Line Reflections in the Cartesian Plane (UMAP)
A unit that involves line reflections in the Cartesian plane. Let f: R2 --> R2 be reflection in the line Ax + By + C…
Why Do Cells Compete? (UMAP)
This unit introduces current data about brightness constancy and contrast in visual perception, and shows that data of…
Randomization Tests (UMAP)
In this module the data are permuted (divided or rearranged) repeatedly, in a manner consistent with the nature of the…
The Sturmian Sequence for Isolating Zeros of Polynomials (UMAP)
This module analyzes Sturm's theorem about zeros of polynomials and describes a finite procedure for finding the number…
Population Dynamics of Governmental Bureaus (UMAP)
This module presents, calibrates, and tests a mathematical model of the birth and death of bureaucratic units - briefly…
Negotiation in Nonzero Sum Games (UMAP)
A unit that relates finite mathematics through the topic of negotiating in nonzero sum games. The formulation of a nonz…
A (Not Really) Complex Method for Finding Solutions to Linear Differential Equations (UMAP)
A unit using a method to find solutions to linear differential equations. By completion of this module students will be…
The Design of Honeycombs (UMAP)
A unit that involves calculus to the design of honeycombs. By completion of this module students will be able to unders…
The Relationship Between Directional Heading of an Automobile and Steering Wheel Deflection (UMAP)
A unit that applies calculus to engineering. The relationship between the directional heading of an automobile and the…
The Shape of the Surface of a Rotation Liquid (UMAP)
A unit that applies calculus to engineering and physics. By completion of this module students will be able to analyze…
3D Graphics in Calculus (UMAP)
This module helps students to strengthen their multidimensional visual intuition and their ability to solve problems th…
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 refe…
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-hea…
Calculus Optimization in Information Technology (UMAP)
This module considers three optimization problems in the design of computer hardware and software and solves them by us…
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 fu…
Calculus in a Movie Theater (UMAP)
Using elementary calculus techniques, this unit explores the concept of viewing angle as a criterion for determing the…
Sharing a Secret (UMAP)
This module considers the problem of devising a scheme for predesignated subsets of a group of people to hold a secret…
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 consider…
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 st…
A Mathematical Survey of Justice (UMAP)
A systematic mathematical survey of various approaches to justice. The module discusses various requirements that a jus…
Conditional Probability and Ambiguous Information (UMAP)
A unit that involves conditional probability and ambiguous information. The purpose of this module is to allow students…
National Decisions to Enter War (UMAP)
This module uses basic conditional probability, lotteries, and expected utility to analyze the process by which governm…
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 co…
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 seri…
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 fit…
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 directio…
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 module…
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 gi…
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 an…
Approximations in Probability Calculations (UMAP)
With completion of this module students will be able to: 1) discuss how approximation is pervasive in statistics; 2) co…
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-worl…
Linear Programming in Two Dimensions: I (UMAP)
This module introduces a variety of linear programming problems and describes in detail a graphical method for solving…
Genetic Counseling (UMAP)
A unit that involves probability and statistics and genetic counseling. The purpose of this module is to: 1) provide an…
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 and…
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) understan…
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 w…