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Articles 1 - 18 of 18
Full-Text Articles in Applied Mathematics
Numerical Methods For Multipoint Boundary Value Problems, Mahoud Abdul-Ghani Sarhan
Numerical Methods For Multipoint Boundary Value Problems, Mahoud Abdul-Ghani Sarhan
Mathematics & Statistics ETDs
Existence and uniqueness theory for ordinary differential systems subject to linear constraints is presented in some detail. Finite difference schemes, shooting methods, orthonormalization procedures and projection methods are studied. Orthonormalization procedures are shown to be ineffective for the general linear problem. Projection methods for linear differential systems with fairly general multipoint boundary conditions are thoroughly developed. Two particular examples of such methods are given: Galerkin and collocation. The various numerical methods considered are evaluated and compared. Several examples are discussed and numerical results are displayed .
A Christian Point Of View, A. Wayne Roberts
A Christian Point Of View, A. Wayne Roberts
ACMS Conference Proceedings 1977
Does the fact that you are a Christian affect the way that you teach mathematics? This paper seeks to answer the question, what contributions can a mathematics teacher in a Christian school make to the distinctive purpose of such a school?
Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase
Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase
ACMS Conference Proceedings 1977
The purpose of this paper is to show that both sides of the predestination/free-will discussion are admissible in a way that is more profound than simply the wave-particle duality of light. In wave-particle duality there are two competing physical models of reality which are contradictory. This paper will show that not a contradiction but a difference in viewpoint is the fundamental issue in the discussion of predestination and free will. A discussion of Skolem’s paradox is helpful in this demonstration.
Current Work On Mathematical Truth, Michael Detlefsen
Current Work On Mathematical Truth, Michael Detlefsen
ACMS Conference Proceedings 1977
The overall aim of this paper is to serve as an introduction to the work currently being done on the topic of mathematical truth. It provides an overview of the major developments concerning mathematical truth and also evaluates those developments as potential contributions to mathematician’s understanding of the subject.
Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes
Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes
ACMS Conference Proceedings 1977
This paper describes the three types of theory about universals, beginning in each case with a classical historical formulation and moving to its restatement in recent analytic philosophy. It will then suggest ways in which Christian perspectives bear on theories of universals and so on mathematics.
Recent Problems In The Foundationsof Mathematics, Terence H. Perciante
Recent Problems In The Foundationsof Mathematics, Terence H. Perciante
ACMS Conference Proceedings 1977
This paper examines the foundational crises that have haunted twentieth-century mathematics, beginning with a brief review of the effects generated by Gauss, Lobachevsky, and Bolyai who each developed non-Euclidean parallel axiom. Though of mathematical interest in their own right, the significance of the new geometries was greatly magnified when it was discerned that they could be used to adequately model physical space, even to the extent that Einstein’s theory of relativity later employed as its model a non-Euclidean geometry developed by Riemann. The question that obviously presented itself was how could any given geometry be called true when it and …
Infinity & Reality, John W. Warner
Infinity & Reality, John W. Warner
ACMS Conference Proceedings 1977
This paper examines the topics of infinity and reality as relevant to the conference, proposing a possible relationship between the two in order to stimulate further discussions.
A Brief Introduction To Gödel’S Theorems, Michael Detlefsen
A Brief Introduction To Gödel’S Theorems, Michael Detlefsen
ACMS Conference Proceedings 1977
Gödel’s two famous incompleteness theorems are results that have come up a number of times in the discussions at the 1977 ACMS conference. This paper provides a brief and relatively non-technical statement on these results and of their significance for the foundations of mathematics.
Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley
Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley
ACMS Conference Proceedings 1977
Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of …
Existence In Mathematics, Willis Alberda
Existence In Mathematics, Willis Alberda
ACMS Conference Proceedings 1977
Contemplation of the existence of mathematical entities for very apparent reasons generates a mental cycling of arguments dealing with the nature of mathematical truth, meaning in mathematics, and the obviously related question of which of these two problems should be solved first. The problem of the existence of mathematical entities dates from the first thoughts and ideas of a mathematical nature. The problem of existence in mathematics is fundamental to the domain of speculation and research on the foundations of mathematics. When we try to put ourselves in the place of those philosophers who first explored this problem we must …
The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis
The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis
ACMS Conference Proceedings 1977
In teaching the foundations of mathematics within the framework of a Christian college, and particularly that of a Christian liberal arts college, there are two groups of students which must be served. The first consisted of the non-mathematics majors—those non-scientifically oriented “general anything” students who, as a catalog might put it, are to receive “an introduction to and an appreciation of the history, foundations, culture and applications of mathematics.” The second group consists of the mathematics majors, and the few science majors who have not been frightened away by the calculus. The gulf between these two groups is sufficiently large, …
Epistomology To Ontology, Charles R. Hampton
Epistomology To Ontology, Charles R. Hampton
ACMS Conference Proceedings 1977
This paper offers commentary on the various philosophical approaches to the foundations of mathematics and then indicates how these ideas have implications in consideration of the existence question.
Introduction (1977), Robert Brabenec
Introduction (1977), Robert Brabenec
ACMS Conference Proceedings 1977
No abstract provided.
Table Of Contents (1977), Association Of Christians In The Mathematical Sciences
Table Of Contents (1977), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1977
No abstract provided.
Positive Perturbations Of Unbounded Operators, Joanne Dombrowski
Positive Perturbations Of Unbounded Operators, Joanne Dombrowski
Mathematics and Statistics Faculty Publications
This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.
Superconcentrators, Nicholas Pippenger
Superconcentrators, Nicholas Pippenger
All HMC Faculty Publications and Research
An $n$-superconcentrator is an acyclic directed graph with $n$ inputs and $n$ outputs for which, for every $r \leqq n$, every set of $r$ inputs, and every set of $r$ outputs, there exists an $r$-flow (a set of $r$ vertex-disjoint directed paths) from the given inputs to the given outputs. We show that there exist $n$-superconcentrators with $39n + O(\log n)$ (in fact, at most $40n$) edges, depth $O(\log n)$, and maximum degree (in-degree plus out-degree) 16.
An Investigation Of The Plume Theories Of Briggs And Hanna, George Kyle Cooper
An Investigation Of The Plume Theories Of Briggs And Hanna, George Kyle Cooper
Masters Theses
Many models have been developed for or applied to the prediction of mechanical draft cooling tower plumes. However, due to a serious lack of data up to this date, little has been done to verify the predictive capability of these mathematical models. This thesis attempts to rectify this situation somewhat by undertaking a thorough investigation of the plume theories of G. A. Briggs and S. R. Hanna. A study of their theoretical foundations and development, practical formulations, and ability to predict the height and length of the visible portion of mechanical-draft cooling tower plumes is undertaken. Detailed derivations of their …
Solar Magnetoatmospheric Waves-A Simplified Mathematical Treatment, John A. Adam
Solar Magnetoatmospheric Waves-A Simplified Mathematical Treatment, John A. Adam
Mathematics & Statistics Faculty Publications
The inhomogeneous wave equation for a special class of magnetoatmospheric waves is formally solved, and the principle of stationary phase used to provide information on the group velocity properties of such waves. General results are presented concerning the associated mechanical energy flux. The basic problem considered is relevant to waves initiated by sudden events in the solar atmosphere.