This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit…

The emphasis is on so-called "best solution" problems to questions that frequently arise in practical situations, such as finding an answer for the least amount of time, greatest volume, least amount of work, maximum profit, and minimum cost. One of this module's purposes is to help users become acquainted with the types of calculations necessary…

This document contains three modules. The first of these examines applications of algebra to geometry. It is designed to teach students how to algebraically characterize points which may be constructed with a compass and straight edge, and how to use this characterization to obtain classical geometric nonconstructibility results. The second unit…

Geometrical probability deals with probability on infinite sample spaces where each outcome of an experiment is equally likely to occur. Geometry which identifies sample space regions and event subregions leads to a method of finding a desired probability. A collection of problems with solutions is presented. (MP)

The document notes that in health and medical research the need to compare rates or proportions for some event can often occur. It is the module's goal to illustrate the conditions necessary for recognizing potentially misleading situations, and to show how to cope statistically with such situations. The four sections show: 1) when to adjust…

This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

One of the great strengths of mathematics is viewed as the fact that apparently diverse real-world questions translate into that same mathematical question. It is felt that studying a mathematical problem can often bring about a tool of surprisingly diverse usability. The module is geared to help users know how to use graph theory to model simple…

This unit considers the application of calculus in determining price discrimination and consumer surplus in a competitive market. Producer surplus and two-tier price discrimination are also developed in problems. It is noted that calculus cannot usually provide numerical answers for practical economic problems. The importance of calculus…

Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…

These modules view aspects of computer use in the problem-solving process, and introduce techniques and ideas that are applicable to other modes of problem solving. The first unit looks at algorithms, flowchart language, and problem-solving steps that apply this knowledge. The second unit describes ways in which computer iteration may be used…

The material looks at: 1) Choosing a Clinical Test; 2) Evaluation of Diagnostic Tests; 3) Multi-Disease and Multi-Test Analysis; and 4) Medical Decision Analysis. It is felt users will be able to: 1) calculate the predictive value of a positive or negative test result in model clinical situations; 2) estimate the sensitivity and specificity…

This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…

This module applies linear algebraic methods to solve the following problem: If an object in a three-dimensional coordinate system is first rotated about a given axis through the origin by a given angle, and then rotated about another axis through the origin by another angle, there is a straightforward way to calculate the combined result of the…

It is noted that with the prominence of computers in today's technological society, digital communication systems have become widely used in a variety of applications. Some of the problems that arise in digital communications systems are described. This unit presents the problem of correcting errors in such systems. Error correcting codes are…

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely…