A concept of major importance in human electrophysiology studies is the process by which activation of an excitable cell results in a rapid rise and fall of the electrical membrane potential, the so-called action potential. Hodgkin and Huxley proposed a model to explain the ionic mechanisms underlying the formation of action potentials. However,…

Outlines the facts being presented in the literature about mathematical models, their related components, and their practical and theoretical uses. (Author)

POLYFACT is a learning program that attempts to factor multivariable polynomials. The program has been successful in factoring polynomials (in simplified form) with a maximum of 84 terms, each term consisting of as many as five variables and a maximum degree of 67. The complexity of this learning task placed unusual requirements on the…

Presents a description of a relatively new theory which offers a powerful mathematical tool for rigorously synthesizing common theoretical conflicts between discrete and continuous interpretations of scientific phenomena. One particular note is made in reference to man's conceptualization of time. (Author/EB)

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

Most decision problems are those in which a choice among multiple-objective alternatives must be made. The central difficulty of such decision problems lies in finding single decision criteria that combine the decisionmaker's objectives and interests in an acceptable way. In this paper, a general procedure for the construction of such single…

This report considers a university faculty which is divided into k grades. The total size is to remain fixed, but the proportions in the grades may vary. The problem is to find control strategies which will bring about desired changes in these proportions. This report is confined to investigating what can be achieved by controlling the numbers of…

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

A simple teaching model, designed to show rapidly which are the principal factors in population growth and how they are related, is presented. The apparatus described allows students to play several different active roles. (MP)

Describes the basic philosophy, nomenclature, and techniques used in mathematical modelling to enable biologists, engineers, land managers, and others to understand the concepts and usefulness of models. Contrasts conceptual and empirical approaches, using ecosystem models as an example of the former. (DC)

Mathematical modeling is defined. Examples are used to show that there are models available which illustrate both the traditional use of mathematics in the physical science and its newer use in nonphysical disciplines, and which are at a suitable level for teaching in schools. (Author/MK)

Describes the use of step-functions in modelling instruction. Classifies modelling into three categories: direct, analogical, and creative application. Provides and discusses modelling postal rates and other problems as examples. (YP)

Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…

These modules develop two prevalent explanations among political scientists of who gets what in the budgetary process. Specifically, the problem of how an agency's level of appropriations changes over time is addressed. It is noted that budgeting is a political process in the classic sense, in that it elicits and embodies patterns of conflict and…