Digital Commons Network^™

Reminiscences Of Paul Erdös (1913-1996), Melvin Henriksen

Humanistic Mathematics Network Journal

No abstract provided.

Sand Songs: The Formal Languages Of Warlpiri Iconography, James V. Rauff

Humanistic Mathematics Network Journal

No abstract provided.

Al-Khawarizmi's Algebra: The First Paradigm In Algebra, Murad Jurdak

Humanistic Mathematics Network Journal

No abstract provided.

See-Duction: How Scientists And Artists Are Creating A Third Way Of Knowing, Howard Levine

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Rebuses, Arthur V. Johnson Ii

Humanistic Mathematics Network Journal

No abstract provided.

Book Reviews: Uncommon Sense, By Alan Cromer, And The Physics Of Immortality, By Frank J. Tipler, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

The First Cams Project: A Humanistic Endeavor, Barbara A. Wainwright, Homer W. Austin

Humanistic Mathematics Network Journal

No abstract provided.

Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal

Department of Math & Statistics Faculty Publications

Relative Difference Sets with the parameters (2^a, 2^b, 2^a, 2^a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.

Auslander Systems, K. N. Haddad, Aimee S. A. Johnson

Mathematics & Statistics Faculty Works

The authors generalize the dynamical system constructed by J. Auslander in 1959, resulting in perhaps the simplest family of examples of minimal but not strictly ergodic systems. A characterization of unique ergodicity and mean-L-stability is given. The new systems are also shown to have zero topological entropy and fail to be weakly rigid. Some results on the set of idempotents in the enveloping semigroup are also achieved.

High-Order Finite-Difference Schemes And Their Application To Computational Acoustics, Joe Leo Manthey

Mathematics & Statistics Theses & Dissertations

The primary focus of this study is upon the numerical stability of high-order finite-difference schemes and their application to duct acoustics. Since acoustic waves are known to be non-dissipative and non-dispersive, high-order schemes are favored for their low dissipation and low dispersion relative to the low-order schemes. The primary obstacle to the the development of explicit high-order finite-difference schemes is the construction of boundary closures which simultaneously maintain the formal order of accuracy and the numerical stability of the overall scheme. In this thesis a hybrid seven-point, fourth-order stencil for computing spatial derivatives is presented and the time stability is …

Reverse Engineering Of Aircraft Wing Data Using A Partial Differential Equation Surface Model, Jacalyn M. Huband

Mathematics & Statistics Theses & Dissertations

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of …

Transformations Of Index Set For Skorokhod Integral With Respect To Gaussian Processes, Leszek Gawarecki

Mathematics Publications

We consider a Gaussian process {Xt,t∈T} with an arbitrary index set T and study consequences of transformations of the index set on the Skorokhod integral and Skorokhod derivative with respect to X. The results applied to Skorokhod SDEs of diffusion type provide uniqueness of the solution for the time-reversed equation and, to Ogawa line integral, give an analogue of the fundamental theorem of calculus.

Positive Braids With A Half Twist Are Prime, Michael C. Sullivan

Articles and Preprints

We shall prove that a knot which can be represented by a positive braid with a half twist is prime. This is done by associating to each such braid a smooth branched 2-manifold with boundary and studying its intersection with a would-be cutting sphere.

Solomon's Sea And The Biblical Π, Andrew Simoson

ACMS Conference Proceedings 1997

From I Kings 7:23, the apparent diameter and circumference of a circular ring are given as 10 and 30 cubits which suggests that the Biblical value of π is 3 rather a number closer to π. However we recount seven different somewhat whimsical explanations as to why this conclusion is overly-hasty.

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

ACMS Conference Proceedings 1997

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 …

An Investigation Of The Behavior Of Calculus Students Working Collaboratively In An Interactive Software Environment, Angela Hare

ACMS Conference Proceedings 1997

Recent work in the area of cognitive research in mathematics education focuses on detailed examinations of the learning process of students and how this process is affected by current innovations in the classroom, including collaborative learning and the use of computers and interactive software. Much of this work is supported by the learning framework of constructivism, a school of thought which is based on the work and writings of Jean Piaget. Piaget, a French psychologist in the mid-twentieth century, observed the learning behavior of children and concluded that individuals construct their own knowledge by creating mental structures which explain their …

Mathematics At Chartres Cathedral, Richard Stout

ACMS Conference Proceedings 1997

Having had several opportunities to travel to France, often with groups of students, our trips have usually included a visit to Chartres, especially to visit the magnificent Gothic cathedral that dominates the town. On a recent visit I was again struck by the beauty, majesty and awe that the cathedral inspires. The building not only does a remarkable job of telling Biblical stories and of enclosing a space conducive to worship, it directs one's eyes and one's spirits upward. This is achieved not only by the beautiful stained glass windows and the striking sculptures, but also by the overall design …

Digital Filtering And Smoothing: A Student Simulation Project, Eric Gossett

ACMS Conference Proceedings 1997

A bug tracking problem is used to introduce students to filtering and smoothing real-time data. A predictor-corrector filter/smoother algorithm is developed and a simulation platform is provided so that students can program and test implementations of the filter/smoother. The platform includes the ability to animate the simulation.

The tracking problem: A small computer bug is traveling around the $x-y$ plane trying to avoid detection. We can eliminate the bug if we can produce a reasonably accurate approximation to its trajectory.

We have a bug detecting device which can be pointed at the plane. It can measure the $x$ and $y$ …

The Role Of Mathematics In Culture, W. James Bradley

ACMS Conference Proceedings 1997

This paper examines theories of the role of mathematics in culture and seeks to understand how a Christian should view the role of mathematics.

The Mathematical Sciences And The Mediator Of Creation, W. David Laverell

ACMS Conference Proceedings 1997

This article stems from a conviction that while the development of a theistic view of the mathematical sciences is a laudable goal and much to be encouraged, it is incumbent upon us to explore every avenue that might lead to a distinctively Christian perspective. This leads naturally to a consideration of the unique role played by Christ in Creation, and a convenient framework is provided by seeing Christ as Mediator of Creation. We shall discuss the term itself, examine the biblical passages that seem to present the concept, consider the ways these passages have been understood by theologians, and …

Fractal Geometry And Chaos Theory: From Old Problems To New Models And Methods, Terence H. Perciante

ACMS Conference Proceedings 1997

Fractal geometry and chaos theory are deeply rooted in significant problems in the history of mathematics and science. While mathematicians have geometrical descriptions of space with its properties, scientists have attempted to characterize the physical properties of fundamental entities present in space and time. The separate investigations frequently influenced each other and led to profound theories, answers, and models. However, at the same time new problems repeatedly arose internal to mathematics and externally in the applications to which mathematics was applied. Fractal geometry issues from these antecedents in response to features and processes in nature not easily represented by historical …

Teaching Generalization And Reduction Through An Elementary Probability Problem, Erian Wheeler

ACMS Conference Proceedings 1997

No abstract provided.

On Binary Quadratic Forms, Alain Togbe

ACMS Conference Proceedings 1997

No abstract provided.

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.