Physical Sciences and Mathematics Commons^™

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley

ACMS Conference Proceedings 2007

Enlightenment thinkers saw the universe as mechanistic and mathematics as the language in which the universe is written. They viewed mathematics as eternal, as transcending human minds, and as comprehensible by human beings. Thus mathematics, from their perspective, is our best tool for understanding the secrets of nature. This outlook was nicely summarized by Morris Kline: (Kline, 1953) In brief the whole world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine. From a Christian perspective, however, the Enlightenment outlook is flawed. It privileges …

Chaos Theory And Metaphysical (In) Determinism, Tim Rogalsky

ACMS Conference Proceedings 2007

This paper will begin by introducing the issues that arise from chaos theory for the Christian mathematician and scientist: What is at stake in this debate? It will then briefly review chaos theory, by means of two examples. It will then introduce the metaphysical interpretations given to chaos theory by three different scientist-theologians. The paper will conclude with a brief introduction to open theists, and analyze their use of chaos theory to supper their theological claims.

Objective Truth Versus Human Understanding In Mathematics And In Chess, Olle Häggström

The Mathematics Enthusiast

This paper begins with a review of the collection 18 Unconventional Essays on the Nature of Mathematics edited by Hersh (2006). Inspired especially by the contribution by Thurston to that collection, I then go on to discuss, by means of a couple of thought experiments involving computer "oracles", the nature of mathematics as a human activity, hopefully providing some balance to the simplified view (sometimes held by research mathematicians such as myself) of the discipline as purely a quest for objective truth.

Mathematics Education And Neurosciences: Relating Spatial Structures To The Development Of Spatial Sense And Number Sense, Fenna Van Nes, Jan De Lange

The Mathematics Enthusiast

The Mathematics Education and Neurosciences (MENS) project is aimed at exploring the development of the mathematical abilities of young (four- to six-year old) children. It is initiated to integrate research from mathematics education with research from educational neuroscience in order to come to a better understanding of how the early skills of young children can best be fostered for supporting the development of mathematical abilities in an educational setting. This paper is specifically focused on the design research that is being conducted from the perspective of mathematics education in which we are investigating the relationship between young children’s insight into …

Tme Volume 4, Number 2

The Mathematics Enthusiast

No abstract provided.

Non-Linear Functions In Secondary School Of Lower Qualification Level (German Hauptschule), Astrid Beckmann

The Mathematics Enthusiast

This article reports of the effectiveness of introducing non-linear functions in a German Hauptschule. Some research based recommendations are provided for practitioners with the goal of improving student competencies in lieu of PISA.

Editorial: New Horizons-Four Years Later, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Geodesic Flow On Global Holomorphic Sections Of Ts2, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

We study the geodesic flow on the global holomorphic sections of the bundle π : TS2 → S 2 induced by the neutral K¨ahler metric on the space of oriented lines of R 3 , which we identify with TS2 . This flow is shown to be completely integrable when the sections are symplectic, and the behaviour of the geodesics is described.

The Philosophy Of Mathematics, Values And Keralese Mathematics, Paul Ernest

The Mathematics Enthusiast

This paper explores the philosophical significance of the Keralese and Indian subcontinent contribution to history of mathematics. Identifying the most accurate genesis and trajectory of mathematical ideas in history that current knowledge allows should be the goal of every history of mathematics, and is consistent with any philosophy of mathematics. I argue for the need of a broader conceptualization of philosophy of than the traditional emphasis on scholastic enquiries into epistemology and ontology. For such an emphasis has been associated, though I add need not necessarily be so, with an ideological position that devalues non-European contributions to history of mathematics. …

Mars Exploration Rover: Mathematics And People Behind The Mission, Uffe Thomas Jankvist, Bjørn Toldbod

The Mathematics Enthusiast

This paper is a selective study of the mathematics and people involved with a specific space mission, namely the Mars Exploration Rover (MER) mission launched in 2003. The specific mathematics of the MER mission are sought uncovered through interviews with applied scientists who worked with different aspects of the mission at the Jet Propulsion Laboratory (JPL). Some of the more specific questions attempted answered through this article for instance concerns if the aerospace industry, exemplified by the MER mission, calls for new developments in mathematics or if it mostly relies on well established theories; how much independence the scientists have …

On The Solution To Octic Equations, Raghavendra G. Kulkarni

The Mathematics Enthusiast

We present a novel decomposition method to decompose an eighth-degree polynomial equation, into its two constituent fourth-degree polynomials, as factors, leading to its solution. The salient feature of the octic equation solved here is that, the sum of its four roots being equal to the sum of the remaining four roots. We derive the condition to be satisfied by coefficients so that the given octic is solvable by the proposed method.

New And Noteworthy Books From Sense Publishers

The Mathematics Enthusiast

No abstract provided.

Introduction Of A New Construct: The Conceptual Tool "Flexibility", Mette Andresen

The Mathematics Enthusiast

This paper presents a new construct: the conceptual tool ‘Flexibility’. The construct was a result of an attempt to extract experiences of teaching and learning with the use of laptops. It was further developed and refined on the basis of four small-scale teaching experiments. The teaching experiments, being part of a development project in upper secondary school mathematics, investigated the use of laptops for teaching differential equations from a modeling point of view. The research was double-aimed: one objective was to conclude the project with some recommendations for the design of teaching, in the form of guidelines suitable for a …

Looking Back At The Beginning: Critical Thinking In Solving Unrealistic Problems, Mark Applebaum, Roza Leikin

The Mathematics Enthusiast

We believe that problem-solving skills engage critical thinking at every phase of problem solution. In this research a special attention is given to the fist phase - "understanding the problem". We consider this phase as a continuation of all the previous mathematical experience, in which understanding of new problems requires "looking back" at those solved in the past. Evaluation of the givens in the problem sometimes allows immediate solution whereas in other cases it shows that solution does not exist. We found that it is not easy for mathematics teachers to discover that a problem includes contradictory (i.e. unrealistic) conditions. …

Uniform Estimates For Eulerian-Lagrangian Methods For Singularly Perturbed Time-Dependent Problems, Hong Wang, Kaixin Wang

Faculty Publications

We prove a priori optimal-order error estimates in a weighted energy norm for several Eulerian–Lagrangian methods for singularly perturbed, time-dependent convection-diffusion equations with full regularity. The estimates depend only on certain Sobolev norms of the initial and right-hand side data, but not on ε or any norm of the true solution, and so hold uniformly with respect to ε. We use the interpolation of spaces and stability estimates to derive an ε-uniform estimate for problems with minimal or intermediate regularity, where the convergence rates are proportional to certain Besov norms of the initial and right-hand side data.

The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui

Dissertations

In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dv_s ), where dv_s ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The …

Measures Of Travers Ability In Graphs, Futaba Okamoto

Dissertations

For a connected graph G of order n ≥ 3 and a cyclic ordering sc : v 1, v2,..., vn, v n+1 = v1 of vertices of G, the number d(sc) is defined by d(sc) = i=1n d(vi, vi +1), where d(vi, vi +1) is the distance between vi and vi+1 in G for 1 ≤ i ≤ n. The Hamiltonian number h(G) and upper Hamiltonian number h +(G) of G are defined as h(G) = min{d(sc)} and h+(G) = max{d(sc)}, respectively, where the minimum and maximum are taken over all cyclic orderings s c of vertices of G. For …

A Hexagon Result And Its Generalization Via Proof, Michael De Villiers

The Mathematics Enthusiast

This paper presents the discovery of a hexagon result on Geometer’s Sketchpad and its generalization via proof for any 2n-gon. The result is : If ABCDEF is a hexagon with opposite sides parallel (not necessarily equal), then the respective centroids G, H, I, J, K and L of triangles ABC, BCD, CDE, DEF, EFA and FAB, form a hexagon with opposite sides both equal and parallel.

The Probability Of Relatively Prime Polynomials, Arthur T. Benjamin, Curtis D. Bennett

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

Epsilon-Unfolding Orthogonal Polyhedra, Mirela Damian, Robin Flatland, Joseph O'Rourke

Computer Science: Faculty Publications

An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, …

Closed-Neighborhood Anti-Sperner Graphs, John P. Mcsorley, Alison Marr, Thomas D. Porter, Walter D. Wallis

Articles and Preprints

For a simple graph G let N_G[u] denote the closed-neighborhood of vertex u ∈ V (G). Then G is closed-neighborhood anti-Sperner (CNAS) if for every u there is a v ∈ V (G)\{u} with N_G [u] ⊆ N_G [v] and a graph H is closed-neighborhood distinct (CND) if every closed-neighborhood is distinct, i.e., if N_H[u] ≠ N_H[v] when u ≠ v, for all u and v ∈ V (H).

In this paper we …

Proof Without Words: A Graph Theoretic Decomposition Of Binomial Coefficients, Joseph Demaio

Faculty Articles

No abstract provided.

On The Gauge Equivalence Of Twisted Quantum Doubles Of Elementary Abelian And Extra-Special 2-Groups, Christopher Goff, Geoffrey Mason, Siu-Hung Ng

Christopher Goff

Problems Related To Efficacy Measurement And Analyses, Sibabrata Banerjee

Dissertations

In clinical research it is very common to compare two treatments on the basis of an efficacy variable. More specifically, if X and Y denote the responses of patients on the two treatments A and B, respectively, the quantity P(Y>X) (which can be called the probabilistic index for the Effect Size), is of interest in clinical statistics. The objective of this study is to derive an efficacy measure that would compare two treatments more informatively and objectively compared to the earlier approaches. Kernel density estimation is a useful non-parametric method that has not been well utilized as an applied …

Prediction Of Mrna Polyadenylation Sites In The Human Genome And Mathematical Modeling Of Alternative Polyadenylation, Yiming Cheng

Dissertations

Messenger RNA (mRNA) polyadenylation plays many important roles in the cell, such as transcription termination, mRNA stability and transportation, and mRNA translation in eukaryotic cells. A large number of human and mouse genes have multiple polyadenylation sites (referred to as poly(A) sites) that lead to variable transcripts, some of which are translated into various protein products with different functions. However, the details about when and where the polyadenylation occurs, and how pre-mRNA switches from one poly(A) site to another are still unknown. This kind of 3 '-end processing can be regulated by the cell environment, cell cycle stage, and tissue …

Domains Of Definition Of Monge-Ampère Operators On Compact Kähler Manifolds, Dan Coman, Vincent Guedj, Ahmed Zeriahi

Mathematics - All Scholarship

Let (X, w) be a compact Kahler manifold. We introduce and study the largest set DMA(X, w) of w-plurisubharmonic (psh) functions on which the complex Monge-Ampere operator is well defined. It is much larger than the corresponding local domain of definition, though still a proper subset of the set PSH(X, w) of all w-psh functions. We prove that certain twisted Monge-Ampere operators are well defined for all w-psh functions. As a consequence, any w-psh function with slightly attenuated singularities has finite weighted Monge-Ampere energy.

Introduction (2007), Angela Hare

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

On Connections Between Univalent Harmonic Functions, Symmetry Groups, And Minimal Surfaces, Stephen M. Taylor

Theses and Dissertations

We survey standard topics in elementary differential geometry and complex analysis to build up the necessary theory for studying applications of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the Weierstrauss-Enneper representation formula. Finally, we demand two minimal surfaces M and M' be locally isometric, formulate a system of partial differential equations modeling this constraint, and calculate their symmetry group. The group elements generate transformations that when applied to a prescribed harmonic …