The mean value theorem for differentials is basically a consequence of the fundamental theorem of calculus for Lebesgue integration.

How should men and women be seated around a dinner table to maximize conversation between members of the opposite sex? What can be said about the distribution of points around two concentric circles? How are the white and black keys on the piano keyboard organized? What spin configuration in the Ising model minimizes energy? These four problems…

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

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,…

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…

Five different methods for determining the maximizing condition for x(a - x) are presented. Included is the ancient Greek version and a method attributed to Fermat. None of the proofs use calculus. (LS)

Describes an algorithm for calculating the number of ways of folding a map, and some analytical results. (MM)

A simplified discussion of how a whip cracks and what happens when an ideal chain runs over an ideal pulley or off the edge of an ideal table. (MM)

Two definitions of numeracy are considered. A process for developing numeracy is outlined. (MK)

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

The mathematics involved in a practical application of matrices and vectors to the field of computer graphics where three-dimensional objects are moved and displayed is explained. (DT)

Research reported dealt with designing a mathematics course for undergraduate business students. Of the three groups formed by matching, the control group received traditional instruction in college algebra, utilizing one text, while the two experimental groups used materials selected for their relevance to business students. One experimental…

The calculator is used to determine the formula for computing annual yield from a savings account. (MP)