This is the first of a two-part paper; the conclusion appears in volume 27, number 3 (SE 506 350). (JM)

The author shows that the set of all sequences in which each term is the sum of the two previous terms forms a vector space of dimension two. He uses this result to obtain the formula for the Fibonacci sequence and applies the same technique to other linear recursive relations. (MM)

The author suggests that a close analysis of existing calculus courses indicates that some of the material can be explained much more clearly by using some of the language of set theory. He gives examples showing that many of the pedagogical problems arising in calculus can be overcome by using a graphical approach. (FL)

The purpose of this study was to investigate the interrelationship of general mathematics skills, modern mathematics skills, modern mathematics achievement, prior mathematical attitudes, and postmathematical attitudes of prospective elementary teachers. A sample of 206 students was drawn from 286 students enrolled in a modern mathematics course.…

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)

An instructor taught one group of college freshmen using a modified form of traditional mathematics by including most of the concepts in modern texts, but also assigning a large number of problems for homework; the second group used a modern textbook with less problems for practice. The modified traditional group performed significantly better in…

Proliferation of mathematical knowledge prohibits individual reduplication of all results and causes mathematicians to accept much on faith. To convey the spirit of the mathematical community, and provide maximum content coverage, instruction should allow students to accept some theorems without proof. Students would then find mathematics less…

This experiment attempted to teach abstract mathematics fo college freshmen with A.C.T. scores less than 15 in a three semester terminal course sequence. The course content included a formal mathematical language, set theory, Boolean Algebra, relations and functions, operations, cardinals and ordinals, the rational numbers, and college algebra.…

A new algorithm for computing roots of any order is presented, along with the historical roots of its development.

The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)

Considered are what discrete mathematics includes, some parallels and differences between new math and discrete mathematics (listed in a table), and lessons to be learned. A list of references is included. (MNS)