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…

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

In an effort to enhance the quality of education, universities and colleges are developing programs that help faculty and staff internationalize curriculum. These programs will purposefully develop the intercultural perspectives of students. "Curriculum Internationalization and the Future of Education" is a critical scholarly resource…

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)

The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)

Clarified is the assertion that the so-called complementary function is indeed the general solution of the homogeneous equation associated with a linear nth-order differential equation. Methods to obtain the particular integral, once the complementary function is determined, are illustrated for both cases of constant and of variable coefficients.…

Vietnamese students now enrolled in American high schools incur an extremely special need in English. After being taught subject matter disciplines in Vietnamese for many years, and while English is still a foreign language for them, these students are bound to go through two linguistic processes. First, while reading or sitting through lectures…

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…

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)

Demonstrated is the use of BASIC computer programs to simulate a binomial experiment and test a simple statistical hypothesis. The theoretical results are reached with the third programing attempt. All results, as well as computer programs, are included. (JJK)

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…

Discussed are the results of a study which suggests that people remember more mathematics and other high school material when learning occurs spaced out over several years and when each subsequent session involves broader applications of previously learned information. Highlights of this study and related studies are presented. (CW)

Presents an intellectual context and critical analysis of specific material from undergraduate mathematics. Although not definitive in any sense of the word, the sample discussions provided for the included "test" questions all contain significant remarks bearing on significant mathematical concepts. (23 references) (Author/JJK)

Proposes a mathematical computer model for the behavior of liquids using the classical dynamic principles of Sir Isaac Newton and the molecular dynamics method invented by other scientists. Concludes that other applications will be successful using supercomputers to go beyond simple Newtonian physics. (CW)

Described is an outline for a school mathematics project dealing with the theory of equations, specifically solutions to polynomials of the third and of the fourth degree. Cardano's method for solution of cubic equations and Ferrari's method for solution of quartic equations are included with examples. (JJK)