This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

This textbook is designed primarily to follow the third book of the author's series of textbooks of secondary mathematics. Therefore, it presupposes the essentials of high-school algebra, plane and solid geometry, and trigonometry. It aims to combine the work which is commonly covered in separate courses in college algebra and in analytical…

A criterion (formula) for the termination of a continued fraction expansion leading to the solution of a standard differential eigenvalue problem from mathematical physics is presented. The criterion generates the eigenvalues in any specific case and is illustrated by elementary examples yielding well-known polynomial eigenfunctions. This…

In this paper the power of the [gamma] algorithm for obtaining the dual of a given cone and some of its multiple applications is discussed. The meaning of each sequential tableau appearing during the process is interpreted. It is shown that each tableau contains the generators of the dual cone of a given cone and that the algorithm updates the…

The familiar property of integral of f (x) = 1/x led to the discovery of other functions with this property.

This article looks at how a particular curve associated with tangents of an exponential function is a copy of the exponential itself.

The origins of this paper lay in making beds by putting pieces of plywood on a frame: If beds need to be 4 feet 6 inches by 6 feet 3 inches, and plywood comes in 4-foot by 8-foot sheets, how should one cut the plywood to minimize waste (and have stable beds)? The problem is of course generalized.

This article describes some of the work of Jan Hudde who anticipated some results of calculus. Prior to a career as a Burgomaster of Amsterdam, Hudde engaged in mathematics. His method of finding maxima and minima is especially interesting.

In this article I discuss the factors that led me to implement study groups in the teaching of mathematics. An important influence in this decision began with an experimental study conducted with two College Algebra classes in which students were randomly assigned to treatment groups. While there was no statistical difference between the study…

Although the WebQuest has been around for several years, it appears that not many educators are aware of it, or know how to use it. Thus, it is important to not only expose developmental educators to the use of this strategy, but also to help them realize how they can easily implement it into their curriculum. The use of a Webquest integrates…

Difficulties that are encountered by dyslexic undergraduates with their learning and understanding of mathematics are explored. Specific consideration is given to issues arising through mathematical content, its delivery, the procedures and processes of doing mathematics, and its assessment. Particular difficulties, which have emerged through…

In this article the main characteristics of the dMath project are introduced. With the mathematical modules developed within this project a new tool is made available to the different users as a support of the teaching and learning of mathematics in the context of EHEA and of the Bologna declaration. (Contains 7 figures.)

In this article we describe a hands-on activity for a liberal arts mathematics course that focuses on the beauty and unity of mathematics. The purpose of the activity is to tie together several topics in the context of a "real-world" situation. These topics include: fractals, non-Euclidean geometry, symmetry, and Platonic solids. This activity…

This article offers our ideas on why it is important to teach our students how to speak about mathematics and some practical resources for incorporating speaking activities, helping students prepare, evaluating student presentations, and getting your department to talk about student presentations. The ideas in this article were compiled when the…

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…