Other Mathematics Commons^™

Kate Jones – A Tribute, Karen Farrell, Jeremiah Farrell

Scholarship and Professional Work - LAS

Kate is also an accomplished recreational mathematician and poet. To try to match in a small way her creative ability, we offer three puzzle-games in her honor: O'BEIRNE's TRI-HEX, PAPPUS and "KATe JONES". These three are specific examples of (9,3) symmetric configurations. More generally an (n,r) configuration is a collection of n "points"and n "lines" subject to the following requirements:

Rl: Any two points belong to at most one line.

R2: Each line has r points, and each point belongs to r lines.

Time-Dependent Neutral Stochastic Functional Differential Equations Driven By A Fractional Brownian Motion, B Boufoussi, S Hajji, E Lakhel

Communications on Stochastic Analysis

No abstract provided.

On The Second Fundamental Theorem Of Asset Pricing, Rajeeva L Karandikar, B V Rao

Communications on Stochastic Analysis

No abstract provided.

A Stochastic Transport Theorem, Pedro Catuogno, Simão N Stelmastchuk

Communications on Stochastic Analysis

No abstract provided.

Solution Of The Dirichlet Problem For A Linear Second-Order Equation By The Monte Carlo Method, José Villa-Morales

Communications on Stochastic Analysis

No abstract provided.

Mean-Field Limit Versus Small-Noise Limit For Some Interacting Particle Systems, Samuel Herrmann, Julian Tugaut

Communications on Stochastic Analysis

No abstract provided.

Moments Estimates For Local Times Of A Class Of Gaussian Processes, Olga Izyumtseva

Communications on Stochastic Analysis

No abstract provided.

Probability Distributions And Orthogonal Polynomials Associated With The One-Parameter Fibonacci Group, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

Communications on Stochastic Analysis

No abstract provided.

Stochastic Integral Representations Of F-Selfdecomposable And F-Semi-Selfdecomposable Distributions, Nadjib Bouzar

Communications on Stochastic Analysis

No abstract provided.

Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of single valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets. We apply the concept of single valued neutrosophic sets, an instance of neutrosophic sets, to graphs. We introduce certain types of single valued neutrosophic graphs (SVNG) and investigate some of their properties with proofs and examples.

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.

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 …

On The Equivalence Of Probability Spaces, Daniel Alpay, Palle Jorgensen, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a general class of Gaussian processes W, indexed by a sigma-algebra F of a

general measure space (M,F, _), we give necessary and sufficient conditions for the validity

of a quadratic variation representation for such Gaussian processes, thus recovering _(A),

for A 2 F, as a quadratic variation of W over A. We further provide a harmonic analysis

representation for this general class of processes. We apply these two results to: (i) a computation

of generalized Ito-integrals; and (ii) a proof of an explicit, and measure-theoretic

equivalence formula, realizing an equivalence between the two approaches to Gaussian processes,

one …

Restricted Lie Algebras With Maximal 0-Pim, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel

University Faculty and Staff Publications

In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p ^MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced …

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.

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.

Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover

A Simple Introduction to Rates

Before beginning this section of handouts, students will be introduced to a variety of vocabulary words often associated with calculus. These words will be used in an intuitive sense only and will not have been formally defined. Vocabulary should include graphical terms such as continuous, increasing, decreasing, maximum and minimum points, concave up, concave down, and point of inflection. In addition, discussion of the concept of "rate of change" should begin. It should be mentioned that many quantities change – population, cost, and temperature, to name just a few. All that is specifically required at this point can be related …