Mathematics Commons^™

Exploring Various Methods Of Interpolation, Mark Roberts

ACMS Conference Proceedings 1997

No abstract provided.

Hypothesis, Proof, And Censorship Or How Galileo Changed The Rules Of Science, Owen Gingerich

ACMS Conference Proceedings 1997

No abstract provided.

Hyperbolic Geometry With The Geometer's Sketchpad, Robert Frank

ACMS Conference Proceedings 1997

No abstract provided.

Using Java And Html For Linear Algebra Instruction, Jonathan R. Senning

ACMS Conference Proceedings 1997

This paper addresses some of the issues involved with using the HTML, JavaScript and Java to develop and serve a sequence of laboratory modules for use in teaching linear algebra. Attention is paid to the rationale for this approach as opposed to the more traditional approach of laboratory exercises executed using MATLAB or some similar computational tool. Several methods to display mathematics with HTML are described. Some implementation detail and a brief description of the HTML and Java based Linear Algebra Visualization Assistant (LAVA) is presented.

A Tale Of Two Transitions, David Klanderman, Sharon Robbert, Robert Wheeler

ACMS Conference Proceedings 1997

In this paper, we examine transitions to proof courses at two institutions. Bob Wheeler has taught the course at Northern Illinois University. Both Sharon Robbert and Dave Klanderman have taught a related course at Trinity Christian College. We analyze various features of these courses and offer suggestions for other colleges and universities.

History And Current Situation Of Russian Church, Ioann S. Goncharov, Gennadiy A. Kalyabin

ACMS Conference Proceedings 1997

This paper brief outlines the main periods in Russia's Orthodoxy including latest seven decades. In the Appendix a mathematical model is proposed for explaining the Divine Features such as Omniscience, Omnipotence, Predestination, and the free will of men.

A First Draft Of The History Of Acms, Robert Brabenec

ACMS Conference Proceedings 1997

This paper is a draft of the history of the Association of Christians in the Mathematical Sciences as told by Robert Brabenec.

Introduction (1997), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1997

Eleventh ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (1997), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1997

Eleventh ACMS Conference on Mathematics from a Christian Perspective

Schedule (1997), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1997

Eleventh ACMS Conference on Mathematics from a Christian Perspective

Celluloid Blackness : Race, Modernity, And The Conflicted Roots Of American Cinema (1915-1939), Lincoln Farr

Honors Theses

Introduction: "The Problem of the Twentieth Century" In a full page interview in the New York Times on May 29, 1912, the Swiss psychiatrist Dr. Carl G. Jung told the American people, "It seems to me that you are about to discover yourselves. You have discovered everything else-all the land of this continent; all the resources, all the hidden things of nature."Jung used the interview to address the American people, at a moment which he somehow recognized as crucial in the development of human civilization. America, the "tragic" country which he struggled to comprehend, would soon become the harbinger of …

On Some New Constructions Of Difference Sets, Sarah Agnes Spence

Honors Theses

Difference sets are mathematical structures which arise in algebra and combinatorics, with applications in coding theory. The fundamental question is when and how one can construct difference sets. This largely expository paper looks at standard construction methods and describes recent findings that resulted in new families of difference sets. This paper provides explicit examples of difference sets that arise from the recent constructions. By gaining a thorough understanding of these new techniques, it may be possible to generalize the results to find additional new families of difference sets. The paper also introduces partial and relative difference sets and discusses how …

Temporal Flocking And Cacophony Simulating Agent Communication In A Noisy Environment, Jessica R. Crawford

Honors Theses

Realistic communication is one of the most difficult aspects of simulating group behavior because the patterns produced by group communication are complex and not easily definable. In this paper, we present a model, developed using artificial life methodology, for creating simulations of group communication. Our model employs autonomous, artificial agents to produce emergent group behavior that resembles the communication patterns of a group, specifically, a flock of birds. Each agent collects information about its environment and its neighbors and follows a set of rules designed to meet both group goals and individual agent goals. Because we seek to establish emergent …

On The Automatic Generation Of Network Protocol Simulators, Andrew Chen

Honors Theses

Computers communicate with each other over various communication networks via a language known as a protocol. The design of the protocol can have a significant impact on the efficiency (and effectiveness) of the network. Because building an actual network to test the performance (and reliability) of a new protocol is rather expensive and time consuming, there is an interest in simulating network protocols in order to determine how efficient the communication network is. We are therefore interested in automatically generating simulators that could measure the performance of the new protocols. There are two main parts to this project. The first …

Parallel Programming, Peter Dailey

Honors Theses

The speed of technology is always increasing, especially in the field of computing. Unfortunately, the size of the problems needing to be solved are also growing in many areas. In order to keep up with this, parallel computing has become an important research area. The term parallel computing essentially refers to using multiple processors cooperating to solve a problem. For certain problems this can speed up the solution by a factor ofN, the number of processors being used. There are algorithms, for which there is no speed increase due to certain dependencies.

Circles Of The Gods: Copernicus, Kepler, And The Ellipse, Owen Gingerich

ACMS Conference Proceedings 1997

No abstract provided.

Peak-To-Mean Power Control And Error Correction For Ofdm Transmission Using Golay Sequences And Reed-Muller Codes, James A. Davis, J Jedwab

Department of Math & Statistics Faculty Publications

A coding scheme for OFDM transmission is proposed, exploiting a previously unrecognised connection between pairs of Golay complementary sequences and second-order Reed-Muller codes. The scheme solves the notorious problem of power control in OFDM systems by maintaining a peak-to-mean envelope power ratio of at most 3dB while allowing simple encoding and decoding at high code rates for binary, quaternary or higher-phase signalling together with good error correction.

The Use Of Prime Numbers As An Effective Method Of Cryptology, Joshua Flynn

Honors Theses, 1963-2015

With the increasing amount of information transmitted over networks, there is a need to be able to keep this information from falling into the wrong hands. The method that has been used for the past couple of decades is that of cryptography. This paper gives an explanation of cryptography, as well as different alogorithms that are used to solve the problem. One unique thing about a couple of the algorithms is that they use properties provided by prime numbers. In particular, the RSA model, invented by Rivest, Shamir and Adelman, is one model which utilizes the theory that it is …

Random Walks On Wheels, Matthew Lee, Mark Stamp

Faculty Publications, Computer Science

Suppose two particles occupy distinct vertices of a wheel graph and at each step the two particles move independently to adjacent vertices. In this paper we find the expected number of moves until the particles land on the same vertex.

Mathematics At Chartres Cathedral, Richard Stout

ACMS Journal 2004

Chartres Cathedral is highly regarded as a magnificent Gothic structure including beautiful stained glass windows and striking sculptures. Mathematics, especially geometry, played a central role in the design of this cathedral. This paper explores that mathematics and how it contributes to the overall effectiveness of the design.

Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch

ACMS Journal 2004

The philosophy of mathematics has provided insight on questions of foundations and mathematical truth; however, it has not been very fruitful in guiding the practice of mathematics. This paper attempts to find points of contact between a Christian worldview and the choice of mathematical projects and methods. Three areas are considered: (i) dubitability in current research, (ii) the intrinsic value of contemporary mathematics to contemporary society, and (iii) the affirmation of human value in the use of mathematics. Finally, a framework for valuing mathematics is proposed as an encouragement to think more deeply about how a Christian might choose a …

Genetic Algorithms: A Visual Search, Paul W. Jones

Honors Theses, 1963-2015

Genetic algorithms apply the biological principles of selection, mutation, and crossover to a population set containing individuals representing target solutions to a given problem. Using these principles genetic algorithms attempt to create a migration of the individuals in subsequent generations toward the optimal solution.

This project is an attempt to visually represent the progress of a genetic algorithm. The coordinate fitness program attempts to find the maximum or minimum value of a given function. It visually represents the progress of the algorithm by providing a plot of each individual in each generation in time. It is then possible to view …

Resolution Of Local Inconsistency In Identification, Douglas Ray Anderson, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper reports an algorithm for the resolution of local inconsistency in information-theoretic identification. This problem was first pointed out by Klir as an important research area in reconstructability analysis. Local inconsistency commonly arises when an attempt is made to integrate multiple data sources, i.e., contingency tables, which have differing common margins. For example, if one ha)s an AB table and a BC table, the B margins obtained from the two tables may disagree. If the disagreement can be assigned to sampling error, then one can arrive at a compromise B margin, adjust the original AB and BC tables to …

Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

No abstract provided.

Communication Games, Kimberly I. Noonan

Honors Theses

A communication game combines traditional n-person game theory with graph theory. The result is a model of a bargaining situation where communication is restricted. The game's multilinear extension (MLE), a polynomial that summarizes the solutions of the game, is well known for the case where the graph is a tree or simple cycle. This paper simplifies the computation of MLE of the communication game in the case when the graph is a series of simple cycles. The results are then applied to studying the power of each Canadian province in passing an amendment to the constitution, taking geographic location into …

Ideals Of The Lipschitz Class, Konstantin G. Kulev

Honors Theses

In this paper, a classification of the closed ideals of the Little Oh Lipschitz class of functions on the interval [0,1] is provided. The technique used to classify the ideals of the class of continuous functions is modified and applied to the Little Oh Lipschitz class. It is shown that every ideal of these two classes has the form I = {f : flE = 0} for some closed set E C [0, 1]. Furthermore, it is demonstrated that the same technique cannot be successfully applied to the classification of the closed ideals of the Big Oh Lipschitz class.

Banach Spaces Of Analytic Functions, Michael T. Nimchek

Honors Theses

In this paper, we explore certain Banach spaces of analytic functions. In particular, we study the space A-1, demonstrating some of its basic properties including non-separability. We ask the question: given a class C of analytic functions on the unit disk D and a sequence [Zn] = 0 for all n? Finally, we explore Mz invariant subspaces of A-1, demonstrating that they may possess the codimension-2 property.

The Use Of Non-Commutative Algebra In Cryptographically Secure Pseudo-Random Number Generators, Brian M. Mckeever

Honors Theses

This thesis begins with a general overview of pseudo-random number generators and some of their applications. This thesis then describes their applications to cryptography, and some additional requirements imposed by cryptography. This thesis then provides an introduction to the ring of quaternions, and discusses how they can be included in pseudo-random number generators. Finally, this thesis provides a description of the performance of these generators.

Application Of Neural Networks To The Non-Destructive Testing Of Aluminum Cans, B. Balasubramaniam, Daniel .. Clair

Computer Science Technical Reports

Neural Networks are used to c lassify aluminum beverage containers as acceptable or non acceptable, depending upon their wall thicknesses. For each can, the thickness of the wall of the can at different points is measured using a non-destructive, ultra-sound technique. These measureI\}ents are then applied as inputs to the networks and the classification is provided as the output Three architectures, one unsupervised and two supervised, are tested. Their performances are analyzed and compared and the paradigm best suited to the problem is selected.

Computer Assisted Control Of Robotic Rock Drilling Equipment Using Rock Face Image Mapping, William Robert Macneil, Peter (C. Y.)(Chung You) Ho

Computer Science Technical Reports

Use of a totally unmanned mining robot is an ideal solution in removing humans from the dangerous underground mining environment. However, a complete autonomous system is a long way from reality. In the meantime, steps towards that goal can be made and integrated into current mining technology to take away some of the risk and stress from the miner making him more alert and the environment safer for those that do have to be undergroμnd. For our purposes here, the machine will be an automated robotic platform with the intelligence necessary for accurate placement of the drill tip on an …