Student research projects are open-ended questions or sets of questions intended to give undergraduate students experience doing introductory mathematical research. Proposed is an investigation of a Faro shuffle that is performed by cutting the deck exactly in half and then perfectly interleaving the cards of the two halves. (Author/JJK)

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…

This section provides mathematical activities in reproducible formats appropriate for students in grades 8-10. The activity is designed to provide an experience in model building while developing the concept of slope. (PK)

Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

This paper is part of a series of applied statistics monographs intended to provide supplementary reading for applied statistics students. In the present paper, derivations of the unbiased standard error of estimate for both the raw score and standard score linear models are presented. The derivations for raw score linear models are presented in…

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…

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…

Presents a proof of Euler's Theorem on polyhedra by relating the theorem to the field of modern topology, specifically to the topology of relief maps. An analogous theorem involving the features of mountain summits, basins, and passes on a terrain is proved and related to the faces, vertices, and edges on a convex polyhedron. (MDH)

The framework and procedures of generalizability theory are introduced and illustrated in this instructional module that uses a hypothetical scenario involving writing proficiency. Generalizability analyses are useful for understanding the relative importance of various sources of error and for designing efficient measurement procedures. (SLD)

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…

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)…