Mathematics Commons^™

The Development Of Algebraic Structures During The Nineteenth Century, Richard Stout

ACMS Conference Proceedings 1981

I remember entering the faculty lounge one day while I was in graduate school and hearing a logician chiding some of the algebraists in the room. He said, "Don't you fellows ever get tired of just plus and times?" His remark, said in jest, had more to it than he may have realized. The fact that there is structure to algebra, represented by plus and times, was a vital discovery in the nineteenth century. It would lead algebra away from a reliance on numbers to a much more formal approach, one in which many different types of algebraic structures could …

Mathematics As Rhyme, Vern Poythress

ACMS Conference Proceedings 1981

Using the analogy between the universe and a choral poem, one may view mathematics as the “rhyme” of the universe. In that perspective new light is thrown on the unique subject matter of mathematics, the a priori character of its truths, and the relation of mathematics to other areas of knowledge. A route is thereby opened for richer use of creativity in mathematics.

Communicating Spiritual Insights In Mathematics Classes, Verbal Snook

ACMS Conference Proceedings 1981

No abstract provided.

Science As Allegory, Vern Sheridan Poythress

ACMS Conference Proceedings 1981

No abstract provided.

Microcomputers In Mathematics And Science Courses, Carlos Pereira

ACMS Conference Proceedings 1981

No abstract provided.

Introduction To Computer Science, Millard B. Niver

ACMS Conference Proceedings 1981

No abstract provided.

Mathematics: Freedom Within Bounds, Harold Heie

ACMS Conference Proceedings 1981

No abstract provided.

A Reaction To The Poythress Paper, Paul J. Zwier

ACMS Conference Proceedings 1981

This paper reacts to the metaphor of Vern Sheridan Poythress’s papers, Science as Allegory, exploring what makes a good metaphor and the quality of argument it produces.

Science As Allegory, Vern Poythress

ACMS Conference Proceedings 1981

The universe is God’s choral poem, and science is a system of allegories within it. That is the thesis that I propose to expound and defend. Yet it is not a “thesis” at all, if the word “thesis” commits me to a certain kind of strict logical defense. I am not putting forward my thesis that science is allegory as the endpoint of a deductive or inductive argument. Rather, it is a springboard for a program of exploration and reflection that turns upside-down some conventional ways of thinking about science.

Introduction (1981), Robert Brabenec

ACMS Conference Proceedings 1981

A Third Conference on Mathematics from a Christian Perspective

Table Of Contents (1981), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1981

No abstract provided.

Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Mathematics Faculty Publications

The basic definitions are given in the first section, including those for ω-chain continuity, ω-chain completeness, and the least fixed point property for ω-chain continuous functions. Some of the relations between completeness and fixed point properties in partially ordered sets are stated and it is briefly shown how the question basic to the dissertation arises.

In the second section, two examples are given showing that a partially ordered set need not be ω-chain complete to have the least fixed point property for ω-chain continuous functions.

Retracts are discussed in section 3, where it is seen that they are not sufficient …

Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn

Mathematics Faculty Publications

A partially ordered set is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.

Random Variables And A Sovereign God, Lloyd Montzingo

ACMS Journal 2004

This paper takes a brief look at the history of conflict between the concepts of chance and divine activity. After reviewing some evidence for randomness in the universe, present philosophical and theological views from four different scientists on this subject are presented. The discussion concludes with some questions and observations concerning those questions.

Bounds On The Performance Of Protocols For A Multiple-Access Broadcast Channel, Nicholas Pippenger

All HMC Faculty Publications and Research

A general model is presented for synchronous protocols that resolve conflicts among message transmissions to a multiple-access broadcast channel. An information-theoretic method is used now to show that if only finitely many types of conflicts can be distinguished by the protocol, utilization of the channel at rates approaching capacity is impossible. A random-coding argument is used to show that if the number of conflicting transmissions can be determined (which requires distinguishing infinitely many types of conflicts) then utilization of the channel at rates arbitrarily close to capacity can be achieved.

Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro

All HMC Faculty Publications and Research

In this paper, we study the existence of weak solutions of the problem

□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)

u(t,x) = 0 ; (t,x) є ∂Ω

where □ is the wave operator ∂²/∂t² - ∂²/∂x², G: Rⁿ→R is a function of class C² such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L₂,(Ω))ⁿ and satisfying

f(0,x) = f(π,x) = 0

for all x є [0,π].

A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

For the commonest model of rearrangeable networks with $n$ inputs and $n$ outputs, it is shown that such a network must contain at least $6n \log _6 n + O( n )$ switches. Similar lower bounds for other models are also presented.

Numerical Solution Of A Quadratic Matrix Equation, George J. Davis

Mathematics & Statistics ETDs

This paper is concerned with the efficient numerical solution of the matrix equation AX2 + BX + C =0, where A,B,C and X are all square matrices. Such a matrix X is called a solvent. This matrix equation is very closely related to the problem of finding scalars lambda and nonzero vectors x such that (lambda2A + lambdaB + C)x=0. The latter equation represents a quadratic eigenvalue problem with each lambda and x called an eigenvalue and eigenvector, respectively. Such equations have many important physical applications which we survey.

By presenting an algorithm to calculate solvents, we show how the …

Critical Point Theory And The Number Of Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, A. C. Lazer

All HMC Faculty Publications and Research

No abstract provided.

Double Stochastic Integrals, Tsung-Dow Huang

Mathematics & Statistics ETDs

In this paper we study the double stochastic integral or stochastic quadratic form

Q =integreal(integral(phi(x,y)Z(dx)Z(dy) ))

with respect to a Gaussian random spectral measure Z. Letting F be the corresponding spectral distribution function, the kernel function is required to satisfy a) the function phi(x,x) is integrable respect to F and b) phi(x,y) is square integrable with respect to FxF. A definition of Q is given in terms of a carefully constructed sequence of step functions converging to phi. Iterated integral formulae, a discussion of the stochastic contribution to Q due to the diagonal values of phi, and an improvement of …

Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier

ACMS Conference Proceedings 1979

This paper explores the pedagogical decisions made by those teaching mathematics by discussing the various values and priorities of a mathematics course.

Mathematics In The Christian Philosophy Of Life, C. Ralph Verno

ACMS Conference Proceedings 1979

It is universally agreed that mathematics is important, that it is indeed very significant in life. This would be admitted even by those who are ignorant of or who dislike mathematics. There would be much less agreement, however, about why mathematics is important or significant. Such disagreement exists even more among mathematicians and mathematics educators. Unhappily many of the Christians who think about such things (and there are not very many who think about them at all) basically share the utilitarian view of many non-Christian thinkers, although endeavoring to place it within a Christian context. They think it is wonderful …

Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno

ACMS Conference Proceedings 1979

Some people view a conjoining of Christianity and Mathematics as improper. They miss the point of the relationship. The content of mathematics is not affected by Christianity. The relationship does not concern what, or how (the Christian doesn’t solve equations or differentiate differently), but it concerns why. It concerns such things as the interpretation and appreciation of the beauty, the symmetries, the coincidences, the remarkable properties, man’s creative role, etc. This paper explores the relationship between Christianity and mathematics as part of a panel discussion on the topic.

On Kuyk’S Complementarity In Mathematics, Gene B. Chase

ACMS Conference Proceedings 1979

This paper examines Willem Kuyk’s book, Complementarity in Mathematics, and the interplay between the subjects of mathematics.

Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart

ACMS Conference Proceedings 1979

This essay will consider a few ways that realism in the modern philosophy of mathematics might be understood and defined.

Intuitionism, Terence H. Perciante

ACMS Conference Proceedings 1979

Intuitionism derives philosophically from Kant's Conceptualism -- the object of the mathematical knowledge only have reality within the mind, they do not have reality apart from our thinking. This paper examines the nature of intuitionism and its strengths.

Two Philosophical Problems About Mathematics, Stephen Barker

ACMS Conference Proceedings 1979

Mathematics is a flourishing field of human endeavor, a field that is accorded great respect and high standing. For 2500 years or more, many of the best minds available have worked in this field; and the results produced have indirectly been of enormous value to other fields, such as physics, engineering, architecture, economics, and so on. But with is mathematics about? Physics studies moving bodies; engineering studies bridges; architecture studies buildings; economics studies commercial behavior: here there are phenomena we can point to that constitute the subject matter. But what does mathematics study? If you answer “Numbers”, or “Abstract types …

Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma

ACMS Conference Proceedings 1979

This article surveys the different views of mathematical methodology that occurred from ancient Greek times through the early modern period up until its codification around 1900. After summarizing the axiomatic approach advocated by Aristotle and implemented in mathematics by Euclid, the talk explores the character of analysis in ancient Greek times, its development into a symbolic algebra by Viete and Descartes, and its expansion into a calculus of fluxions and differentials by Newton and Leibniz. The article concludes by touching on the recovery and transformation of the deductive ideal for mathematics by Pasch, Peano, and Hilbert during the late nineteenth …

Non-Standard Calculus, Ron Friewald

ACMS Conference Proceedings 1979

This paper is intended to provide a very cursory introduction to how “nonstandard calculus” works, giving a sketch of how elementary calculus can be presented using hyperreal numbers.

Computer Usage In The College Curriculum, Dick A. Wood

ACMS Conference Proceedings 1979

No abstract provided.