David Gale was one of the mathematicians responsible for the modern form of the theory of duality in linear programming and the associated proof of the minimax theorem in the theory of games. He is a member of the National Academy of Sciences and is Professor Emeritus of Mathematics and Operations Research at the University of California at…

How does artificial gravity affect the path of a thrown ball? This paper contrasts ball trajectories on the Little Prince's asteroid planet B-612 and Arthur C. Clarke's rotating-drum spacecraft of 2001, and demonstrates curve balls with multiple loops in the latter environment.

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…

For a long time, the medieval university maintained relative consistency throughout Europe in teaching topics and methods. But between 1550 and 1650 this came to an end. The evolution concerned the content of the courses and, to a lesser extent, the way the field was taught. The impact of these changes varied greatly from place to place, and new…

As a precursor to lessons on prime decomposition and reducing fractions, rules are generally presented for divisibility by 2, 3, 5, 9, and 10 and sometimes for those popular composites such as 4 and 25. In our experience students often ask: "What about the one for 7?" and we are loathe to simply state that there isn't one. We have yet to see a…

In terms of modern pedagogy, having visual interpretation of trigonometric functions is useful and quite helpful. This paper presents, pictorially, an easy approach to prove all single angle trigonometric identities on the axes. It also discusses the application of axial representation in calculus--finding the derivative of trigonometric functions.

Real-life applications of the use (and misuse) of mathematics invariably pique students' interest. This article describes a legal case in California that occurred in the 1960s in which a couple was convicted of robbery, in part, based on the expert testimony of a statistics instructor. On appeal, the judge noted several mathematical errors in this…

A method of helping students attack the components of mathematics as a language is discussed; examples from arithmetic and from calculus are illustrated. (DT)

Recent developments are explained which use the concepts and methods of mathematical logic to provide a suitable framework for the development of the differential and integral calculus. (DT)

Notation and definition of the derivative function are discussed. (DT)

This is a textbook, originally developed for scientists and engineers, which stresses the actual solutions of practical problems. Theorems are precisely stated, but the proofs are generally omitted. Sample contents include first-order equations, equations in the complex plane, irregular singular points, and numerical methods. A more recent idea,…

This unit provides some activities designed to familiarize the reader with the TI-59 and instructions on creating a library of programs on magnetic cards. (MP)

Twelve problems which can be proved by the "mailbox principle" are stated and discussed. (DT)

An axiomatic development of the derivative and the antiderivative is presented. (DT)

Highlights in the history of the axiomatic method are described, and Hilbert's and Godel's contributions are discussed. (DT)