In the manner of a large rock dropped into a tranquil pool the intellectual stir created in the 1870's by Stanley Jevons in London, Carl Menger in Vienna, and Leon Walras in Lausanne, sent waves in all directions, some of which have not entirely...
The American constitutional experience began as a great experiment. The United States was the first nation to launch representative government. This form of government is now commonplace, but at that time. it was celebrated as the grand discovery of...
The proliferation of hand-held calculators gives new relevance and urgency to the plea of the late G.E. Forsythe that users of numerical methods be made aware of the pitfalls of floating point computation. Although roundoff errors may remain...
Improvement and optimization are consistent themes throughout science. Entropy increases, an object falls to earth to minimize its potential energy, light rays refract in a way that minimizes the time required to travel from a point in one medium t o a...
Courses in calculus have routinely covered applications not only for their own sake but also in response to the students' most frequent question: What's this stuff good for? In the past, most applications centered on physical or engineering problems....
To the typical scientist or mathematician, the computer is a marvelous device for calculating and sorting: it can crunch numbersn a t astonishing speeds, and find needle-like optimal solutions among haystacks of possible options. But in fact it can...
A mathematical model can be a valuable tool in creating structure for a physical phenomenon, provided it capture sessential aspects of the behavior under investigation. A carefully prepared model can lead to a structure that can reveal significant...
The term microcomputer can reasonably apply to the small integrated circuits or chips, based on solid-state physics, used as components in computers. It can also apply to typewriter-sized computers containing such chips, which is the current usage. The...
One of the most important biological applications of integration is the determination of proper ties of flow systems. Among the significant characteristics of a flow system are its flow rate (a heart's output in liters per minute, for example), its...
This article was inspired by the September 1981 issue of Scientific American, which describes the applications of microbiology to past, present, and future technology in a detailed and captivating manner in eight comprehensive articles. Microorganisms...
The use of mathematics as a research language in the social sciences is only now coming into its own, despite the power and versatility of mathematical techniques. Using the Soviet-American arms race as an illustration, the author argues that simple,...
The intuitive appeal of the definition is demonstrated routinely by means of simple examples involving card drawing, dice, and chips in the bowln problems.. These problems are easy to visualize and they do give the student practice in dealing with the...
Suffolk Community College has just completed a major, three-year project to incorporate the use of computers into almost all mathematics courses and related courses in physics, chemistry, earth and space sciences, engineering, and economics. The...
When one asks the question, What do mathematicians do? the immediate answer given by most is that they prove theorems. In this paper we will consider proofs of Euclid's theorem that there are infinitely many primes. Euclid proved this theorem in book...
This paper deals with the philosophy and content of a one semester senior level course entitled Mathematical Systems Analysis. The course was intended for students who had a background including elementary calculus, linear algebra, some ordinary...
The question in the title is intentionally ambiguous. Whom are we interested in--entering students or those already enrolled? The length-of-stay distributions for these two groups will rarely be identical. Social scientists carefully distinguish...
When I taught a calculus class composed mostly of biology students, I looked for a project wherein the students could collect biological data for which a mathematical mode l would be constructed. Although the project was conceived for biology students,...
Anyone who has attempted to teach realistic applied mathematics in a course has no doubt been impressed with the difficulty of this task. In the first place, realworld problems are usually stated in an open-ended fashion, using imprecise terms, and...
Wimbledon watchers and tennis players cannot fail to be aware of the importance of the service. Players like Tanner are noted for the high speed of their service, whilst the fate of a championship often depends on which player manages to get the larger...
This article seeks to trace the historical development of the Principal Axis Theorem. It begins with the work of Rene Descartes and Pierre Fermat (ca. 1640), and is not completely, rigorously established until Karl Weierstrass (ca. 1858). Also,...