The relatively hard problem of transforming a given set of curves to curves with the same shape can sometimes be reduced to the easier problem of rendering curves parallel. In this paper a group is associated with the given curves, and it is shown that the reduction from the hard problem to the easy problem is valid whenever the group is…

This two-volume set is a self-help student text designed as an alternative to the standard algebra text. Each lesson is introduced by and centered around an application of the topic under discussion. For each lesson, questions are given covering the reading, testing understanding of the reading, and for discussion. Some sections contain questions…

This is volume three of a three-volume SMSG junior high school mathematics text. This volume includes the units concerned with applications of mathematics. Unit topics include: (1) what is mathematics and why you need to know it; (2) mathematics at work in science; (3) Uncle Sam as a statistician; and (4) chance. (MP)

This is part one of a two-part manual for teachers using SMSG high school text materials. A chapter-by-chapter commentary on the text and answers to all the exercises are given. Chapter topics include the idea of the derivative, limits and continuity, differentiation, and applications of the derivative. (MP)

This is part two of a two-part manual for teachers using SMSG high school text materials. A chapter-by-chapter commentary on the text and answers to all the exercises are given. Chapter topics include: (1) area and integral; (2) basic integral theorems; (3) logarithmic and exponential functions; (4) growth, decay and competition; and (5)…

This report explains the following mathematical techniques which may be used for relating search requests to documents contained in a library: (1) Boolean Algebraic Retrieval, (2) Linear Statistical Retrieval, (3) Statistical Association Techniques for expanding a query and/or for expanding the set of retrieval documents, (4) Vector Space…

In the development of programed materials, usually all responses are analyzed for a small sample of students. The viable alternative is to perform mathematical transformations on response data from a selected portion of a large sample (more than 400 students) to obtain reliable estimates of item difficulty and item discrimination. (LH)

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

Presented are the results of a study conducted to develop algorithms for ordering and organizing data that can be presented in a two-dimensional matrix form. The purpose of the work was to develop methods to extract latent data patterns, grouping, and structural relationships which are not apparent from the raw matrix data. The algorithms…

The course outline has been prepared as a guide to assist the student in becoming proficient in trigonomical functions. This aids a machinist in making a complicated set-up so that he can perform a precision machine operation. The guide helps the instructor concentrate on the specific review that will be needed. After the review, the student is…

The Omron Company produced a 30 page comic book designed to introduce children of elementary school age to electronic calculators in general and to teach them how to operate its Omron calculator. The book provides sample diagrams of and operating instructions for the machine and illustrates through the activities of its major characters the…

Among the articles in this newsletter are discussions concerning the employment of mathematicians in industry and questioning the necessity of some of the present doctoral programs in the mathematical sciences. Other articles include details of the organization and the members of the Policy Council of the National Institute of Education and a…

Part of a series of four pamphlets providing problems in probability and statistics taken from real-life situations, this booklet develops probability methods through random numbers, simulations, and simple probability models, and presents the idea of scatter and residuals for analyzing complex data. The pamphlet was designed for a student having…

The teacher's guide for Unit 14 of this SMSG series covers the chapter on logic and the chapter on applications of probability and statistics. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives are…

Force diagrams involving angular velocity, linear velocity, centripetal force, work, and kinetic energy are given with related equations of motion expressed in polar coordinates. The computer is used to solve differential equations, thus reducing the mathematical requirements of the students. An experiment is conducted using an air table to check…