The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that…

Three major techniques are employed to calculate [pi]. Namely, (i) the perimeter of polygons inscribed or circumscribed in a circle, (ii) calculus based methods using integral representations of inverse trigonometric functions, and (iii) modular identities derived from the transformation theory of elliptic integrals. This note presents a…

It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

In this paper, the author demonstrates a case study of undergraduate mathematics research in trigonometric sums. Involving undergraduates in research has been a long standing practice in the experimental sciences. However, it has only been recently that undergraduates have been involved in research in mathematics in significant numbers. Obviously,…

The purpose of this study was to determine the effectiveness of a typical California community college Intermediate Algebra course in preparing students for success in the transfer level mathematics courses for which Intermediate Algebra was the prerequisite. The subsequent mathematics course taken by each of the 986 students who received a grade…

This issue of "Indicator of the Month" lists percentages of high school graduates taking selected mathematics and science courses in high school in 1982, 1987, 1990, and 1992. Findings include: (1) High school graduates in 1992 were more likely to take mathematics courses at the level of algebra I or higher and most science courses at the level of…

At Kings River Community College, analyses were conducted of the grades and characteristics of students in Mathematics A (Elementary Algebra), Mathematics B (Plane Geometry), Mathematics C (Trigonometry), and Mathematics D (Intermediate Algebra) to determine which variables were significantly related to student success. Data were gathered on 69…