Computer Sciences Commons^™

A Logic Programming Model Of The Game Of Sprouts, Ralph M. Butler, Selden Y. Trimble, Ralph W. Wilkerson

Computer Science Faculty Research & Creative Works

The Game of Sprouts Has Intrigued Mathematicians for Nearly Twenty Years. This Paper Describes a Representation Scheme Which Simplifies Much of the Geometry of the Game. using This Representation, We Develop a Prolog Program Which Will Play Sprouts. It is Hoped that the Program Will Prove to Be a Useful Research Tool in Finding the Key to a Winning Strategy for Sprouts and that the Representation Will Serve as a Useful Model for Studying Planar Graphs. © 1987, ACM. All Rights Reserved.

Sorting And Selecting In Rounds, Nicholas Pippenger

All HMC Faculty Publications and Research

We present upper bounds for sorting and selecting the median in a fixed number of rounds. These bounds match the known lower bounds to within logarithmic factors. They also have the merit of being “explicit modulo expansion”; that is, probabilistic arguments are used only to obtain expanding graphs, and when explicit constructions for such graphs are found, explicit algorithms for sorting and selecting will follow. Using the best currently available explicit constructions for expanding graphs, we present the best currently known explicit algorithms for sorting and selecting in rounds.

The Complexity Of Computations By Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

We survey the current state of knowledge concerning the computation of Boolean functions by networks, with particular emphasis on the addition and multiplication of binary numbers.

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 …

[Introduction To] A Gentle Introduction To The Vax System, John R. Hubbard

Bookshelf

This book was written originally for students enrolled in computer science courses at the University of Richmond. Very few had worked on a large time-sharing system like the VAX.

The purpose of this book is to help the novice become comfortable using any of the Digital Equipment Corporations VAX computers, from the Micro-VAX to the powerful VAX 8000 system. The book is meant to be used as a tutorial.

Computing The Largest Empty Rectangle, B. Chazelle, R. L. Drysdale, D. T. Lee

Dartmouth Scholarship

We consider the following problem: Given a rectangle containing N points, find the largest area subrectangle with sides parallel to those of the original rectangle which contains none of the given points. If the rectangle is a piece of fabric or sheet metal and the points are flaws, this problem is finding the largest-area rectangular piece which can be salvaged. A previously known result [13] takes $O(N^2 )$ worst-case and $O(N\log ^2 N)$ expected time. This paper presents an $O(N\log ^3 N)$ time, $O(N\log N)$ space algorithm to solve this problem. It uses a divide-and-conquer approach similar to the ones …

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.

Introduction (1985), Robert Brabenec

ACMS Conference Proceedings 1985

A Fifth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

Table Of Contents (1985), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1985

A Fifth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

Expressive Power In First Order Topology, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of …

On Monotone Formulae With Restricted Depth, Maria M. Klawe, Wolfgang J. Paul, Nicholas J. Pippenger, Mihalis Yannakakis

All HMC Faculty Publications and Research

We prove a hierarchy theorem for the representation of monotone Boolean functions by monotone Boolean functions by monotone formulae with restricted depth. Specifically, we show that there are functions with Π_k-formulae of size n for which every Σ_k-formula has size exp Ω(n^1/(k-1)). A similar lower bound applies to concrete functions such as transitive closure and clique. We also show that any function with a formula of size n (and any depth) has a Σ_k-formula of size exp O(n^1/(k-1)). Thus our hierarchy theorem is the best possible.

Ua66/10/2 Newsletter, Wku Mathematics

WKU Administration Documents

Newsletter created by and about the WKU Mathematics department.

Using Mathematical Concepts To Illustrate Scriptural And Spiritual Ideas, Robert Brabenec

ACMS Conference Proceedings 1983

Christian mathematics faculty and students respond in differing ways to this idea of applying mathematics to Scripture, and vice-versa. Mathematics is man-made, while Scripture is inspired by God, so they should be disjoint entities. However, it is well known that the Scripture used analogies of familiar human objects and ideas in order to explain spiritual ideas. This paper discusses various mathematical concepts and how they illustrate Scriptural and spiritual ideas.

The Activitiy And Application Of Mathematics, R. S. D. Thomas

ACMS Conference Proceedings 1983

There are four so-called philosophies of mathematics that I regard as totally discredited, formalism, intuitionism, logicism, and Platonism. It is a common feature of the ism philosophies of mathematics that they do not take the application of mathematics very seriously. This paper examines a view of mathematics that takes applications seriously.

Arrogance And Humility In The Philosophy Of Mathematics, James Murdock

ACMS Conference Proceedings 1983

This paper explores the philosophical, sociological, and theological questions related to the field of mathematics and whether or not it is ethical to pursue when its discoveries are used for evil.

An Outline Of A Complementarist Philosophy Of The Sciences, With A Special Reference To Mathematics, Willem Kuyk

ACMS Conference Proceedings 1983

No abstract provided.

A Neuropsychodynamical Theory Of Mathematics Learning, Willem Kuyk

ACMS Conference Proceedings 1983

No abstract provided.

One Possible Outline For A First Undergraduate Course In Philosophy Of Mathematics, Harold Heie

ACMS Conference Proceedings 1983

No abstract provided.

The Role Of Creativity In Mathematics, John M. Dubbey

ACMS Conference Proceedings 1983

No abstract provided.

Mathematics: The Loss Of Certainty, Calvin Jongsma

ACMS Conference Proceedings 1983

Morris Kline was a contentious mathematician and author, documenting (as he saw it) both the deficiencies of mid-twentieth-century reformist trends in mathematics education and formalist views of the foundations (and practice) of mathematics. This brief introduction to a discussion of Kline's 1980 book and its mixed reception by the mathematics community provides a context for assessing his ideas as part of his overall views on the nature of mathematics.

A Comparative Study Of Christian Mathematical Realism And Its Humanistic Alternatives, Paul Zwier

ACMS Conference Proceedings 1983

This paper explores what sort of stance a Christian should have on important mathematical questions such as realism.

Introduction (1983), Robert Brabenec

ACMS Conference Proceedings 1983

No abstract provided.

Table Of Contents (1983), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1983

A Fourth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

A Comparative Study Of Christian Mathematical Realism And Its Humanistic Alternatives, Paul Zwier

ACMS Journal 2004

This paper addresses the growing popularity of views of mathematics that see it primarily as a social entity and that reject Platonism. It contrasts two Christian realist philosophies - those of Alvin Plantinga and Vernon Poythress - with the secular perspective of Philip Davis and Reuben Hersch. It affirms the insight of Davis and Hersch that mathematics is indeed a social entity. However, it argues that belief in God enables a fuller understanding of mathematics - one that accounts for the apparent transcendence of mathematics and its power to explain concepts in the physical world.