3D Graphics in Calculus (UMAP)
This module helps students to strengthen their multidimensional visual intuition and their ability to solve problems ...
Using Real Quaternions to Represent Rotations in 3D (UMAP)
This module raises the general question of representing rotations in three dimensions. It motivates quaternions by re...
A Mathematical Rating System (UMAP)
This module develops a mathematical model for rating a group of contestants based on the results of several head-to-h...
Calculus Optimization in Information Technology (UMAP)
This module considers three optimization problems in the design of computer hardware and software and solves them by ...
Noncomputability and the Busy Beaver Problem (UMAP)
This module describes the Busy Beaver problem and explores the Busy Beaver and shift functions. It proves that these ...
Calculus in a Movie Theater (UMAP)
Using elementary calculus techniques, this unit explores the concept of viewing angle as a criterion for determing th...
Sharing a Secret (UMAP)
This module considers the problem of devising a scheme for predesignated subsets of a group of people to hold a secre...
Ocean Circulation (UMAP)
This module looks first at how an ocean current is affected by the fact that it moves on a rotating sphere. It consid...
Decision Analysis for Multi-Candidate Voting Systems (UMAP)
A unit that relates finite mathematics to decision analysis for multi-candidate voting systems. By using this module ...
A Mathematical Survey of Justice (UMAP)
A systematic mathematical survey of various approaches to justice. The module discusses various requirements that a j...
Conditional Probability and Ambiguous Information (UMAP)
A unit that involves conditional probability and ambiguous information. The purpose of this module is to allow studen...
National Decisions to Enter War (UMAP)
This module uses basic conditional probability, lotteries, and expected utility to analyze the process by which gover...
Modeling Jury Verdicts (UMAP)
The expected distribution of jury verdicts in a jury of size N, requiring K of N votes to convict, can be modeled by ...
Series and Games: From Paradox to Paradox (UMAP)
Zeno's paradox of Achilles and the turtle was an early encounter between the human mind and the notion of infinite se...
An Iterative Approach to Linear Regression (UMAP)
In this module, a method is given for finding a line or plane fitted to a set of data by using the concept of best fi...
The Gradient and Some of its Applications (UMAP)
This module considers some relationships between curves and surfaces: How is the rate of climb in the vertical direct...
Evaluating Definite Integrals on a Computer: Theory and Practice (UMAP)
A unit that involves the theory and practice of evaluating definite integrals on a computer. By the end of this modul...
Fitting Equations to Data: Part 1 (UMAP)
With completion of this module students will: 1) be able to state four purposes for fitting an equation to data, and ...
Application of Vertex Coloring Problems of Graphs (UMAP)
With completion of this module students will: 1) know how to use graph theory to model simple problems; and 2) have a...
Approximations in Probability Calculations (UMAP)
With completion of this module students will be able to: 1) discuss how approximation is pervasive in statistics; 2) ...
Some Applications of Exponential and Logarithmic Functions (UMAP)
This unit contains five examples of exponential and logarithmic functions being used to study the behavior of real-wo...
Linear Programming in Two Dimensions: I (UMAP)
This module introduces a variety of linear programming problems and describes in detail a graphical method for solvin...
Genetic Counseling (UMAP)
A unit that involves probability and statistics and genetic counseling. The purpose of this module is to: 1) provide ...
An Application of Dihedral Groups (UMAP)
This module has students become familiar with the basic properties of a group through an approach which is concrete a...
An Introduction to Groups (UMAP)
A unit that involves applications of abstract algebra. By the end of this module students will be able to: 1) underst...
Calculus of Variations with Applications in Mathematics (UMAP)
A unit that involves calculus of variations with applications in mathematics. With completion of this module students...
Kepler's Law and the Inverse Square Law (UMAP)
A unit that involves Kepler's Law and the Inverse Square Law. With completion of this module students will be able to...
Applications of Nominal and Effective Rates of Interest (UMAP)
The purpose of this module is to: 1) introduce the terms nominal rate and effective rate; 2) show how they are used i...
Measures of Voting Unit I: The Rice Index (UMAP)
A unit that applies probability and statistics to measures of voting. The purpose of this module is to help students:...
A Linear Programming Model for Scheduling Prison Guards (UMAP)
A work-scheduling model for corrections officers at state correctional institutions is described. This model can elim...
Listening to the Earth: Controlled Source Seismology (UMAP)
The purpose of this module is to give students a better understanding of how mathematics can be used to learn about p...
Price Discrimination and Consumer Surplus (UMAP)
With completion of this module students will understand the concepts of price discrimination and consumer surplus. St...
Exponential Models of Legislative Turnover (UMAP)
The turnover of the membership of a legislative body is described by the exponential probability distribution, where ...
Dynamics of Political Mobilization I: A Model of the Mobilization Process (UMAP)
With this module, the student gains an understanding of the role of recruitment and defection rates in political mobi...
The Diffusion of Innovation in Family Planning (UMAP)
From this module students develop flexibility in analyzing difference equations in quadratic format. Chaundy and Phil...
Growth of Partisan Support I: Model and Estimation (UMAP)
This unit introduces the student to nonlinear representation (first order quadratic difference equation) for politica...