Applied Mathematics Commons^™

Introduction (1999), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

Schedule (1999), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (1999), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1999

Twelfth ACMS Conference on Mathematics from a Christian Perspective

Can Mathematics Be Taught In A Christian Way?, Johan Deklerk

ACMS Journal 2004

Some people would argue that mathematics cannot be taught in a Christian way. Others would say it can be done, but that they are unsure how to do it, and therefore do not do it. Some methods mentioned from time to time will be briefly discussed in this address. The question will be asked whether these techniques bring one closer to a Christian perspective on mathematics. My view is that some of these methods are just not sufficient and that more should be done. More attention should be paid to the context in which a mathematical subject is imbedded. Attention …

Lewis Carroll: Author, Mathematician, And Christian, David L. Neuhouser

ACMS Journal 2004

Although a Christian, an author, and a mathematician, Charles Letwidge Dodgson (better known as Lewis Carroll) wrote very few works in which these three aspects of his person was present. The only examples of him merging these interests are in Sylvie and Bruno and Sylvie and Bruno Concluded. This paper will explore what motivated him to make these works and whether or not they were successful.

The Deconstruction Of Mathematics, David J. Stucki

ACMS Journal 2004

Mathematics, as an academic discipline, has stood for many years as the last bastion against a growing tide of intellectual relativism that has become all but ubiquitous. More recently, however, efforts have been made to "humanize" mathematics by advocating a social-constructivist approach to the philosophy of mathematics, both in practice and education. This paper is intended to serve as a critical response to one advocate of this approach, Reuben Hersh (What Is Mathematics, Really?, 1997), and in the process a defense of Platonism.

On The P-Connectedness Of Graphs – A Survey, Luitpold Babel, Stephan Olariu

Computer Science Faculty Publications

A graph is said to be p-connected if for every partition of its vertices into two non-empty, disjoint, sets some chordless path with three edges contains vertices from both sets in the partition. As it turns out, p-connectedness generalizes the usual connectedness of graphs and leads, in a natural way, to a unique tree representation for arbitrary graphs.

This paper reviews old and new results, both structural and algorithmic, about p-connectedness along with applications to various graph decompositions.

Validation Of Waimss Incident Duration Estimation Model, Wei Wu, Pushkin Kachroo, Kaan Ozbay

Electrical & Computer Engineering Faculty Research

This paper presents an effort to validate the traffic incident duration estimation model of WAIMSS (wide area incident management support system). Duration estimation model of WAIMSS predicts the incident duration based on an estimation tree which was calibrated using incident data collected in Northern Virginia. Due to the limited sample size, a full scale test of the distribution, mean and variance of incident duration was performed only for the root node of the estimation tree, white only mean tests were executed at all other nodes whenever a data subset was available. Further studies were also conducted on the model error …

Maximally Disjoint Solutions Of The Set Covering Problem, David J. Rader, Peter L. Hammer

Mathematical Sciences Technical Reports (MSTR)

This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP­ complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, …

On Circulant Weighing Matrices, K. T. Arasu, Jennifer Seberry

Mathematics and Statistics Faculty Publications

Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 82 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.

The Adjoint Alternative For Matrix Operators, C. H. Cooke

Mathematics & Statistics Faculty Publications

The following inverse problem is considered: given a matrix B of rank r, does there exist a matrix A such that

B = T(A) = adjoint (A)

where the classical adjoint operation is intended? Conditions are determined on the rank of B which decides whether or not B lies in the range of the matrix adjoint operator.

Asymptotically Tight Bounds For Performing Bmmc Permutations On Parallel Disk Systems, Thomas H. Cormen, Thomas Sundquist, Leonard F. Wisniewski

Dartmouth Scholarship

This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bit-matrix-multiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index by an affine transformation over GF(2), where the source and target indices are treated as bit vectors. The class of BMMC permutations includes many common permutations, such as matrix transposition (when dimensions are powers of 2), bit-reversal permutations, vector-reversal permutations, hypercube permutations, matrix reblocking, Gray-code permutations, and inverse Gray-code permutations. The upper bound improves upon the asymptotic …

On The Structure Of Graphs With Few P4s, Luitpold Babel, Stephan Olariu

Computer Science Faculty Publications

We present new classes of graphs for which the isomorphism problem can be solved in polynomial time. These graphs are characterized by containing — in some local sense — only a small number of induced paths of length three. As it turns out, every such graph has a unique tree representation: the internal nodes correspond to three types of graph operations, while the leaves are basic graphs with a simple structure. The paper extends and generalizes known results about cographs, P₄-reducible graphs, and P₄-sparse graphs.

A Fast Parallel Algorithm To Recognize P4-Sparse Graphs, Rong Lin, Stephan Olariu

Computer Science Faculty Publications

A number of problems in mobile computing, group-based collaboration, automated theorem proving, networking, scheduling, and cluster analysis suggested the study of graphs featuring certain “local density” characteristics. Typically, the notion of local density is equated with the absence of chordless paths of length three or more. Recently, a new metric for local density has been proposed, allowing a number of such induced paths to occur. More precisely, a graphG is called P4-sparse if no set of five vertices inG induces more than one chordless path of length three. P4-sparse graphs generalize the well-known class of cographs corresponding to …

Corrigendum To “Post-Surgical Passive Response Of Local Environment To Primary Tumor Removal”: Mathl. Comput. Modelling, Vol. 25, No. 6, Pp. 7–17, 1997, J. A. Adam, C. Bellomo

Mathematics & Statistics Faculty Publications

The computer program that was used to generate the graphs for the concentration of inhibitor contained an error. This influenced the scaling in the original Figures 2 and 3. As an example, a sample of the corrected graphs are given below. Copies of other corrected figures can be obtained from the authors. It is important to note that the “pulse” appears for the function rC(r, t). As can be seen, it travels slowly outward with decreasing amplitude. The mathematical analysis in the paper remains unchanged.

Fast Discrete Polynomial Transforms With Applications To Data Analysis For Distance Transitive Graphs, J. R. Driscoll, D. M. Healy, D. N. Rockmore

Dartmouth Scholarship

Let $\poly = \{P_0,\dots,P_{n-1}\}$ denote a set of polynomials with complex coefficients. Let $\pts = \{z_0,\dots,z_{n-1}\}\subset \cplx$ denote any set of {\it sample points}. For any $f = (f_0,\dots,f_{n-1}) \in \cplx^n$, the {\it discrete polynomial transform} of f (with respect to $\poly$ and $\pts$) is defined as the collection of sums, $\{\fhat(P_0),\dots,\fhat(P_{n-1})\}$, where $\fhat(P_j) = \langle f,P_j \rangle = \sum_{i=0}^{n-1} f_iP_j(z_i)w(i)$ for some associated weight function w. These sorts of transforms find important applications in areas such as medical imaging and signal processing.

In this paper, we present fast algorithms for computing discrete orthogonal polynomial transforms. For a system …

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.