Applied Mathematics Commons^™

Augustine's Mathematical Realism, Paul J. Zwier

ACMS Conference Proceedings 1989

After a review of Philip Kitcher's argument against Mathematical Realism, this paper presents the case for Mathematical Realism by looking at the life and writings of Saint Augustine.

Beauty In Mathematics: Some Theological Implications, David L. Neuhouser

ACMS Conference Proceedings 1989

It may come as a surprise to some that science or mathematics could be considered beautiful, but many prominent sciences and mathematicians from around the world have made such claims. Furthermore, the beauty of mathematics and order of the universe inspired some of the greatest developments in science and mathematics. This paper examines the beauty of mathematics and what scientists and other individuals have said about the subject.

Using Writing In The Mathematics Classroom, Dr. Barbara J. Rose

ACMS Conference Proceedings 1989

No abstract provided.

Mathematics Between The Lines Of Ecclesiates, Donald A. Joesphson

ACMS Conference Proceedings 1989

No abstract provided.

Writing Across The Curriculum Using Statistics, Carlos A. Pereira

ACMS Conference Proceedings 1989

No abstract provided.

Written Assignments In College Freshman And Sophomore Mathematics Courses, Jean Alliman

ACMS Conference Proceedings 1989

No abstract provided.

Mathematical Modeling In The Classroom, Jefferson Hartzler

ACMS Conference Proceedings 1989

No abstract provided.

The Fourth Dimension And The Theology Of Edwin Abbot Abbott, Thomas F. Banchoff

ACMS Conference Proceedings 1989

No abstract provided.

Schedule (1989), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor

Introduction (1989), Gene B. Chase

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor

Table Of Contents (1989), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1989

A Seventh Conference on Mathematics from a Christian Perspective

Gene B. Chase, Editor

The Fourth Dimension And The Theology Of Edwin Abbott Abbott, Thomas Banchoff

ACMS Conference Proceedings 1989

This paper is a brief biography of Edwin Abbott Abbott, author of Flatland, and a sketch of the main ideas in the book. It also incorporates some personal reflections.

The Secondary Role Of Parallelism In Geometry And The Real Difference Between Euclidean And Hyperbolic Geometry, Panagiotis Pittas

Theses

After a brief survey of the foundations of absolute geometry, we state certain definitions (that of an angle and an ordering between them) and properties (Theorem 1, lemma 1) of the absolute plane. Then. by adding the Playfair axiom (Statement E₁) to the axioms of absolute geometry, we obtain the Euclidean plane. We introduce statement E₂ and then we prove that it is equivalent to E₁. We then reason that E₂ is superior to E₁ in terms of geometric content, that it expresses a characteristic property of the Euclidean plane, and we show …

Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng

Department of Mathematics: Faculty Publications

A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbolic equilbrium points of ordinary differential equations. It consists of a special normal form called admissible variables, exponential expansion, strong A-lemma, and Lyapnunov- Schmidt reduction for the Poincare maps under Sil'nikov variables. The method is based on the Center Manifold Theory, the contraction mapping principle, and the Implicit Function Theorem.

Some Estimates For Finite Difference Approximations, José-Luis Menaldi

Mathematics Faculty Research Publications

Some estimates for the approximation of optimal stochastic control problems by discrete time problems are obtained. In particular an estimate for the solutions of the continuous time versus the discrete time Hamilton-Jacobi-Bellman equations is given. The technique used is more analytic than probabilistic.

Specified Subgraphs And Subgraph-Defined Parameters In Graphs, Karen S. Holbert

Dissertations

No abstract provided.

Nonnegative Solutions To A Semilinear Dirichlet Problem In A Ball Are Positive And Radially Symmetric, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We prove that nonnegative solutions to a semilinear Dirichlet problem in a ball are positive, and hence radially symmetric. In particular, this answers a question in [3] where positive solutions were proven to be radially symmetric. In section 4 we provide a sufficient condition on the geometry of the domain which ensures that nonnegative solutions are positive in the interior.

Turnpike Structures For Optimal Maneuvers, Arthur T. Benjamin

All HMC Faculty Publications and Research

This dissertation is concerned with problems of optimally maneuvering a collection of objects ("pieces") from one location to another, subject to various restrictions on the allowable movements. We illustrate and prove that when the "distance" from the origin to the destination is large, and the movement rules and environment satisfy certain "homogeneity" properties, there exist near-optimal trajectories with very special (turnpike) structure.

These results are obtained by representing the problem through a configuration graph. Here, we have a node for each configuration and an arc for every "different" legal move. Each arc is endowed with a scalar weight …

Report On The Application Of An Evapotranspiration Equation To The Waca Dome, P R. Scott

Resource management technical reports

No abstract provided.

Viscous Cross-Waves: An Analytical Treatment, Andrew J. Bernoff, L. P. Kwok, Seth Lichter

All HMC Faculty Publications and Research

Viscous effects on the excitation of cross‐waves in a semi‐infinite box of finite depth and width are considered. A formalism using matched asymptotic expansions and an improved method of computing the solvability condition is used to derive the relative contributions of the free‐surface, sidewall, bottom, and wavemaker viscous boundary layers. This analysis yields an expression for the damping coefficient previously incorporated on heuristic grounds. In addition, three new contributions are found: a viscous detuning of the resonant frequency, a slow spatial variation in the coupling to the progressive wave, and a viscous correction to the wavemaker boundary condition. The wavemaker …

Augustine’S Mathematical Realism, Paul Zwier

ACMS Journal 2004

This paper begins by outlining an argument advanced against mathematical realism by Philip Kitcher. It then sketches the life and work of the great Christian philosopher and theologian, Augustine of Hippo. It discusses Augustine’s view that there exist eternal ideas in the mind of God that God used as templates in his creation of material objects. Among these are ideas about numbers and other mathematical objects. It also discusses Augustine’s understanding of how human beings have access to such ideas. It concludes with a discussion of some possible objections to Augustine’s perspective.

The Fourth Dimension And The Theology Of Edwin Abbott Abbott, Thomas Banchoff

ACMS Journal 2004

This paper is a brief biography of Edwin Abbott Abbott, author of Flatland, and a sketch of the main ideas in the book. It also incorporates some personal reflections.

On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.

Pixley-Roy Hyperspaces Of Ω-Graphs, Joe Mashburn

Mathematics Faculty Publications

The techniques developed by Wage and Norden are used to show that the Pixley-Roy hyperspaces of any two ω-graphs are homeomorphic. The Pixley-Roy hyperspaces of several subsets of Rⁿ are also shown to be homeomorphic.

On The Existence And Symmetry Properties Of Finite Total Mass Solutions Of The Matukuma Equation, The Eddington Equation And Their Generalizations, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

On Vector Sequence Transforms And Acceleration Techniques, Steven L. Hodge

Mathematics & Statistics Theses & Dissertations

This dissertation is devoted to the acceleration of convergence of vector sequences. This means to produce a replacement sequence from the original sequence with higher rate of convergence.

It is assumed that the sequence is generated from a linear matrix iteration x_i+ i = Gx_i + k where G is an n x n square matrix and x_I+1 , x_i,and k are n x 1 vectors. Acceleration of convergence is obtained when we are able to resolve approximations to low dimension invariant subspaces of G which contain large components of the error. When …

Weak Bipolarizable Graphs, Stephan Olariu

Computer Science Faculty Publications

We characterize a new class of perfectly orderable graphs and give a polynomial-time recognition algorithm, together with linear-time optimization algorithms for this class of graphs.

Effect Of Computer Graphics Use On Student Understanding Of Calculus Concepts, Charlene E. Beckmann

Dissertations

Student understanding of selected calculus concepts as developed through use of a Cartesian coordinate graphical representation system were investigated. Subjects (N = 163) enrolled in first-semester calculus sections at Western Michigan University participated in one of four treatment conditions: Graphics (G), exposure to a computer-graphically-developed conceptual course; Graphics Plus (G+), exposure to the same course as G subjects plus provision of computer graphics software and related supplemental assignments; Standard 1 (S1), exposure to a graphically-developed, conceptual course; and Standard 2 (S2), exposure to a traditional skill-oriented course.

Two investigations were undertaken. In Investigation 1, comparisons were made between G and …

On The Numerical Approximations Of An Optimal Correction Problem, M. C. Bancora-Imbert, P. L. Chow, J. L. Menaldi

Mathematics Faculty Research Publications

The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure.

The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner

Pitzer Faculty Publications and Research

This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields.