Mathematics Commons^™

Of Men, Models, And Mathematics, Charles Hatfield

ACMS Conference Proceedings 1977

No abstract provided.

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.

Introduction (1977), Robert Brabenec

ACMS Conference Proceedings 1977

No abstract provided.

Table Of Contents (1977), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1977

No abstract provided.

Epistemology To Ontology, Charles R. Hampton

ACMS Journal 2004

This paper argues for mathematicians thinking about the philosophy of math, especially Christians. It briefly sketches the limitations of formalism, intuitionism, and logicism and uses Christian concept of creation to argue that one can take the best of each of these philosophies and avoid the pitfalls. It also argues for the real existence of mathematical objects apart from the human mind.

Recent Problems In The Foundations Of Mathematics, Terence H. Perciante

ACMS Journal 2004

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 …

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley

ACMS Journal 2004

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 …

A Comparative Investigation Of The Effects Of Frequent Testing Upon Achievement In Secondary Advanced Algebra, John Thomas Fullerton

All Master's Theses

Relatively speaking, few studies have concerned themselves with the problem of frequent testing, and as Keys pointed out, empirical evidence, uncomplicated by differences in the amount of testing material employed, on the effects of frequent testing is, at best, scarce (14:427). Also many studies used tests and test results for direct instruction, thus introducing additional variables. Furthermore, the choice of subjects and disciplines has been limited, the better part being taken from college psychology and sociology classes or high school science classes. This investigation was not an attempt to modify previous experiments, nor was it an attempt to identify which …

Linear Programming In High School Mathematics, Vernon Earl Cotter

Dissertations and Theses @ UNI

"Modern mathematics," a term associated with experimental and revised programs for the teaching of mathematics, should be interpreted only in part as meaning new subject matter. It is true that modern mathematics is associated with such subject matter as the theory of sets and the revision of the definitions of 'relation' and 'function.' But it also connotes a new spirit, a new method of approach, and a new organization of material and problems. Also it may retain much of the traditional subject matter. Of course the order of presentation may be changed and traditional subject matter bounds may be disregarded …

The Spieker Circle And Certain Related Configurations, Berthola Elmo Lumzy

Electronic Theses and Dissertations

This thesis, presented to the Department of Mathematics at Xavier University in partial fulfillment of requirements for the degree of Master of Arts in 1952, examines the Spieker circle, a circle inscribed in the median triangle of a given triangle, and extends its defining properties to related geometric configurations. Lumzy first establishes a series of analogies between the Spieker circle and the nine-point circle, demonstrating parallel relationships involving radius, center, harmonic conjugates, and homothetic centers relative to the incenter, median point, and Nagel point of a triangle.

The thesis then proves that the Spieker circle is inscribed in two congruent …

The Solution Of Ordinary & Partial Differential Equations In Series, Kenneth Wood

Masters Theses & Specialist Projects

The purpose of this thesis is to compile and discuss some of the methods of solution of both ordinary and partial differential equations, whose solutions are expressible in the form of a series. An exhaustive study is not attempted. A few of the methods of most common occurrence for finding solutions in series are discussed and examples illustrating these methods are presented.

Experimental And Observational Geometry, Albert D. Field

University of the Pacific Theses and Dissertations

Geometry has the distinction of being one of the oldest subjects given in the high-school.

Its subject-matter was formulated and organized by the Greeks into a fine system of thought before the time of Christ. Since leaving the hands of the Greeks, geometry has received only a few minor changes, and these largely in recent years.

Heretofore, the study of geometry has been made almost entirely dependent upon memory and reasoning. Geometricians have been slow in adopting the laboratory and observational methods.

This thesis has been written to encourage the student in his work of observing geometrical forms, and in …