The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

These modules develop two prevalent explanations among political scientists of who gets what in the budgetary process. Specifically, the problem of how an agency's level of appropriations changes over time is addressed. It is noted that budgeting is a political process in the classic sense, in that it elicits and embodies patterns of conflict and…

This module is designed for students with a high school algebra background. The goal is to present the elements of the group idea, primarily by way of a geometric model, and to see its application to the study of kinship relations within certain human groups. The material opens with a presentation of clans in a hypothetical society in an early…

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 document includes three units on applications of first-order difference equations to American politics. The first module is designed to help the user: 1) develop flexibility in analyzing difference equations in quadratic format; 2) understand how Choundy and Phillips' Theorem can be used to provide information about the time path of a…

A work-scheduling model for Corrections Officers at State Correctional Institutions is described. This is a real-life model that was developed to deal with a problem of unacceptably large expenditures for overtime work by state prison guards. The problem involves more than 200 constraints and more than 800 variables. It is felt the model can be…

This module is designed to apply mathematical models to nuclear deterrent problems, and to aid users in developing enlightened skepticism about the use of linear models in stability analyses and long-term predictions. An attempt is made at avoiding overwhelming complexities through concentration on land-based missile forces. It is noted that after…

This document is addressed primarily to students in analytically oriented courses in political science and secondarily to students in mathematics courses in which applications and modeling are stressed. Except for one optional exercise and material in the appendix, only high school level mathematics is assumed. The emphasis is less on mathematical…

This unit, which looks at applications of linear algebra to population studies, is designed to help pupils: (1) understand an application of matrix algebra to the study of populations; (2) see how knowledge of eigen values and eigen vectors is useful in studying powers of matrices; and (3) be briefly exposed to some difficult but interesting…

Designed for use as supplementary instructional material in a cultural anthropology course, this learning module uses a systems approach to allow students to see the connections and similarities which most cultural groups share on the basis of the type of economic organization that they exhibit. The module begins with a general discussion of…

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…

Models of the motion of an object through space are discussed. The material begins with the simplest view possible in which gravity is the only force examined. Discussion progresses to an examination of the drag force, which is the resistive air force of the wind. Suggestions for further improvements are made at the conclusion of the presentation.…

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…

Two units make up this material. They focus on applications of second-order difference equations to American politics. The goals of the first module include helping the user understand: 1) the difference between a theoretical construct and an observable; 2) the nature of choices which exist in modeling any particular empirical phenomenon; and 3)…

This learning module is concerned with the temperature field, the heat transfer rates, and the coolant pressure drop in typical high temperature gas-cooled reactor (HTGR) fuel assemblies. As in all of the modules of this series, emphasis is placed on developing the theory and demonstrating its use with a simplified model. The heart of the module…