Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…

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,…

Frequently in Management Science courses, instructors focus primarily on teaching students the mathematics of linear programming models. However, the ability to discuss mathematical expressions in business terms is an important professional skill. The authors present an analysis of student abilities to discuss management science concepts through…

The method of proof by mathematical induction follows from Peano axiom 5. We give three properties which are often used in the proofs by mathematical induction. We show that these are equivalent. Supposing the well-ordering property we prove the validity of this method without using Peano axiom 5. Finally, we introduce the simplest form of…

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)

Mathematics provides a language by which man can explore, and describe precisely and profoundly, any possible set of characteristics or relationships in nature. Discussed in this article are several mathematical topics including some historical perspectives in mathematics and new pioneering in hypernumbers. Supplementary sections include…

Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…

Discusses how the International System (SI) abbreviations for numerical factors designated as prefixes may be treated in quantity calculus as free-standing algebraic symbols. Illustrative examples are also presented. (HM)

Describes a variation of the familiar laboratory investigation on the spring and mass oscillator. (SK)

Demonstrates that the number of kilometers of highway in the U.S. tends to grow exponentially and discusses what can be done to modify this growth. (MLH)

Describes an experimental type of science course which involves theoretical and practical approaches to scientific topics by using mathematics to develop and explain scientific problems and theory. Gives an example of such a course applied to the teaching of physical anthropology. (MLH)

Objectives of teaching mathematics to engineering and science students are defined, and the role of the computer, especially the interactive terminal, in achieving these objectives is discussed. (SD)

By considering colors as sets of wavelengths and using Boolean Algebra of sets, the effects of combining colors can be represented in a formal mathematical system. (SD)

The principles of modern genetics are extended to study the extinction probabilities of such genetic diseases as sickle-cell anemia, Tay-Sachs disease, and cystic fibrosis. (JT)

Described is a "studio" procedure utilized at The University of Michigan for teaching mathematical modeling. (SL)