Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

This article will describe a writing assignment designed for use in a liberal arts college whose mission stresses effective written communication both within and across disciplines. In this assignment, students write three separate solutions to the same mathematics problem: one for a mathematical peer, a second for a contemporary that does not…

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)

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

This paper first defines the bridge club scheduling problem that was presented to the author and then explores the meaning of an optimal solution. Next, an analytical solution is sought based on the classification of the problem as a resolvable partially balanced incomplete block design. Finally, four increasingly sophisticated techniques of…

Results obtained from investigating number properties are discussed, along with six points that are felt, in general, to be the ingredients necessary for a successful learning experience. Two programs written in BASIC designed to aid in aspects of Number Theory are included. (MP)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)

A possible logical flaw based on similar triangles is discussed with the Sherlock Holmes mystery, "The Muskgrave Ritual." The possible flaw has to do with the need for two trees to have equal growth rates over a 250-year period in order for the solution presented to work. (MP)

A discussion of the mathematics of rugby is related to an earlier article about mathematics and the physical world. (MP)

The focus of this book is on a rationale and a set of strategies for problem generation in mathematics. Six chapters attempt to involve readers in the process of posing problems and in understanding why that process is important. Chapter 1 discusses two problem posing perspectives, while chapter 2 looks at the first phase of problem posing. The…

This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit…

A Norman window consists of a semi-circular section mounted surmounting a rectangular section. Modifications to a simple problem are presented that assume parts of the window are made with stained glass. The goal is to maximize the level of light transmission with a fixed perimeter. (MP)

Details of an instructor's attempt to solve a problem in combinatorics taken from a textbook used by some of his students are presented. It is felt the material raises a number of significant points about problem solving and mathematics. Teachers are encouraged to put themselves in such situations. (MP)

A brief introduction to the broad field of curve-fitting is provided to help explain the reasoning behind least-squares data fitting, and also to provide useful equations for two functional forms of interest in chemistry. Appendices give program examples written in Fortran and detail the method of Guggenheim. (MP)