The role of optimization in mathematical, physical, biological, social, and management sciences is examined. A plea is made for giving optimization a central place in the mathematics education of scientists and technologists. (Author/MK)

Discusses a computer calculus game which follows the path of a parabola in stepwise progression. The educational value of the game is a simple example of nonlinearity, a subject which is just beginning to earn some attention in the mathematical community. The Applesoft program listing is included. (JN)

Newton's method for finding roots of equations is described. How to find complex roots using the BASIC computer language is then presented, with the computer program included. (MNS)

Several examples are given of a variety of nonstandard problems, not ordinarily found in texts or courses, now accessible to students who have programmable calculators. These include: (1) finding limits; (2) evaluating infinite series; (3) calculating finite series; (4) computing variable length products; (5) solving equations; (6) searching for…

Briefly described is a numerical calculus course which provides (1) experience and practice in programing and the use of the computer in problem solving, (2) intermediate and/or advanced techniques in FORTRAN IV programing, (3) elementary error analysis, (4) programing efficiency, and (5) documentation of programs. The course, designed to fulfill…

Describes numerical differentiation and the central difference formula in numerical analysis. Presents three computer programs that approximate the first derivative of a function utilizing the central difference formula. Analyzes conditions under which the approximation formula is exact. (MDH)

This paper merges state-of-the-art calculator technology with examples drawn from the Harvard Consortium Calculus Curriculum. A brief rationale for selection of the Harvard project and the TI-85 is provided, and four different mathematical situations are examined using different capabilities of the TI-85. Two short TI-85 programs are given.…

An experiment at Boston University was designed to demonstrate that the computer can be successfully integrated into the traditional introductory calculus course. Over half of the students in an introductory course in 1976 voluntarily participated in a programming project involving applications of the concepts to be studied during the semester.…

It is noted that there are some integrals which cannot be evaluated by determining an antiderivative, and these integrals must be subjected to other techniques. Numerical integration is one such method; it provides a sum that is an approximate value for some integral types. This module's purpose is to introduce methods of numerical integration and…

Various ways in which computers can be used in the classroom depending on the subject, students' background, and individual teaching style are discussed. A way to evaluate professional software packages for use in the classroom is included. (KR)

A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation…

Examines the use of the computer to approximate the value of the definite integral normally calculated by mathematical means. Presents four examples using BASIC programs to approximate single and double integrals by numerical integration and the Monte Carlo method. Programs are provided. (MDH)

This study investigated the cognitive benefits of learning how to program by determining the degree of cognitive transfer of programming skills at a construct level to solving analogous problems in other domains. Subjects, who were students enrolled in four sections of the beginning Pascal programming course and two sections of a calculus course,…

The relationship between learning to program at a construct level and learning and study strategies was studied for college students enrolled in a beginning Pascal programing course and a calculus course (four sections of the programing course and two of the mathematics course). For both the experimental group (n=42) and the first control group…

Proposes an alternative means of approximating the value of complex integrals, the Monte Carlo procedure. Incorporating a discrete approach and probability, an approximation is obtained from the ratio of computer-generated points falling under the curve to the number of points generated in a predetermined rectangle. (MDH)