In Volume 26, Number 2, we reported on a group case study run for level 3 mathematics students at the University of Brighton. At the core of the study was a quadratic assignment problem, and we reported on attempts by students to use Excel to solve the problem, and on the attendant difficulties. We provided an elegant solution. In this article, we…

Presented are solutions to variations of a combinatorics problem from a recent International Mathematics Olympiad. In particular, the matrix algebra solution illustrates an interaction among the undergraduate areas of geometry, combinatorics, linear algebra, and group theory. (JJK)

Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

Computer graphics are used to display the sum of the first few terms of the series solution for the problem of the vibrating string frequently discussed in introductory courses on differential equations. (MNS)

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)

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,…

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Discussed are the mathematical methods for detecting a variety of common error patterns within the bar-coded identification numbers utilized in conjunction with scanning devices. Schemes for the use of check digits are examined that ensure conditions for detecting errors of specific types, including single digit error, transposition error, twin…

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

Examples of diversions with cards that may be used to illustrate the concept of a cyclic group and structural properties of the integers modulo a prime are presented. (MNS)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Presents classroom curriculum and student projects that use dynamical systems--something that changes over time, such as weather or populations--to capture students' attention. (MKR)

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)