Reasons for using Rolle's Theorem in calculus are discussed, with comparisons to the theorems of Lagrange and Cauchy. (MNS)

University entrance examinations in China are described. Then the 1985 test is presented. (MNS)

Standard calculus textbooks often include a related rates problem involving light cast onto a straight line by a revolving light source. Mathematical aspects to these problems (both in the solution and in the method by which that solution is obtained) are examined. (JN)

A general solution to a problem in linear algebra is provided. (DT)

Ways of drawing Venn diagrams to display 16 and 32 subsets are illustrated. (DT)

A "proof" is given to show that the set of natural numbers is not countable. (DT)

The approximate value of a given sum is obtained through the development of some results of inequalities. Inequalities are also used to show how the concepts of sum and integral are related. (MP)

Results are investigated when the axioms for a group have been altered. (DT)

Asserts that when college mathematics is taught as one of the liberal arts, Euclid's Elements of Geometry, which is one of the oldest math textbooks, may still be the best, because it helps students understand what is "lovely about mathematics". Suggests that "Elements of Geometry" promotes the mental exercise that comes from…

Described are some major developments in the history of ideas in which mathematics has played a central role. The discussion is organized around four key features of mathematics: certainty, applicability, more than one geometry, and opposition. (MNS)

Summarizes the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards document and suggests 10 implications for college mathematics. (MKR)

Offers an extended review of the book "Advanced Mathematical Thinking." Discusses each chapter, details connections and reactions, and responds in the context both of research in mathematics education and of writing about mathematics. (MKR)

Outlines a three-step approach to proof writing: exploration, explanation, and formalization. Provides a detailed example of its use. Offers reflections on this approach and adaptations to it. (Author/MKR)

Closed forms are computed for parametric integrals, generally using induction formulas. It is shown that these integrals can be core activities, mixing hand-work, computations with a computer algebra system and experimental mathematics with an interactive website.

A criterion (formula) for the termination of a continued fraction expansion leading to the solution of a standard differential eigenvalue problem from mathematical physics is presented. The criterion generates the eigenvalues in any specific case and is illustrated by elementary examples yielding well-known polynomial eigenfunctions. This…