This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…

Presented are the results of a study designed to determine the effect of computer applications on achievement in a college introductory calculus course. Experimental and control classes were compared at each of three participating colleges. The experimental classes solved calculus homework assignments using timesharing remote computer terminals.…

College students' performance in their first two calculus-level mathematics courses was studied by comparing students skipping, on any basis, one or more courses in the regular calculus sequence and students reaching these same courses through the regular sequence. Those skipping via CEEB AP and those skipping for any other reason were also…

This document constitutes a complete revision of the report of the same name first published in 1965. A new list of basic courses is described, consisting of Calculus I, Calculus II, Elementary Linear Algebra, Multivariable Calculus I, Linear Algebra, and Introductory Modern Algebra. Commentaries outline the content and spirit of these courses in…

A method of approximating the point "c" at which a continuous function attains its mean value over an interval is described. The method is applied to tax tables. (SD)

Functions with a variety of properties (sets of discontinuities, unbounded derivations, etc.) are discussed. (SD)

A discussion of differential equations is accompanied by an analysis of two situations whose solutions require differential equations. A computer program is given that will solve these equations. (MP)

The graph of this function is analyzed by using calculus methods and the computer. The graph in most texts is shown to be misleading. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

Comparisons are made between the errors obtained when approximating the integral with the midpoint rule, the trapezoidal rule, and Simpson's rule. (MP)

It is advocated that introductory calculus texts should present topics in a manner that is understandable to students without necessarily sacrificing rigour. Illustrative examples are given of a conversational approach to problem solving. (Author/MN)

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

A simple geometric construction giving acceptable approximations to the locations of twelve points for placing frets on a guitar is described both geometrically and analytically. (DT)

Provides examples to show that parallel coverage of convergence theorems for both series and improper integrals will tend to strengthen each other. Indicates that such coverage should also help students to better understand the concept of asymptote. (JN)

About half of the half-million students taking the introductory college calculus course each year fail. Some ways to change the course and the way it is taught were discussed at a conference attended by 25 persons. (MNS)