Series Reversion and Applications (UMAP)
This module applies advanced calculus to astronomy and engineering. Five conceptually different techniques for finding…
Inversion Theory and Peaucellier Linkage (UMAP)
A unit that involves inversion theory and Peaucellier linkage. Table of Contents: 1. INTRODUCTION 2. THE CIRCLE OF…
Reflections, Rotations and the Sextant (UMAP)
This module applies geometry to the topic of navigation. It focuses on the navigational instrument, the sextant. Tabl…
The Spacetime World: Introduction to Spacetime (UMAP)
By an approach more geometrical than algebraic, this unit makes a quantitative understanding of relativistic kinematics…
Methods of Linear Programming for Students of Mathematics and Science (UMAP)
This module involves methods of linear programming for students of mathematics and science. Table of Contents: 1. IN…
Determining the Size for a Mussel Culture Farm in a Tidal Estuary Based on Local Biological Factors (UMAP)
A unit that involves pre-calculus in determining the size for a mussel culture farm in a tidal estuary based on local b…
Elements and Applications of Integral Equations (UMAP)
This module deals with the Volterra and Fredholm integral equations and their applications. In addition to problems tha…
Whales and Krill: A Mathematical Model (UMAP)
A predator-prey system involving whales and krill is modeled by a system of differential equations. Although the equati…
Simple Capital Theory (UMAP)
This module applies multivariable calculus to economics. Some of the models which economists have developed to show how…
Self-Organizing Files (UMAP)
This module applies linear algebra to computer science. Students will become familiar with probabilistic modelling of a…
Classifying Probability Distribution Functions (UMAP)
In this module, the Cantor set is used to construct a distribution that is not discrete or absolutely continuous. An ur…
Analysis of the Vibrating Spring Using the Complex Method (UMAP)
This module uses differential equations to analyze a vibrating spring by the complex method. The motions of a vibrating…
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…