How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

The College Success in Mathematics Project began in 1996 with the production of a framework for student success in university-level mathematics courses at the University of Guam. The project continued with a one-week workshop followed by the preparation of "Preparing for Mathematics" at the University of Guam (UOG), which outlined specific topics…

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

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

Presents a program in Level II BASIC for a TRS-80 computer that simulates a Turing machine and discusses the nature of the device. The program is run interactively and is designed to be used as an educational tool by computer science or mathematics students studying computational or automata theory. (MP)

Included are a detailed example of a calculator demonstration, the general principles to be followed in preparing a calculator demonstration, a list of demonstration topics for a calculus course, and some suggested topics for other courses. (MK)

Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)

The calculus of finite differences and finite sums is used to create a context in which the computer can be incorporated into calculus courses. Analyses of the experimental implementations are included. (MP)

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)

Identifies requisite math skills for a microeconomics course, offering samples of supply curves, demand curves, equilibrium prices, elasticity, and complex graph problems. Recommends developmental mathematics competencies, including problem solving, reasoning, connections, communication, number and operation sense, algebra, relationships,…

Discussed are two approaches to determining which regular polygons, either inscribed within or circumscribed about the unit circle, exhibit rational area or rational perimeter. One approach involves applications of abstract theory from a typical modern algebra course, whereas the other approach employs material from a traditional…

Utilizing composition of elementary functions as prototype of dynamical system, notions of periodic points and their orbits in relation to concept of shift map are used to illustrate concept of continuity. A special case of Sarkovskii's theorem, dealing with period-3 point, is presented with proof relying solely upon Intermediate Value Theorem and…