyre, Sarah Glaz

Journal of Humanistic Mathematics

A poem about the Pythagoreans' beliefs and way of life.

Pension Building, Washington Dc, E Laura Golberg

Journal of Humanistic Mathematics

No abstract provided.

Jay Leno And Abstract Algebra, Adam Glesser, Martin Bonsangue

Journal of Humanistic Mathematics

The Jay Leno skit Jaywalking, showing ordinary people struggling to answer basic questions, is both entertaining and applicable to teaching. This article describes how an instructor can strengthen students' conceptual understanding by creating an element of confusion, or "cognitive dissonance," in the students' minds using Jaywalking-style interactions in the classroom.

Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.

A Meeting Of Minds: An Alternate Humor For Teaching Mathematics To Non-Stem Majors, Paul H. Grawe

Journal of Humanistic Mathematics

John Allen Paulos argued essentially for three forms of humor dear to mathematics: Incongruity, Gotcha, and Word Play. Unfortunately, these three are often combative forms and easily drive non-STEM majors out of mathematics and statistics.

William Dunham in The Mathematical Universe shows how a fine mathematician can use humor to draw non-specialists in. Central to Dunham’s success is his use of Sympathetic Pain humor, which creates softer synthetic Reconciler, Consoler, or Bridgebuilder humor styles.

What If?: Mathematics, Creative Writing, And Play, Emily Clader

Journal of Humanistic Mathematics

Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.

The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam

Journal of Humanistic Mathematics

Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed …

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

Kaleidoscopes, Chessboards, And Symmetry, Tricia M. Brown

Journal of Humanistic Mathematics

This paper describes the n-queens problem on an n by n chessboard. We discuss the possible symmetries of n-queens solutions and show how solutions to this classical chess question can be used to create examples of colorful artwork.

A Beautiful Proof By Induction, Lars-Daniel Öhman

Journal of Humanistic Mathematics

The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

Some Results On Analysis And Implementation Of Hc-128 Stream Cipher., Shashwat Raizada Dr.

Doctoral Theses

The HC-128 stream cipher is a successful entrant in the eStream candidate list (software profile) and is the lighter variant of HC-256 stream cipher. Apart from the analysis by the designer of the cipher (Hongjun Wu) to conjecture the security of this cipher, there are only a few other observations on this cipher despite being the focus of researchers during the three phases of eStream evaluation and later efforts in the community. Till date none of the security claims in favor of HC-128 by the designer could be broken. One may expect HC-128 stream cipher to be popular in commercial …

Alan Turing: The Man Behind The Machine, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

An Introduction To Differential Geometry Through Computation, Mark E. Fels

Mathematics and Statistics Faculty Presentations

No abstract provided.

Large Outgoing Solutions To Supercritical Wave Equations, Marius Beceanu, Sover Avy

Mathematics and Statistics Faculty Scholarship

We prove the existence of global solutions to the energy-supercritical wave equation in R^{3+1} u_{tt}-\Delta u + |u|^N u = 0, u(0) = u_0, u_t(0) = u_1, 4

Sexual Assault And The Doctrine Of Chances In The Courtroom, Ryan Wallentine

Research on Capitol Hill

Sexual assault can have devastating and long-lasting effects on victims, but many assailants get away with their crime without being prosecuted.

The doctrine of chances is a rule of evidence allowing evidences of past crimes, wrongs, or acts to show it is unlikely a defendant would be repeatedly and innocently involved in similar, suspicious circumstances.

Given that about 63.3% of assailants are repeat offenders, the doctrine of chances could effectively be used in sexual assault cases.

The main objective is to determine a precise probabilistic threshold for allowing the use of the doctrine of chances in sexual assault cases such …

An Introduction To Differential Geometry Through Computation, Mark E. Fels

Textbooks

The outline of the book is as follows. Chapter 1 reviews some basic facts about smooth functions from IRⁿ to IR^m, as well as the basic facts about vector spaces, basis, and algebras. Chapter 2 introduces tangent vectors and vector fields in IRⁿ using the standard two approaches with curves and derivations. Chapter 3 reviews linear transformations and their matrix representation so that in Chapter 4 the push-forward as an abstract linear transformation can be defined and its matrix representation as the Jacobian can be derived. As an application, the change of variable formula for vector …

Application Of Combinatorial Structures In Wireless Communication., Samiran Bag Dr.

Doctoral Theses

Wireless communication has a compelling need in today’s world. This need is driven by the sudden surge in the demand of ad-hoc networks like wireless sensor networks. These networks consist of many isolated devices called nodes that use the wireless medium for communication. There are three security notions attached to any wireless communication. These are data confidentiality, data integrity and data availability. Cryptographic protocols are required for achieving the first two notions which in turn require shared secret keys. The last notion viz. data availability mainly deals with protecting the data from ‘denial of service attack’.In this thesis, we apply …

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 …