Computer Sciences Commons^™

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.

A New Conjecture About Minimal Imperfect Graphs, H. Meyniel, Stephan Olariu

Computer Science Faculty Publications

H. Meyniel proved that in every minimal imperfect graph, every pair of vertices is joined by a chordless path containing an odd number of edges. We conjectured that in every minimal imperfect graph, every pair of vertices is joined by a path containing an even number of edges. We give an equivalent version of this new conjecture.

The Strong Perfect Graph Conjecture For Pan-Free Graphs, Stephan Olariu

Computer Science Faculty Publications

A graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals the largest number ω(F) of pairwise adjacent vertices in F. Berge's famous Strong Perfect Graph Conjecture asserts that a graph G is perfect if and only if neither G nor its complement G contains an odd chordless cycle of length at least five. Its resolution has eluded researchers for more than twenty years. We prove that the conjecture is true for a class of graphs which strictly contains the claw-free graphs.

Transformation Based Endorsement Systems, Thomas Sudkamp

Computer Science and Engineering Faculty Publications

Evidential reasoning techniques classically represent support for a hypothesis by a numeric value or an evidential interval. The combination of support is performed by an arithmetic rule which often requires restrictions to be placed on the set of possibilities. These assumptions usually require the hypotheses to be exhausitive and mutually exclusive. Endorsement based classification systems represent support for the alternatives symbolically rather than numerically. A framework for constructing endorsement systems is presented in which transformations are defined to generate and update the knowledge base. The interaction of the knowledge base and transformations produces a non-monotonic reasoning system. Two endorsement based …

Odd Primary Periodic Phenomena In The Classical Adams Spectral Sequence, Paul L. Shick

Mathematics and Computer Science

We study certain periodic phenomena in the cohomology of the mod ρ Steenrod algebra which are related to the polynomial generators υ_n ∈ π∗ΒΡ. A chromatic resolution of the Ε₂ term of the classical Adams spectral sequence is constructed.

Atamm Multicomputer System Design, William Robert Tymchyshyn

Electrical & Computer Engineering Theses & Dissertations

The Algorithm To Architecture Mapping Model, or ATAMM, is a graph theoretic design methodology that has been created to resolve design and performance issues involved with concurrent processing. Petri-net marked graphs are used to represent the computational environment.

This thesis describes the development of a multicomputer system which will operate within the bounds specified by the ATAMM model. The system is first designed and implemented using the framework of standard multicomputer design theory. A validation is then performed by the comparison of the system's computational performance to results predicted by ATAMM. This validation is shown to be successful for three …

Fault Tolerance In Networks Of Bounded Degree, Cynthia Dwork, David Peleg, Nicholas Pippenger, Eli Upfal

All HMC Faculty Publications and Research

Achieving processor cooperation in the presence of faults is a major problem in distributed systems. Popular paradigms such as Byzantine agreement have been studied principally in the context of a complete network. Indeed, Dolev [J. Algorithms, 3 (1982), pp. 14–30] and Hadzilacos [Issues of Fault Tolerance in Concurrent Computations, Ph.D. thesis, Harvard University, Cambridge, MA, 1984] have shown that Ω(t) connectivity is necessary if the requirement is that all nonfaulty processors decide unanimously, where t is the number of faults to be tolerated. We believe that in forseeable technologies the number of faults will grow with the size of the …

Wide-Sense Nonblocking Networks, Paul Feldman, Joel Friedman, Nicholas Pippenger

All HMC Faculty Publications and Research

A new method for constructing wide-sense nonblocking networks is presented. Application of this method yields (among other things) wide-sense nonblocking generalized connectors with n inputs and outputs and size O( n log n ), and with depth k and size O( n^{1 + 1/k} ( log n )^{1 - 1/k} ).

Test Generation By Fault Sampling, Vishwani Agrawal, Hassan Farhat, Sharad C. Seth

Mathematics Faculty Publications

This paper presents a novel technique of generating tests from a random sample of faults. The entire fault population of the circuit is randomly divided into two groups. Only one group, usually the smaller one, is used for test generation by the test-generator and fault-simulator programs. This group is known as the sample and its coverage is deterministic. The coverage of faults in the remaining group is similar to that of random vectors and is estimated from the distribution of fault detection probabilities in the circuit. As the sample size increases, the fraction of unsampled faults reduces. At the same …

No Antitwins In Minimal Imperfect Graphs, Stephan Olariu

Computer Science Faculty Publications

It is customary to call vertices x and y twins if every vertex distinct from x and y is adjacent either to both of them or to neither of them. By analogy, we shall call vertices x and yantitwins if every vertex distinct from x and y is adjacent to precisely one of them. Lovász proved that no minimal imperfect graph has twins. The purpose of this note is to prove the analogous statement for antitwins.

A Proposed C Language Binding For The Graphical Kernel System 3-D, M. G. Bolten, C. Y. Ho

Computer Science Technical Reports

This thesis introduces a proposed C language binding definition for the International standards Organization's draft international standard of the Graphical Kernel System-JD. This work augments the earlier C language binding of the two-dimensional version of the Graphical Kernel System commonly known as GKS. The proposed function interface will provide a basis for, if not a final, C language binding for the three-dimensional version of the Graphical Kernel System.

Model Of Hot-Film Sensor With Substrate Effects, David Mcalpine Judge

Electrical & Computer Engineering Theses & Dissertations

A detailed mathematical model is constructed to investigate the frequency response of a hot-film anemometer system. Since several diverse factors affect the frequency response, the analysis is broken down into three main parts. Each part is a detailed mathematical model. The first model consists of the ordinary differential equations which govern the electronics of the feedback system and heat transfer of the sensor. An important simplification in this model is that the rate of heat conduction from the sensor to its substrate is constant.

In the second model the unsteady state heat transfer properties of the substrate are examined by …

Reduced Coproducts Of Compact Hausdorff Spaces, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to …

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.

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.

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

Rise To Power Of Senator Joseph R. Mccarthy: Reflections Of The Cold War Mccarthy Era In American Film, Scott Lainer

Honors Theses

The common bond between much of the film industry and Joseph McCarthy was insecurity and the drive for national approval. If one grasps the specific characteristics of McCarthy the man, and the methods of these politically "inspired" movies, we can to better place the period into context and acknowledge the fact that, if the citizenry is not aware, and is again caught by an ever-building wave of trickle down sentiment, the 1950s might not prove to be an isolated period in American history. Insecurity was not a fifties novelty. It still exists, and could potentially escalate anti-Communist policy and sentiment …

On Root Invariants Of Periodic Classes In Exta(Z/2,Z/2), Paul L. Shick

Mathematics and Computer Science

We prove that if a class in the cohomology of the mod 2 Steenrod algebra is υ_n-periodic in the sense of [10[, then its root invariant must be υ_n+1-periodic, where υ_n denotes the nth generator of π∗(ΒΡ).

Periodic Phenomena In The Classical Adams Spectral Sequence, Mark Mahowald, Paul L. Shick

Mathematics and Computer Science

We investigate certain periodic phenomena in the classical Adams spectral sequence which are related to the polynomial generators υ_n in π∗(ΒΡ). We define the notion of a class α in Ext_Α(Ζ/2,Ζ/2) being υ_n-periodic or υ_n-torsion and prove that classes that are υ_n-torsion are also υ_κ-torsion for all κ such that 0 ≤ κ ≤ n. This allows us to define a chromatic filtration of Ext_Α(Ζ/2,Ζ/2) paralleling the chromatic filtration of the Novikov spectral sequence Ε₂-term …

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.