Methods of Congressional Apportionment (UMAP)
In this module six methods of congressional apportionment are explained and illustrated by simple examples and exercise…
Modeling Using the Derivative: Numerical and Analytic Solutions (UMAP)
In this module the derivative is reviewd, physically as an instantaneous rate of change, and geometrically as the slope…
Regression Methods and Problem Banks (UMAP)
This module is designed to help the students understand regression analysis. A model (using real data) is developed to…
Competitive Hunter Models (UMAP)
In this module various assumptions about the growth in isolation of a single species are modeled and analyzed both grap…
Examining Data: A General Strategy and One-Sample Methods (UMAP)
This module gives some general comments about an overall strategy for analyzing data. It discusses certain general cons…
The Q-Q Plot, A Graphical Method for Comparing Two Samples (UMAP)
This module presents a graphical method that is useful for displaying and comparing two sets of data. This method displ…
Expected Value at Jal Alai and Pari Mutual Gambling (UMAP)
This module will explain the concepts of expected value, fixed-payoff, and pari-mutuel gambling. It will discuss gambli…
The Use of Dimensionless Analysis in Mathematical Modeling (UMAP)
This module demonstrates how dimensional analysis can be incorporated in the various stages of the modeling process. Th…
Two Sieves for Prime Numbers (UMAP)
In this module two algorithms for allocating prime natural numbers are presented: 1) Sundaram's Sieve based upon a tabl…
Probability in Contested Election (UMAP)
In this module the 1975 mayoral election in the city of Flint, Michigan is analyzed. True vote is estimated with an est…
Differential Growth, Huxley's Allometric Formula, and Sigmoid Growth (UMAP)
This module relates analytical geometry and calculus with differential growth, Huxley's Allometric Formula, and sigmoid…
The St. Louis Arch Problem (UMAP)
This module is a solution to a restatement of a contest problem that had a major influence in correcting misconceptions…
The Consumer Price Index: What Does It Mean? (UMAP) 4th ed.
EDITOR'S NOTE: This is the 4th edition of a Module that was originally published in Vol. 4, No. 3 of this Journal, in 1…
Internal Rates of Return (UMAP)
This module shows how to compute the present value, future value, and internal rate of return for investments and annui…
Cassette Tape Counters (UMAP)
This module applies linear equations and the quadratic formula to cassette tape counters. The techniques of elementary…
Continuous Time, Discrete State Space Markov Chains (UMAP)
This module develops a model for the number of components operating in a multicomponent device. Using the number of bul…
The Unit of Analysis and the Independence of Observations (UMAP)
This module addresses two problems that have received insufficient attention in the statistical literature, namely, the…
Spacecraft Attitude, Rotations and Quaternions (UMAP)
This module applies linear algebra to space flight and astrophysics. The rotational orientation of a spacecraft is call…
The Pace of Life: An Introduction to Empirical Model-Fitting (UMAP)
In this moduel data collected by two psychologists and published in a professional science journal are used to introduc…
Graphical Analysis of Some Difference Equations in Biology (UMAP)
This module shows how the behavior of the solutions to certain equations can be predicted by graphical techniques. Stud…
Differential Equations and Root Cellars (UMAP)
This module derives the one-dimensional heat equation, proves the uniqueness of its solutions, and finds the solutions…
The t-Test for Independent Samples (UMAP)
In using this module students will gain: 1) the ability to carry out the t-test of the statistical significance of the…
One-Sided Operators in Rings (UMAP)
This module provides concrete examples (n x n matrices with n greater than or equal to 4) of one-sided identities and b…
Passive Solar Heating (UMAP)
A unit that relates linear algebra through the topic of passive solar heating. A problem in solar heating is formulated…
Some Card Tricks: Algebra in Disguise (UMAP)
Many card tricks are counting problems solved by elementary algebra. Each card trick (world problem) is transformed to…
Finding the Shortest Distance on the Earth's Surface from Here to Timbuktu (UMAP)
A unit that involves pre-calculus in finding the shortest distance on the Earth's surface from here to Timbuktu. This m…
Keeping Dimensions Straight (UMAP)
With this unit, the student will be able to: 1) distinguish between dimensions and units; 2) to algebraically manipulat…
Layout Design and Sheet Metal Fabrication (UMAP)
A unit that involves calculus with layout design and sheet metal fabrication. In sheet metal fabrication a pattern is s…
A Mathematical Model of a Universal Joint (UMAP)
In this module a universal joint is modeled to study its output pulsations. The angle of coupling that will alleviate t…
Zeller's Congruence and Modular Systems (UMAP)
Section 1 introduces Zeller's congruence with motivational problems. Section 2 deals with the greatest integer function…
The Cost Accounting Problem (UMAP)
This module that applies linear algebra to accounting. Several different techniques (including those used by accountant…
3 x 3 Rotation Matrices in Air Traffic Control (UMAP)
This module shows how orthogonal matrices are used to translate into local coordinates the airplane coordinate sent by…
Tiltup Panels: Locate the Pulleys (UMAP)
This module discusses the location of the pulleys for a cable rigging currently in use. The key differenetial equation…
The Use of Continued Fractions in Botany (UMAP)
Students will 1) become acquainted with some of the most interseting aspects of continued fractions; 2) realize and app…
Evaluating and Analyzing Probabilistic Forecasts (UMAP)
This module presents an analysis of the quality of probabilistic forecasts, such as weather forecasting and sporting ev…
Expected Loss in Keno (UMAP)
This module uses a simplified version of keno to explain the method for calculating probabilities and expected value in…