Other Mathematics Commons^™

The Eight Monarchs (Some Mathematical Magic), Jeremiah Farrell, Eric Nelson

Scholarship and Professional Work - LAS

The eight Monarchs are the four Kings and four Queens of an ordinary deck of cards. We can perform our magic without a deck by using the grid below with the K-Q token ( a coin can be used instead if one wishes).

The Effect: The magician's back will be turned while Mark, the subject, places the token on one of the suit nodes. Mark is to remember this starting position. Then Mark makes a sequence of moves; a move being one of four possibilities: a horizontal move, a vertical move, or a diagonal move to a new node or …

Cube Mentalism, Jeremiah Farrell, Ivan Moscovich

Scholarship and Professional Work - LAS

Our tour of multidimensional cubes begins with the marking of the eight comers of a 3-cube with the eight words HOT, POT, POD, HOD, HAD, HAT, PAT, and PAD. The figure below shows how these eight inherit the labels of the HOT-PAD).die where the letter H is opposite P, the letter O is opposite T and the letter T is opposite the letter D...

The Stenographic Affine Plane, Oscar Thumpbindle, Jeremiah Farrell

Scholarship and Professional Work - LAS

This square, composed of familiar words, is semimagic because any row or column (the rook sweeps) anagrams into STENOGRAPHIC. "Semi" means the diagonals don't. However, there are four very special diagonals; those that have words with one of the four vowels of STENOGRAPHIC in common. These four bishop sweeps will be important later. Keeping with the chess piece theme, the reader will take notice of the knight 4-tours using the consonants P, H, Rand C. For example one of these is the P-tour SAP, PEG, PIN and TOP. Another set of knight tours traces the letters S, T, G and …

Prague Six, Jeremiah Farrell

Scholarship and Professional Work - LAS

Draft of the 'Solution Page' for Jeremiah's puzzle "Prague Six", which was exchanged at the 2008 Prague International Puzzle Party. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exhange them. This puzzle is also mass produced by Kadon Enterprises as "Chasing Squares".

The Magic Octagon, Jeremiah Farrell, Tom Rodgers

Scholarship and Professional Work - LAS

The black nodes mark the corners of an octagon and each of these nodes in connected to four others by lines. The (rather hard) puzzle is to assign the sixteen numbers 0 through 15 to each of the sixteen lines so that each black node has a sum of 30 when the line numbers leading into it are added.

The word version of the puzzle was described in the article "Most-Perfect Word Magic", Oscar Thumpbindle, Word Ways Vol. 40(4). Nov. 2007.

Bailey's Hexameters, Jeremiah Farrell, Al Shapiro

Scholarship and Professional Work - LAS

Nat. Bailey was the most important English lexicographer before Samuel Johnson. Our interest in this essay is to report on some of the 1730 dictionary's entries for the "Entertainmen of the Curious".

The First Gathering, Jeremiah Farrell

Scholarship and Professional Work - LAS

The following is a photocopy of a letter I sent to my good friend James P. Fink shortly after the first Gathering in 1993. It is not reqritten or edited in any way in hopes of conveying to you some sense of my awe at how very special this event really way. My son David, then a student in Boston, was also privileged to be invited by Tom Rodgers and David and I still feel overwhelmed by the experience.

There are so many memories- and so many friends. After you have read the letter, I will remark on some of …

The Magic Octahedron, Jeremiah Farrell

Scholarship and Professional Work - LAS

An octahedral die has several advantages over its cubic cousin, not the least of which is its ability to magically model a four dimensional tesseract. We will use a four coloring of the die to illustrate the magic.

Dynamic Web Tools For Trigonometry, Steven J. Wilson

Innovations in Math Technology

In the last 20 years, computer technology having mathematical capability has been developed, improved, and become widely available, but textbook presentations are still largely free of any discussion that might require technology. Technology could be used in mathematical instruction for student drill and practice, for instructor demonstrations that promote conceptual understanding, or for the exploration of mathematical ideas, but software is often designed to be pedagogically generic, leaving its use to the creativity of the instructor. Technological solutions for local machines can be quite extensive, but cost and time constraints then limit availability for student use. The internet has the …

On The Reproducing Kernel Hilbert Spaces Associated With The Fractional And Bi-Fractional Brownian Motions, Daniel Alpay, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting we consider.

Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan

Engineering Faculty Articles and Research

Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the presheaf semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate …

Sir Francis Galton, Sandra J. Peart, David M. Levy

Jepson School of Leadership Studies articles, book chapters and other publications

Cousin to Charles Darwin and a talented statistician, Sir Francis Galton had an influence on social science that was profound. His major contributions to mathematical statistics included the initial development of quantiles and linear regression techniques. Along with F. Y. Edgeworth and Karl Pearson, he developed general techniques of multiple regression and correlation analysis, statistical devices that serve as substitutes for experiments in social science. Galton had a major impact on economics, and with W. R. Greg, was instrumental in creating the “science” of eugenics.

The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza

MPP Published Research

Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …

Rational Functions Associated To The White Noise Space And Related Topics, Daniel Alpay, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida’s white noise space. The Fueter polynomials are replaced by a basis computed in terms of the Hermite functions, and the Cauchy-Kovalevskaya product is replaced by the Wick product.

A Characterization Of Schur Multipliers Between Character-Automorphic Hardy Spaces, Daniel Alpay, M. Mboup

Mathematics, Physics, and Computer Science Faculty Articles and Research

We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.

Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a paradigm shift is essential in this computerized …

N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …

Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Octahedral Dice, Todd Estroff, Jeremiah Farrell

Scholarship and Professional Work - LAS

All five Platonic solids have been used as random number generators in games involving chance with the cube being the most popular. Martin Gardenr, in his article on dice (MG 1977) remarks: "Why cubical?... It is the easiest to make, its six sides accomodate a set of numbers neither too large nor too small, and it rolls easily enough but not too easily."

Gardner adds that the octahedron has been the next most popular as a randomizer. We offer here several problems and games using octahedral dice. The first two are extensions from Gardner's article. All answers will be given …