Described are stages in the development of a computer program to solve a particular algebra problem and the nature of algebraic computation is presented. A program in BASIC is provided to give ideas to others for developing their own programs. (MP)

A few examples are discussed of situations where some solution to writing a computer program for an algorithmic problem is immediately evident, but the best solution is some distance away. (MP)

A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)

A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)

A mathematics contest for community colleges is described. A two-hour written examination is followed by a problem-solving competition between teams. (MP)

Details are provided of a program on actuarial training developed at the State University of New York (SUNY) at Binghamton through the Department of Mathematical Sciences. An outline of its operation, including a few statistics on students in the program, is included. (MP)

The demise of mathematics of finance as a subject is discussed and a resurgence is seen as possible, but the traditional instructional presentation is seen as in need of modernization. Financial mathematics is referred to as a beautiful subject when inflation is incorporated, provided that calculators are used in computations. (Author/MP)

The overall results of the fourth U.S.A. Mathematical Olympiad are discussed. The names of the eight finalists are listed, as are the problems in the test. (SD)

Forty-eight mathematicians in industry, business, and government replied to a questionnaire on the relative merits of the traditional undergraduate curriculum, advanced topics in pure mathematics, computer programing, additional computer science, and specialized or applied topics. They favored programing and applied mathematics, along with a…

A sophomore-level course in applications of mathematics was designed to introduce students to the diversity of situations in which mathematical models are used. The course precedes the study of the calculus, and is composed of a sequence of modules. A problem-solving approach is used. (SD)

Four of the author's favorite calculus word problems are presented. These aid students in recognizing and applying concepts in contexts unlike those in typical textbook problems. (MNS)

A mathematician who has been teaching for 58 years discusses 3 types of knowledge that are subjects for teaching or learning (what, how, and why) and why teaching must include problem solving or the use of the Socratic, Moore, or discovery method. (MKR)

The possibility of teaching students to recognize and apply problem-solving strategies used by experts is explored. (MP)

Contends that, although the introduction of problem solving, intended to involve students more actively in their learning and understanding of the nature of mathematics, is a positive factor, the need for proof, which is an integral part of mathematics, must not be overlooked. (25 references) (MKR)