This paper presents a study of instructors' and students' perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I modeled these perceptions using a theoretical framework that combines elements of the Anthropological Theory of the Didactic, developed…

The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses…

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

Through an account of the history of exponential functions as presented in traditional calculus textbooks, I present my observations and remarks on the spiral development of the concept, and my concerns about the general presentations of the subject. In this article I emphasize how the different arrangements and sequencing of the subjects required…

To achieve the vision of mathematics set forth in "Crossroads" ("AMATYC," 1995), students must experience mathematics as a sensemaking endeavor that informs their world. Embedding the study of mathematics into the real world is a challenge, particularly because it was not the way that many of us learned mathematics in the first place. This article…

For many years, the author has been involving his students in classroom teaching of their own classes. The day-to-day practice is described, and the advantages and disadvantages for both the instructor and the students are discussed. Comparisons with the Moore Method of teaching are made.

This article shows how to use six parameters describing the International Space Station's orbit to predict when and in what part of the sky observers can look for the station as it passes over their location. The method requires only a good background in trigonometry and some familiarity with elementary vector and matrix operations. An included…

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

This textbook presents a course in elementary mathematics adapted to the needs of students in the freshman year of an ordinary college or technical school course, and of students in the first year of a junior college. The material of the text includes the essential and vital features of the work commonly covered in the past in separate courses in…

In this note the authors investigate ways to shorten the amount of work involved in using the Rational Roots Theorem to find the rational roots of a polynomial with integral coefficients. The first result is a proof of a fact that we had long suspected, but were never able to find the statement of in any of the college algebra textbooks we had…

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…

Teaching the art of counting can be quite difficult. Many undergraduate students have difficulty separating the ideas of permutation, combination, repetition, etc. This article develops some examples to help explain some of the underlying theory while looking carefully at the selection of various subsets of objects from a larger collection. The…

This paper reports on young women students participation in their undergraduate mathematics degree programme: their gendered trajectory is characterized in terms of their being both "invisible" in the dominant university mathematics community and yet "special" in their self -conception. It draws on data collected from a…

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)