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…

Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)

Described is an example of a piecewise defined function developed naturally as a consequence of the solution to the given problem statement, thereby allowing calculus students the uncommon opportunity to generate such an otherwise, seemingly contrived function. (JJK)

An outline of some of the essential differences, both in content and methods, between statistics and core mathematics is provided, along with subsequent discussion of the practical implications that these differences portend for a mathematics department at a liberal arts college. (JJK)

Reports on ongoing developmental research efforts to adapt the instructional design perspective of Realistic Mathematics Education (RME) to learning and teaching of collegiate mathematics using differential equations as a specific case. Focuses on the RME design heuristic of guided reinvention as a means to locate the starting point for an…

Preparing for an oral examination is an alternative way for students to learn mathematics by working cooperatively in small teams to solve problems. Reformed college mathematics courses are emphasizing the ability to communicate ideas clearly, both orally and in writing. The instructor is able to ask probing questions that are not usually possible…

Reported are results of a study of a sample of 259 students at the University of Massachusetts who scored low on a math placement test and later took precalculus math classes. Several possible conclusions are presented to explain the test results. A significantly higher percentage (p<.05) of a remedial sample (compared to a non-remedial sample)…

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

A noncredit course in a workshop format is described, with sessions focusing on recognizing and defining problems; organizing information and using modeling techniques; analyzing data, recognizing trends, and making decisions; being flexible and thinking creatively; and generalizing and consolidating. (MNS)

Algebraic and transcendental curves are discussed, with attention focused on computing the area of some special regions bounded by the curves. (MNS)

Shows how a simple spreadsheet program can be used to teach calculus concepts more effectively through simultaneous use of review questions and instructions, actual manipulation of data and formulas, and visual illustration of results. Concepts illustrated include the difference quotient and derivation of a function; difference and differential;…

A method of teaching introductory statistics using student-selected project topics is described. Several activities are noted, with a model for student research projects. (MNS)