Two traditional presentations introducing the calculus of exponential functions are first presented. Then the suggested direct presentation using calculators is described. (MNS)

The role of optimization in mathematical, physical, biological, social, and management sciences is examined. A plea is made for giving optimization a central place in the mathematics education of scientists and technologists. (Author/MK)

Derivations of elementary trigonometric identities involving constants (namely, particular values of the sine function) are presented. (MK)

A brief description is given of the lives and the mathematical contributions of Hypatia, Maria Agnesi, Sophie German, Sonya Kovalevsky, Emmy Noether, and Mary Cartwright. (DT)

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Presents a theorem and its converse to generate all of the primitive Pythagorean quadruples. Provides a BASIC program generating them. (YP)

Discusses numerical methods to compute approximate solutions of a differential equation. Provides a Pascal program for the extended Euler-Heun method. (YP)

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Questions students raise about the meaning of zero to the zero power present an opportunity for mathematics teachers to involve students in active participation in exploring mathematical relationships. Calculators are the needed tool to make this exploration accessible to students. How they can be used is described. (MNS)

A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)

Knot theory has been inspirational to algebraic and geometric topology. The principal problem has been to ascertain whether two links are equivalent. New methods have been discovered which are effective and simple. Considered are background information; the oriented polynomial; the Jones polynomial; the semioriented polynomial; and calculations,…

A new algorithm for computing roots of any order is presented, along with the historical roots of its development.

In university mathematics courses, the activity of proof construction can be viewed as a problem-solving task in which the prover is asked to form a logical justification demonstrating that a given statement must be true. The purposes of this paper are to describe some of the different types of reasoning and problem-solving processes used by…

We introduce a cooperative learning, group lab for a Calculus III course to facilitate comprehension of the gradient vector and directional derivative concepts. The lab is a hands-on experience allowing students to manipulate a tangent plane and empirically measure the effect of partial derivatives on the direction of optimal ascent. (Contains 7…

Using Newton's method as an intermediate step, we introduce an iterative method that approximates numerically the solution of f(x) = 0. The method is essentially a leap-frog Newton's method. The order of convergence of the proposed method at a simple root is cubic and the computational efficiency in general is less, but close to that of Newton's…