Mathematics Commons^™

Math & Society: An Introduction To Mathematical Thought, Verbal Snook

ACMS Conference Proceedings 1979

No abstract provided.

Mathematics And Christian Faith - Some Personal Perceptions, Richard Laatsch

ACMS Conference Proceedings 1979

No abstract provided.

Implications Of Recent Developments In Philosophy Of Science For An Axiological Approach To Foundations Of Mathematics, Harold Heie

ACMS Conference Proceedings 1979

No abstract provided.

Logic In The Mathematics Curriculum, Nigel Cutland

ACMS Conference Proceedings 1979

No abstract provided.

Introduction (1979), Robert Brabenec

ACMS Conference Proceedings 1979

No abstract provided.

Table Of Contents (1979), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1979

A Second Conference on the Foundations of Mathematics

Stochastic Approximation Procedures For Mixing Stochastic Processes, Katherine Campbell

Mathematics & Statistics ETDs

Stochastic approximation methods for estimating the parameters of a stationary autoregressive process of finite order are investigated. The emphasis is on robust methods, and the non-linear scoring functions associated with such methods require the development of new techniques for establishing convergence. A mixing condition falling between the traditional strong and uniform mixing conditions is investigated in detail, and used to establish almost sure and mean square convergence of the proposed algorithms when the underlying process satisfies this condition. A short Monte Carlo study verifies the desirable properties of the robust algorithm in the presence of heavy-tailed innovations.

A Semilinear Dirichlet Problem, Alfonso Castro

All HMC Faculty Publications and Research

Let Ω be a bounded region in R^n. In this note we discuss the existence of weak solutions (see [4, Section 2]) of the Dirichlet problem:

Δu(x) + g(x, u(x)) + f(x, u(x), ∇u(x)) = 0 ; x є Ω

u(x) = 0 ; x є ∂Ω

where Δ is the Laplacian operator, g : Ω x R → R and f : Ω x Rⁿ⁺¹ → R are functions satisfying the Caratheodory condition (see [2, Section 3]), and ∇ is the gradient operator.

Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier

ACMS Journal 2004

This paper clearly presents eight aspects of mathematics and contrasting perspectives in each that will affect the teaching of mathematics and the design of curricula. It also presents a collection of affirmations that could reasonably characterize a Christian perspective on teaching mathematics.

An Illustrative Model Describing The Refraction Of Long Water Waves By A Circular Island, Gregory A. Kriegsmann

Department of Mathematics: Faculty Publications

The refraction of small shallow water waves by an idealized island is studied in this paper. The island's shoal is modeled by a quartic polynomial in the radial variable. This particular model allows the explicit construction of the rays (wave orthogonals) and the determination of several important features of the wave motion. The various shortcomings of the particular profile are discussed.

Groups Expressed As The Set-Theoretic Union Of Proper Subgroups, Lana Barrett

Masters Theses & Specialist Projects

In their paper “Groups as Unions of Proper Subgroups,” published in 1959, Haber and Rosenfeld posed the problem of characterizing groups which can be expressed as the set theoretic union of a finite collection of their proper subgroups. Haber and Rosenfeld established that a group G is the union of three proper subgroups (such a group G shall be called a U₃-group) if and only if the Klein 4-group is a homomorphic image of G. Further results concerning U₃-groups were obtained in the paper “Groups which are the Union of Three Subgroups” by Bruckhemier, Bryan and …

Estimation Of The Acceleration Function, Le Than Chap

Mathematics & Statistics ETDs

Let x1, x2,…, xm be a random sample of m failure times under normal conditions with the underlying distribution function F(x) and Y1, Y2,…, Yn be a random sample on n failure times under accelerated conditions with the underlying distribution function G(x):

G(x)=f(F(x))

Where f(x) is the acceleration function.

In this dissertation we propose several estimators for the acceleration function f(x) and investigate their properties.

A Random Walk In A Random Environment, Edwin Andrew Sanchez

Mathematics & Statistics ETDs

In this dissertation we consider a model of a random walk, (Z_n}, on R(1) where the distribution of (Z_n} is dependent on a stochastic process (Y_n} and is given by g_y(z) where Y_n-1 = y . Conditions on the environmental process (Y_n} are given for which transience or recurrence of the random walk (Z_n} can be detennined. The probability of n absorption and mean time problems are solved when (Y_n} is a finite Markov chain and (Z_n} is a classical random walk on …

Complementary Extremum Principles, J. Swetits, C. Rogers

Mathematics & Statistics Faculty Publications

Important complementary extremum principles are generated without recourse to general variational theory. The results are illustrated by an application to a class of boundary value problems in Magnetohydrodynamics.

Quasi-Triangular Matrices, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

It is shown that there exist quasitriangular operators which cannot be represented as quasitriangular matrices.

Nonlinear Resonance In Celestial Mechanics With Applications To The Rotation Of Mercury, Timothy John Burns

Mathematics & Statistics ETDs

Two planar, fixed-orbit models of the rotation of the planet Mercury are studied using the method of averaging. The first model includes only the solar torques on the planet's permanent asymmetry and on its solar tidal bulge. For this model, it is shown that the zero of the averaged tidal torque corresponds to an asymptotically stable periodic solution of the second kind which, for two tidal torque representations, is close to the asymptotically stable equilibrium point corresponding to an exact 3:2 spin-orbit resonance. This periodic solution restricts the possible initial rotation states of Mercury, and it may account for the …

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 .

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 …

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.

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.

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 …

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, …

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.

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.

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 …

Formalizing The Liar Paradox, Frank Meyer

ACMS Conference Proceedings 1977

No abstract provided.

God: All Sufficient Or Infinite, Thomas E. Iverson

ACMS Conference Proceedings 1977

No abstract provided.

Getting Their Interest - Initiating Students Into The Study Of Foundational Issues In Mathematics, Harold Heie

ACMS Conference Proceedings 1977

No abstract provided.

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.

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?