Mathematics Commons^™

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

Infinitely Many Radially Symmetric Solutions To A Superlinear Dirichlet Problem In A Ball, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

In this paper we show that a radially symmetric superlinear Dirichlet problem in a ball has infinitely many solutions. This result is obtained even in cases of rapidly growing nonlinearities, that is, when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem. Our methods rely on the energy analysis and the phase-plane angle analysis of the solutions for the associated singular ordinary differential equation.

Cyclic Operators, Commutators, And Absolutely Continuous Measures, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.

Applied Mathematics As Social Contract, Philip J. Davis

Humanistic Mathematics Network Journal

The author takes the position that mathematical education must redefine its goals so as to create a citizenry with sufficient knowledge to provide social backpressure on future mathematizations. This can be accomplished by increasing the part of mathematical education that is devoted to the description and interpretation of the processes of mathematization and by allowing the technicalities of the formal operations within mathematics itself to be deemphasized or automated out by computer.

Mathematical Reflections: Standing On The Shoulders Of Giants, Karl J. Smith

ACMS Conference Proceedings 1987

The layperson's response to mathematics is often that of desperation. When we tell people our occupation, do we more often than not hear about their unpleasant experiences with mathematics. They often tell us, "I studied algebra in high school and haven't used it since!" Indeed, that may be true. However, we can reply, "How many times has algebra been used on you?" We are all restricted, and protected, by the formulas of mathematics. In the mysterious metaphors we have agreed to cal mathematics, all creation is involved, from the symbol-happy logician down to the cunning geometers, the bees. When I …

Observations On Mathematics And The Christian Faith, W. David Laverell, Carl J. Sinke

ACMS Conference Proceedings 1987

There is little doubt that mathematicians are becoming more concerned with the foundations on which their discipline rests, the meaning of their work, and the philosophical stance implicit in what they do. This concern is prompted by serious questions which have been raised in recent years, questions dealing with the nature of mathematical truth, the nature of proof, certainty (or lack thereof) in mathematics, and the relationship of mathematics to the physical world. This has been particularly true for those of us involved in teaching since it is apparent that good mathematics education cannot ignore these issures.

Proof And Intution, Michael Detlefsen

ACMS Conference Proceedings 1987

This paper discusses various perspectives on proof and intuition by examing two epistemic systems, Intuition Intensive and Logic Intensive, and Jules Henri Poincaré's objections to the latter.

Logic And Proof For Mathematics: A Twentieth Century Perspective, Calvin Jongsma

ACMS Conference Proceedings 1987

This talk reports on the author's experience in teaching college mathematics students the basics of logic and proof in preparation for their transitioning to upper-level proof-based mathematics courses, following that up with a philosophical and historical analysis of mathematicians' attitudes toward such a project going back to nineteenth- and twentieth-century developments in logic and foundations (De Morgan, Boole, Frege, Russell, and Hilbert). The natural deduction approach to logic and inference developed in the mid-twentieth century by Jaskowski and Fitch is recommended as a much better focused approach for learning how to do proofs in mathematics. This idea is systematically developed …

Riesz Spaces And Their Applications In Economics, Calvin E. Piston

ACMS Conference Proceedings 1987

We will examine an economic model of pure exchange and some results concerning different notions of equilibrium. In particular, we will focus on the role played by the theory of Riesz space.

Variations On A Theme, Robert Creighton Buck

ACMS Conference Proceedings 1987

An autobiographical narration by Robert Creighton Buck, detailing his experiences in the field of mathematics, and the various questions and themes reoccurring in the mathematical sciences.

The Role Of Computer Science In A Liberal Arts College, Russell C. Bjork

ACMS Conference Proceedings 1987

The question the panel has been asked to discuss actually encompasses two related, but distinct, questions - each of which, in turn, has two subquestions.

The first question concerns the place of a computer science as a major program of study among the offerings of a liberal arts college. The two subquestions here are as follows: First, is computer science an appropriate field of study to offer in a liberal arts college? (Is it a liberal art?) Second, is a liberal arts college an appropriate home for a computer science program? (Can a high quality program be offered in such …

Another Look At Pick's Theorem, Dale Varberg

ACMS Conference Proceedings 1987

In this paper, the author discusses his experience building a proof for Pick's Theorem and theorem's history.

Computer Science In Liberal Arts Colleges, James Bradley

ACMS Conference Proceedings 1987

This paper looks at the strengths and weaknesses of computer science curricula and how liberal arts colleges can best teach the concepts of mathematics required in computer science.

An Activist Model Of The Metaphysics Of Mathematics, Christopher Menzel

ACMS Conference Proceedings 1987

No abstract provided.

Conic Sections In Ip, Richard Laatsch

ACMS Conference Proceedings 1987

No abstract provided.

3:16 - An Approach To Bible Study, Donald E. Knuth

ACMS Conference Proceedings 1987

No abstract provided.

Introduction (1987), Paul Zwier

ACMS Conference Proceedings 1987

A Sixth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec

Table Of Contents (1987), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1987

A Sixth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec

Proof And Intuition, Michael Detlefsen

ACMS Journal 2004

This paper aims to give a clear exposition of two critiques of logicism. The intuitionist, Brouwer, is best known for rejecting the law of the excluded middle (his "special critique.") The paper argues that Brouwer's "general critique" is deeper and more extensive than this. That is, Brouwer is arguing that mathematical knowledge requires a kind of direct mathematical experience, analogous to sensory experience and this cannot be attained simply by linguistic operations independently of experience. It also discusses Poincare's critiques - that there is a huge difference between genuine mathematical insight and an ability to logically manipulate mathematical truths and …

Designing The Optimal Placement Of Spaces In A Parking Lot, R. Bingle, D. Meindertsma, W. Oostendorp, Gene A. Klaasen

University Faculty Publications and Creative Works

We develop a method for determining the optimal size and placement of parking spaces and approach aisles for an automobile parking lot. In particular, our solution concerns a parking lot of size 100' x 200' located at the corner of an intersection of two streets in a New England town. We begin by arguing the superiority of driver operation over attendant operation of vehicles to be parked. Then a statistical analysis is performed on a sampling of 160 1987 model automobiles to determine upper bounds and ideal values for the length and width of a parking space and for the …

Orthogonal Polynomials, Measures And Recurrence Relations, Joanne Dombrowski, Paul Nevai

Mathematics and Statistics Faculty Publications

Properties of measures associated with orthogonal polynomials are investigated in terms of the coefficients of the three term recurrence formula satisfied by the orthogonal polynomials.

L(P) Estimates For Maximal Functions And Hilbert-Transforms Along Flat Convex Curves In R(2), Hasse Carlsson, Michael Christ, Antonio Cordoba, Javier Duoandikoetxea, Jose L. Rudio De Francia, Jim Vance, Stephen Wainger, David Weinberg

Mathematics and Statistics Faculty Publications

No abstract provided.

Reliable Computation In The Presence Of Noise, Nicholas Pippenger

All HMC Faculty Publications and Research

This talk concerns computation by systems whose components exhibit noise (that is, errors committed at random according to certain probabilistic laws). If we aspire to construct a theory of computation in the presence of noise, we must possess at the outset a satisfactory theory of computation in the absence of noise.

A theory that has received considerable attention in this context is that of the computation of Boolean functions by networks (with perhaps the strongest competition coming from the theory of cellular automata; see [G] and [GR]). The theory of computation by networks associates with any two sets Q and …

On Universal Tests For The Truth Of World Views: Their Existence And Identifiability, William Buttelmann, Paul Fienberg

ACMS Conference Proceedings 1985

In his book, Christian Apologetics, Norman Geisler proposes a universal test for the truth of world views. We examine this concept and find that it raises serious difficulties. This paper first presents some basic definitions for "world view" and "truth-value of a world view," then studies the concept of a universal test for the truth of world views in light of these definitions. Geisler has proposed what amounts to a universal decision procedure to determine the truth-value of world views. We show that, in the general case, no such universal decision procedure exists. Whether or not such universal tests for …

Selected Bibliography Of Donald Maccrimmon Mackay, Gene B. Chase

ACMS Conference Proceedings 1985

A selected bibliography of Donald MacCrimmon MacKay, including his written works and biographical sources.

The Significance Of Formally Undecidable Propositions For The Use Of Classical Logic In Theological Arguments, Gordon E. Whitney

ACMS Conference Proceedings 1985

No abstract provided.

Faith And Mathematics - A Different Perspective, James E. Mann, Jr.

ACMS Conference Proceedings 1985

No abstract provided.

Artificial Intelligence? - A Christian Appraisal, Donald M. Mackay

ACMS Conference Proceedings 1985

No abstract provided.

Is Rational Thinking The Best Thinking?, Richard Laatsch

ACMS Conference Proceedings 1985

No abstract provided.

Undergraduate Mathematical Modeling: When And What To Teach, Frank R. Giordano, Maurice D. Weir

ACMS Conference Proceedings 1985

No abstract provided.