This document contains nine research papers presented at the Joint Special Session on Research in Undergraduate Mathematics Education at the annual meeting of the American Mathematical Society and the Mathematical Association of America (San Francisco, California, January 1991). Paper titles are: "The Teaching and Learning of College…

The conference of which these are the proceedings was held in June-July 1982 at Williams College in Williamstown, Massachusetts. The purpose was to discuss the restructuring of the first two years of college mathematics to provide some balance between the traditional calculus-linear algebra sequence, and discrete mathematics. The volume contains…

This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

This paper presents preliminary hypotheses about the relationship between faculty goals for the introductory calculus-based physics course and their beliefs about student learning of problem solving. All faculties have problem solving as a major goal for their courses. There appears to be however, an instructional paradox. When discussing how…

This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…

MathView is a computer algebra system designed to foster interactive exploration of mathematics. MathView is designed so that mathematics, both symbolic and graphic, is highly interactive. Change to a proposition in a MathView notebook produces a cascade of changes to the conclusions that are tied to the proposition. This structure helps to create…

This paper reviews an approach for finding optimal solutions to the traveling salesman problem, a well-known problem in combinational optimization, and describes implementing the approach using the MAPLE computer algebra system. The method employed in this approach to the problem is similar to the way ant colonies manage to establish shortest…

The University of South Carolina at Hilton Head offers a major in Hotel, Restaurant, and Tourism Administration (HRTA). Many students in the HRTA major take both the HRTA Tourism course and a business calculus course. An interdisciplinary research project was designed in an effort to interest these students in the power of calculus as a…

Describes a rugby problem designed to help students understand the maximum-minimum situation. Presents a series of explorations that locate an optimal place for kicking the ball to maximize the angle at the goalposts. Uses interactive geometry software to construct a model of the situation. Includes a sample student activity. (KHR)

Solutions for a problem in which the time necessary for an object to fall into the sun from the average distance from the earth to the sun are presented. Both calculus- and noncalculus-based solutions are presented. A sample computer solution is included. (CW)

Presented is a method of interchanging the x-axis and y-axis for viewing the graph of the inverse function. Discussed are the inverse function and the usual proofs that are used for the function. (KR)

Discussed are the vital properties that an operator must have to be called a derivative and how derivatives work. Presented is an extension of the derivative that uses least squares to find the line of best fit. (KR)

Presented is L'Hopital's rule for the evaluation of limits in the case when x goes to infinity using geometric concepts. Included are the rule, extensions, counterexamples, and a rule for sequences. (KR)

Some appearances of pi in a wide variety of problems are presented. Sections focus on some history, the first analytical expressions for pi, Euler's summation formula, Euler and Bernoulli, approximations to pi, two and three series for the arctangent, more analytical expressions for pi, and arctangent formulas for calculating pi. (MNS)

The history of the journal "Esercitazioni Matematiche" (1921-43) edited by the "Circolo Matematico di Catania" for university students is described. A selection of proposed problems with some of their solutions is reported. (Author)