THIS PAPER DEALS WITH SOME TESTS OF HYPOTHESIS FREQUENTLY ENCOUNTERED IN THE ANALYSIS OF MULTIVARIATE DATA. THE TYPE OF HYPOTHESIS CONSIDERED IS THAT WHICH THE STATISTICIAN CAN ANSWER IN THE NEGATIVE OR AFFIRMATIVE. THE DOOLITTLE METHOD MAKES IT POSSIBLE TO EVALUATE THE DETERMINANT OF A MATRIX OF HIGH ORDER, TO SOLVE A MATRIX EQUATION, OR TO…

This guide presents many new experimental designs for data analysis and reviews certain standard procedures. It is hoped that the treatment of the material will stimulate new applications since the emphasis of the guide is on the problems encountered in running experiments rather than on an elaboration of mathematical models. Discussed are:…

This final report summarizes past research and suggests new approaches to the problem of estimating long-term individual constants using path analysis. The general objective of the research was to detect and measure the likelihood that one variable, x, measured at time, t, has a causal influence on another variable, y, measured at a subsequent…

This is a final report, for administrative purposes, of studies to be published in the general category of mathematical theory of social groups, with emphasis on the large groups typical of educational communities. Since the study of the large and complicated structures of high school and college communities is difficult by purely empirical…

Criticizes the current method of formalization in Italian schools and the use of tools of the mathematical method. Proposes a general three-stage formalization method which can used for physical quantities, the particular significance of certain quantities, and the description and interpretation of phenomena. (TW)

An activity involving the charting of the spread of a disease is described. Arrows are used to develop models of the progression of the disease. (MNS)

Four types of experiences in problem solving are identified, and steps children must learn to do problem solving are presented. (MP)

Reports a project that incorporated mathematical modeling into a college course. Reports evaluation of the course in terms of criteria derived from the stated aims: modeling performance, modeling framework, pedagogy assessment, and personal growth. Included are two sample problems. (YP)

Explored are responses of students aged 9 to 13 to linear generalizing problems from both a technical and strategic point of view. The methods commonly used were the same in all age groups and across all three questions, although some students choosing each model varied. (YP)

Highlights an activity that focuses on learning the geometric concepts needed for students to design blueprints for a city park by mastering fifth-grade geometry concepts and applying their knowledge in a real-world context. (ASK)

This unit views applications of elementary game theory to international relations. It is noted that of all the significant world problems, the nuclear arms race has proved one of the most intractable. The main concern of the module is to investigate a possible solution to the arms race, based on extending the classic two-person game of Prisoner's…

This collection of nine case studies in applied mathematics was written primarily for the use of the instructor by a Conference sponsored by the Committee on the Undergraduate Program in Mathematics (CUPM). Each chapter contains exercises of varying degrees of difficulty and several include student projects. The materials were used on a trial…

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

Discusses the classification of binary oxides as acidic, basic, or amphoteric. Demonstrates how a numerical scale for acidity/basicity of binary oxides can be constructed using thermochemical data for oxoacid salts. Presents the calculations derived from the data that provide the numeric scale values. (TW)

Discusses how all applications of mathematics have a unifying theme, namely, that of mathematical modeling. Three examples of models in science and technology are briefly described. These are suggested as suitable project work in the classroom, which involve collaborative work between science and mathematics. Advantages and benefits of modeling…