Computer Sciences Commons^™

On Determinism Versus Non-Determinism And Related Problems, Wolfgang J. Paul, Nicholas Pippenger, Endre Szemeredi, William T. Trotter

All HMC Faculty Publications and Research

We show that, for multi-tape Turing machines, non-deterministic linear time is more deterministic Turing machines (that receive their input on their work tape) require time Q(n2) to powerful than deterministic linear time. We also recognize non-palindromes of length n (it is easy to discuss the prospects for extending this result to see that time O(n log n) is. sufficient for a more general Turing machines. non-deterministic machine). 1. Introduction

Coarse Topologies In Nonstandard Extensions Via Separative Ultrafilters, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Topological Extensions And Subspaces Of Ηα-Sets, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The η_x-sets of Hausdorff have large compactifications (of cardinality ≽ exp(α); and of cardinality ≽ exp(exp(2^<α)) in the Stone-Čech case). If Q_α denotes the unique (when it exists) η_α -set of cardinality α, then Q_α can be decomposed (= partitioned) into homeomorphs of any prescribed nonempty subspace; moreover the subspaces of Q_α can be characterized as those which arc regular T₁, of cardinality and weight ≼ α, whose topologies are closed under < α intersections.

A Comparison Of Processor Technologies, Eddie R. Wachter

Theses and Dissertations

The purpose of this paper is to present a discussion of the technology implementation and design of four very high performance mainframe computer systems. The systems evaluated are:

Amdahl 580 Series

CDC 170 Series 800

IBM 308x Series

Univac 1100/90 Series

Included in this evaluation is a survey of the technology used, its characteristics, packaging and performance. Each system component is evaluated on the basis of design philosophy, technology, and the total system design with regards to reliability, availability, and performance.

Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 3, No. 1, Wku Mathematics & Computer Science

WKU Administration Documents

Newsletter created by the Ogden Computer Laboratory to promote services, courses, hardware, software and student activities.

Reality And Imagination In Mathematics And Religion, Dave Neuhouser

ACMS Conference Proceedings 1981

What does either reality or imagination have to do with mathematics? What does either reality or imagination have to do with religion? The thesis of this paper is that mathematics and religion, both, should be closely related to reality and that imagination is essential in both areas. In fact, imagination is essential in our attempts to understand reality.

Theology And Philosophy Of Mathematics, Russell V. Benson

ACMS Conference Proceedings 1981

This paper examines history and philosophy to explore the answer to the theological question of whether or not Christians should pursue the mathematical sciences.

A Response To Professor Poythress’S “Science As Allegory”, Paul Devries

ACMS Conference Proceedings 1981

This paper critiques some of the arguments given by Vern Sheridan Poythress in his paper, Science as Allegory, particularly about the claims that the universe is poetry and that science is poetry.

Teaching Mathematics Distinctively, Paul J. Zwier

ACMS Conference Proceedings 1981

By examining previously used education models, Paul Zwier how he developed his current methods of teaching mathematically distinctively.

Probabilistic Ways Of Thinking, Garnet Hauger

ACMS Conference Proceedings 1981

Events of the tiniest probabilities occur every day, and yet we tend to think of these events as unusual and even miraculous. So what should be a Christian's response to such events? Beginning with some simple concepts of probability, this paper examines the role that chance plays in our lives.

An Integration Of Integrations Of Christianity And Mathematics—A Response To Harold Heie, Gene B. Chase

ACMS Conference Proceedings 1981

There are three general approaches taken to integrate Christianity and Mathematics: the applicational, the incarnation, and the philosophical. This paper discusses these views and responds to the approaches of Harold Heie.

Some Contributions Of Stanley Jaki To An Understanding Of Mathematics, Paul Devries

ACMS Conference Proceedings 1981

This paper comments on passages from the books by Stanley L. Jaki, Science and Creation, The Relevance of Physics, and The Road to Science and The Ways to God.

Random Variables And A Sovereign God, Lloyd Montzingo

ACMS Conference Proceedings 1981

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.

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.

Algebraic Complexity Theory, Nicholas Pippenger

All HMC Faculty Publications and Research

Algebraic complexity theory, the study of the minimum number of operations sufficient to perform algebraic computations, is surveyed with emphasis on the general theory of bilinear forms and two of its applications: polynomial multiplication and matrix multiplication. Though by no means exhausting algebraic complexity theory, these topics illustrate well its development and its methods, and provide examples of its most striking successes.

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.

On Some Dependencies Between Functional Forms In Functional Programming Systems, Atanas Radenski

Mathematics, Physics, and Computer Science Faculty Articles and Research

In the present paper, some dependencies between functional forms in functional programming systems are demonstrated. It is shown that any functional form can be expressed by using only the forms composition, condition and construction.

Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 2, No. 1, Wku Mathematics & Computer Science

WKU Administration Documents

Newsletter created by the Ogden Computer Laboratory to promote services, courses, hardware, software and student activities.

On The Evaluation Of Powers And Monomials, Nicholas Pippenger

All HMC Faculty Publications and Research

Let $y_1 , \cdots ,y_p $ be monomials over the indeterminates $x_1 , \cdots ,x_q $. For every $y = (y_1 , \cdots ,y_p )$ there is some minimum number $L(y)$ of multiplications sufficient to compute $y_1 , \cdots ,y_p $ from $x_1 , \cdots ,x_q $ and the identity 1. Let $L(p,q,N)$ denote the maximum of $L(y)$ over all $y$ for which the exponent of any indeterminate in any monomial is at most $N$. We show that if $p = (N + 1^{o(q)} )$ and $q = (N + 1^{o(p)} )$, then $L(p,q,N) = \min \{ p,q\} \log N …

Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 1, No. 2, Wku Mathematics & Computer Science

WKU Administration Documents

Newsletter created by the Ogden Computer Laboratory to promote services, courses, hardware, software and student activities.