Other Mathematics Commons^™

The Mathematics Portfolio: An Alternative Tool To Evaluate Students’ Progress, Marla A. Sole

Publications and Research

This article describes the need for more thorough and varied forms of assessment to evaluate students’ level of understanding in mathematics. Portfolios are one type of assessment tool that, when added to a teacher’s repertoire can improve students’ comprehension and retention and enable students to monitor their own progress and to take more responsibility for their own learning. Portfolio assignments can also help students and teachers to detect and remedy weaknesses and misunderstandings and can increase students’ self-confidence in mathematics. This article discusses what a portfolio is, gives an example of a unit portfolio used in an undergraduate Finite Mathematics …

A Multidimensional Ruin Problem, S Ramasubramanian

Communications on Stochastic Analysis

No abstract provided.

Roots Of States, B V Rajarama Bhat

Communications on Stochastic Analysis

No abstract provided.

Lévy Processes Through Time Shift On Oscillator Weyl Algebra, Luigi Accardi, Habib Ouerdiane, Habib Rebei

Communications on Stochastic Analysis

No abstract provided.

A Vacuum-Adapted Approach To Quantum Feynman-Kac Formulae, Alexander C R Belton, J Martin Lindsay, Adam G Skalski

Communications on Stochastic Analysis

No abstract provided.

Multiple Q-Adapted Integrals And Itô Formula Of Noncommutative Stochastic Calculus In Fock Space, V P Belavkin, M F Brown

Communications on Stochastic Analysis

No abstract provided.

The Early Years Of Quantum Stochastic Calculus, R L Hudson

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For Random Matrices, Sourav Chatterjee, S R S Varadhan

Communications on Stochastic Analysis

No abstract provided.

Some Problems Involving Airy Functions, V S Varadarajan

Communications on Stochastic Analysis

No abstract provided.

An Interpolating Family Of Means, Rajendra Bhatia, Ren-Cang Li

Communications on Stochastic Analysis

No abstract provided.

Hilbert Von Neumann Modules, Panchugopal Bikram, Kunal Mukherjee, R. Srinivasan, V S Sunder

Communications on Stochastic Analysis

No abstract provided.

Bell's Inequality Violations: Relation With De Finetti's Coherence Principle And Inferential Analysis Of Experimental Data, Franco Fagnola, Matteo Gregoratti

Communications on Stochastic Analysis

No abstract provided.

From Velocities To Fluxions, Marco Panza

MPP Published Research

"Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."

Outer Restricted Derivations Of Nilpotent Restricted Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel

University Faculty and Staff Publications

In this paper we prove that every finite-dimensional nilpotent restricted Lie algebra over a field of prime characteristic has an outer restricted derivation whose square is zero unless the restricted Lie algebra is a torus or it is one-dimensional or it is isomorphic to the three-dimensional Heisenberg algebra in characteristic two as an ordinary Lie algebra. This result is the restricted analogue of a result of Tôgô on the existence of nilpotent outer derivations of ordinary nilpotent Lie algebras in arbitrary characteristic and the Lie-theoretic analogue of a classical group-theoretic result of Gaschütz on the existence of p-power automorphisms …

A Fast-Slow Analysis Of The Dynamics Of Rem Sleep, Victoria Booth, Cecilia G. Diniz Behn

Math Faculty Publications

Waking and sleep states are regulated by the coordinated activity of a number of neuronal population in the brainstem and hypothalamus whose synaptic interactions compose a sleep-wake regulatory network. Physiologically based mathematical models of the sleep-wake regulatory network contain mechanisms operating on multiple time scales including relatively fast synaptic-based interations between neuronal populations, and much slower homeostatic and circadian processes that modulate sleep-wake temporal patterning. In this study, we exploit the naturally arising slow time scale of the homeostatic sleep drive in a reduced sleep-wake regulatory network model to utilize fast-slow analysis to investigate the dynamics of rapid eye movement …

The Seaborgium Chemical Table, Jeremiah Farrell

Scholarship and Professional Work - LAS

The diagram is an example of a connected, cubic graph with its ten nodes labelled with the letters of SEABORGIUM, chemical element 106. Connected means it is in one piece and cubic means that each node has exactly three edges on it.

Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin

All HMC Faculty Publications and Research

I still recall my thrill and disappointment when I read Mathematical Carnival, by Martin Gardner. I was thrilled because, as my high school teacher had recommended, mathematics was presented in a playful way that I had never seen before. I was disappointed because it contained a formula that I thought I had "invented" a few years earlier. I have always had a passion for mental calculation, and the following formula appears in Gardner's chapter on "Lightning Calculators." It was used by the mathematician A. C. Aitken to mentally square large numbers.

Oyun: A New, Free Program For Iterated Prisoner’S Dilemma Tournaments In The Classroom, Charles H. Pence, Lara Buchak

Faculty Publications

Evolutionary applications of game theory present one of the most pedagogically accessible varieties of genuine, contemporary theoretical biology. We present here Oyun (oy-oon, http://charlespence.net/oyun), a program designed to run iterated prisoner's dilemma tournaments, competitions between prisoner's dilemma strategies developed by the students themselves. Using this software, students are able to readily design and tweak their own strategies, and to see how they fare both in round-robin tournaments and in “evolutionary” tournaments, where the scores in a given “generation” directly determine contribution to the population in the next generation. Oyun is freely available, runs on Windows, Mac, and Linux computers, …

Strongly Complete Logics For Coalgebras, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary set-functor is given and proven to be strongly complete under additional assumptions. We proceed in three parts.

Part I argues that sifted colimit preserving functors are those functors that preserve universal algebraic structure. Our main theorem here states that a functor preserves sifted colimits if and only if it has a finitary presentation by operations and equations. Moreover, the presentation of the …

Applications Of Extenics To 2d-Space And 3d-Space, Florentin Smarandache, Victor Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this article one proposes several numerical examples for applying the extension set to 2D- and 3D-spaces. While rectangular and prism geometrical figures can easily be decomposed from 2D and 3D into 1D linear problems, similarly for the circle and the sphere, it is not possible in general to do the same for other geometrical figures.