Exponential Growth and Decay (UMAP)
This unit reviews exponents and introduces the notions of doubling time and half-life. Students, given a table of data…
Development of the Function y=Ae^cx (UMAP)
This unit involves applications of exponential functions. The applications present the concepts of half-lives and doubl…
Numerical Approximations to y=e^x (UMAP)
A unit that introduces exponential functions. With completion of this module students will be able to: 1) describe the…
How to Solve Problems Involving Exponential Functions (UMAP)
This unit shows how to find the formula for an exponential function given a point on its graph and the slope at that po…
Descriptive Models for Perception of Optical Illusions: Part II (UMAP)
This unit presents experimental determination of the numerical parameter that determines the strength of an illusion, a…
Discretionary Review by the Supreme Court II: Analysis of the Model (UMAP)
This module is a continuation of an analysis of Supreme Court decision-making presented in Part I. The problem is to ex…
The Dynamics of Political Mobilization II: Deductive Consequences and Empirical Application of the Model (UMAP)
This module consists of a framework which is developed to deduce the properties of a mobilization process based on math…
General Equilibrium: A Leontief Economic Model (UMAP)
This unit discusses an application leading to large sets of linear simultaneous equations. It also calculates equilibri…
The Growth of Partisan Support II: Model Analytics (UMAP)
This unit investigates mathematical properties of first order quadratic difference equation a) equilibria, b) local sta…
Linear Programming in Two Dimensions: II (UMAP)
With this unit, the student will understand the nature of sensitivity analysis by investigating the ways in which the g…
The Spacetime World: Foundations of Special Relativity Theory (UMAP)
With this unit, the student will be able to: 1) recognize the relative nature of simultaneity, and fundamental implicat…
The Spacetime World: The Minkowski World (UMAP)
With this unit, the student will be able to: 1) recognize the speed of light as the limiting speed of ordinary particle…
The Spacetime World: Loedel's Spacetime Diagram (UMAP)
With this unit, the student will be able to: 1) relate the Loedel diagram to the required invariance of spacetime inter…
History and Uses of Complex Numbers (UMAP)
This unit presents the history, the algebra, the geometry, and a few uses of complex numbers, including complex square…
Orthogonal Projections and Applications in Linear Algebra (UMAP)
This module demonstrates how real applications require orthogonal projections in abstract linear spaces. The material p…
Elementary Cryptology (UMAP)
This module discusses a few of the methods used in earlier times to illustrate the nature of cryptology, then discusses…
Basic Analysis of Z12 Music Chords (UMAP)
This module teaches how to use the additive group Z12 and a group of musical transformations called the twelve-tone ope…
Geometric Programming (UMAP)
This module presents a simple method of optimization that: 1) tells how much an engineering design would cost before kn…
The Hardy-Weinberg Equilibrium (UMAP)
This module uses elementary probability to show how genotypes in a population reach an equilibrium in a single generati…
Measuring Stream Discharge: A Precalculus Field Exercise (UMAP)
This module consists of a set of four collaborative field-based exercises and labs. All of the materials derive from ef…
Waves and Strong Tides (UMAP)
This module analyzes the motion of water underneath a surface wave in the ocean in order to determine formulas for the…
Graphs, Digraphs, and Rigidity of Grids (UMAP)
This module studies the rigidity of frameworks made of rigid rods in the plane that are connected by two-dimensional ba…
Pinochle Numbers (UMAP)
This module uses the setting of the card game of pinochle to develop and practice counting techniques, including combin…
How to Win at Nim (UMAP)
This module uses a variant of the Moore Teaching method to stimulate the students to derive the theory of impartial gam…
The Terminator and Other Geographical Curves (UMAP)
This module seeks to: 1) strengthen students' intuition in multidimensional geometry; 2) consolidate their command of d…
Differentials and Geographical Maps (UMAP)
This module seeks to: 1) strengthen the students' intuition in multidimensional geometry; 2) consolidate their command…
Fuzzy Sets (UMAP)
This module explores elementary operations of set theory in a fuzzy setting and examines some applications of fuzzy set…
Closing in on the Internal Rate of Return (UMAP)
This module describes three iterative methods for solving equations, motivated by the computation of the internal rate…
Clock Time vs. Sun Time: The Analemma (UMAP)
In this module equations are constructed for the position of the sun in the sky at any time of day, any day of the year…
Applications of Geometrical Probability (HiMAP)
Students are encouraged to experiment and estimate when analyzing probability problems, and use their estimates to deve…
Drawing Pictures With One Line (HiMAP)
This unit uses Euler's Theorem and the fascinating one-line drawings of the Malekula people in the South Pacific to dem…
Loads of Codes (HiMAP)
This unit explores the mathematics of protecting and communicating information, through cryptography and digital data s…
UMAP Journal 19.4, Winter 1998
Table of Contents: GUEST EDITORIAL Social Sources for Renewal in Academic Mathematics ARTICLES Modeling the Organi…
Concepts of Math for Business: Background Mathematics (UMAP)
This unit contains several modules which introduce students to various concepts of math for business. The modules invol…
Concepts of Math for Business: The Mathematics of Finance (UMAP)
A unit that shows the student how to solve business problems involving percents, to use formulas to solve problems in f…
An Application of Mathematical Groups to Structures of Human Groups (UMAP)
A unit that utilizes mathematical groups in studying structures of human groups. The purpose of this module is to learn…