This essay investigates the rhetoric surrounding the appearance of the concept of the infinitesimal in the seventeenth-century Calculus of Sir Isaac Newton and Gottfried Wilhelm Leibniz. Although historians often have positioned rhetoric as a supplemental discipline, this essay shows that rhetoric is the "material" out of which a new and powerful…

A few problems to dispel the notion that mathematics today admits no unsolved problem are presented. The vast area of the unknown and challenges that befit a twenty-first-century attack are discussed.

Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.

The calculation of the upper and lower quartile values of a data set in an elementary statistics course is done in at least a dozen different ways, depending on the text or computer/calculator package being used (such as SAS, JMP, MINITAB, "Excel," and the TI-83 Plus). In this paper, we examine the various methods and offer a suggestion for a new…

The paper considers a class of real integrals performed by using a convenient integral in the complex plane. A complex integral containing a multi-valued function with two branch points is transformed into another integral containing a pole and a unique branch point. As a by-product we obtain a new class of integrals which can be calculated in a…

This paper deals with a simple method of evaluation of certain multiple definite integrals. This is followed by two main theorems concerning multiple definite integrals. Some examples of applications are given.

This article shares investigation possibilities that lie within familiar concepts of greatest common factor and least common multiple.

The recent considerable developments in the field of biology have necessitated the knowledge of mathematics and its applications in biology. Therefore; most of the universities, now, believe that it is essential to include mathematics courses in the curricula of biology departments. Taking this fact into consideration, this study aims at exploring…

This article presents the basic ideas of statistical trend charts and their utility as a pedagogical tool for sparking statistical thinking. (Contains 7 tables and 11 figures.)

Students learn to use linear algebra covered in their first algebra course to design mobiles like those created by artist Alexander Calder. (Contains 17 figures and 2 tables.)

We report a dissociation between higher order mathematical ability and language in the case of a man (SO) with severe aphasia. Despite severely impaired abilities in the language domain and difficulties with processing both phonological and orthographic number words, he was able to judge the equivalence of and to transform and simplify…

In this article, we explore the game based on the following problem from the 1st Mathematical Olympiad of Central America and the Caribbean, held in Costa Rica in 1999: Player A turns on the calculator, presses a digit key and then presses the + key. A second later, player B presses a digit key in the same row or column of the last digit key…

This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.

This paper presents a generic method of calculating accurate horizontal and vertical object distances from digital images taken with any digital camera and lens combination, where the object plane is parallel to the image plane or tilted in the vertical plane. This method was developed for a project investigating the size, density and spatial…