Examines infinite sets and cardinality classifications of empty, finite but not empty, and infinite through discussions of numbers that fall into particular categories. Categories discussed include perfect numbers, Mersenne primes, pseudoprimes, and transcendental numbers. Discusses the Null Or Infinite Set Effect (NOISE) and infinitude resulting…

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

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)

Describes the history of five selected problems from mathematics that are included in an undergraduate honors course designed to utilize original sources for demonstrating the evolution of ideas developed in solving these problems: area and the definite integral, the beginnings of set theory, solutions of algebraic equations, Fermat's last…

A method that enables people to obtain the benefits of statistics and probability theory without the shortcomings of conventional methods because it is free of mathematical formulas and is easy to understand and use is described. A resampling technique called the "bootstrap" is discussed in terms of application and development. (KR)

Describes a course designed by Moravian College, Pennsylvania, to integrate precalculus topics as needed into a first calculus course. The textbook developed for the course covers the concepts of functions, Cartesian coordinates, limits, continuity, infinity, and the derivative. Examples are discussed. (MDH)

This paper merges state-of-the-art calculator technology with examples drawn from the Harvard Consortium Calculus Curriculum. A brief rationale for selection of the Harvard project and the TI-85 is provided, and four different mathematical situations are examined using different capabilities of the TI-85. Two short TI-85 programs are given.…

Described are the background, structure, themes, methodology, projects, and assessment for the course. A list of themes is provided. Results of the piloting of the course are discussed. (CW)

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features that present book and software reviews and math problems. The first of two issues of volume 9…

Focusing on the question that is being discussed in a mathematics lesson is suggested as an approach to teaching developmental mathematics at the college level. Ways in which students can be involved with the question are described. First, some contagious cliches that are used by students are given. Then a few antidotal aphorisms and educational…

Research supports the premise that various mathematical topics can be categorized as being performed better by the left or right brain hemisphere. This study examined the effect of left and right brain hemispheric lateralization exercises upon course grades in two sections of Analysis I (beginning calculus for mathematics/science majors) at a…

Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…

The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

This document consists of seven chapters. The first chapter analyzes the modeling process and gives reasons for introducing a modeling approach in classrooms, arguing that students will develop more confident and positive attitudes toward mathematics. The next five chapters contain case studies, which focus, respectively on: whether it is more…

Noting the growing interest in how writing activities might complement current teaching techniques and improve learning in mathematics, this paper presents a progress report on the use of writing assignments in freshman precalculus courses at a Minnesota university. The paper first presents a rationale for this teaching technique and the original…