# Full Member Resources

COMAP offers members access to numerous mathematics and modeling programs, products, and materials in a variety of collections and formats. Our online library has more than 1500 resources. This page lists resources with most recent first. Please use the Search box or the filter options in the Find Resources menu to assist in locating desired products. For additional assistance or if you have questions, please don't hesitate to contact us.

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### Expected Loss in Keno (UMAP)

This module uses a simplified version of keno to explain the method for calculating probabilities and expected value ...

### Getting in Touch with Touchy Questions (UMAP)

A unit that involves probability and statistics with questionnaires. This module explains a bias-reducing technique c...

### Harmonic Motion and the Circular Functions (UMAP)

A unit that involves precalculus, harmonic motion, and circular functions. In this module an explanation of simple ha...

### The Three Dimensional Trapezoid Rule (UMAP)

The Three Dimensional Trapezoid Rule is a very simple ad reasonably accurate method which can be used to approximate ...

### Atmospheric Pressure in Relation to Height and Temperature (UMAP)

A unit using calculus applied to the study of atmospheric pressure in relation to height and temperature. Students ap...

### The Levi-Civita Tensor and Identities in Vector Analysis (UMAP)

A unit that involves applications of vector field identities. This module allows students to gain the ability to deri...

### Basic Descriptive Statistics (UMAP)

With completion of this module students will be able to: 1) use frequency distributions and histograms to summarize d...

### An Application of Geometry to Economics: The .6 Rule for Industrial Costs (UMAP)

A unit that applies calculus to industrial economics. By completion of this module students will be able to examine t...

### The Cobb - Douglas Production Function (UMAP)

A unit that applies calculus to economics and management science. This module develops the Cobb-Douglas Production Fu...

### The Manufacturing Progress Curve (UMAP)

A unit that applies precalculus to industrial management. The purpose of this module is to teach students about learn...

### Lagrange Multipliers and the Design of Multistage Rockets (UMAP)

A unit that uses Lagrange multipliers to compute the minimum total mass of an n-stage rocket capable of placing a giv...

### An Application of Calculus in Economics: Oligopolistic Competition (UMAP)

In this module some of the elementary models for duopolies that utilize calculus are examined. Table of Contents:1. I...

### Random Walks: An Introduction to Stochastic Processes (UMAP)

In this module random walks are introduced by an example of a gambling game. The associated finite difference equatio...

### Unconstrained Optimization (UMAP)

This module introduces Gradient Search Procedures, with examples and applications. Students are introduced to the use...

### Representing Integers as Sums or Differences of Squares (UMAP)

In this module the problem of presenting an integer as a sum or as a difference of two squares is studied. Key questi...

### Dimensional Analysis (UMAP)

A unit that relates linear algebra to dimensional analysis. In using this module given a physical system and the fact...

### A Cash Flow Model for Magazine Subscriptions (UMAP)

In this module a matrix model is developed for projecting the quarterly cash flow of a magazine. Interpretations and ...

### Perturbation Theory (UMAP)

This module gives a historical and self-contained introduction to the method of solving nonlinear differential equati...

### The Statistical Evaluation of Burn Care (UMAP)

A model for the probability of death from a burn is developed in this module. This model is used in comparisons of pa...

### Descriptive Models for Perception of Optical Illusions: Part I (UMAP)

In this unit, the historical background of the study of stable illusions of angle is sketched to show how a 19th cent...

### Random Walks and Fluctuations (UMAP)

This module presents new and simplified proofs of several theorems, including the arc sine law for sojourn times. The...

### I Will if You Will...A Critical Mass Model (UMAP)

This module introduces the critical mass model, which is applied to examples in which individuals must decide to chea...

### Measurement Scales (UMAP)

This unit introduces four types of measurement scales -- nominal, ordinal, interval, and ratio -- and considers their...

### Using Percent (HiMAP)

This comprehensive unit emphasizes that understanding percentages is essential for survival in today's world of compl...

### Problem Solving Using Graphs (HiMAP)

This examination of graph theory introduces techniques such as minimum-cost spanning tress, shortest-route algorithms...

### The Mathematics of Conflict (HiMAP)

Students see how decision mathematics can be used to understand conflict and give us a new historical perspective. Hi...

### Symmetry, Rigid Motion, and Patterns (HiMAP)

Students examine patterns in wallpaper and ancient artifacts to discover the fascinating applications of basic aspect...

### The Mathematical Theory of Elections (HiMAP)

This module illustrates how mathematics can design and analyze election and ranking methods. Preference schedules, fa...

### Recurrence Relations - 'Counting Backwards' (HiMAP)

Introduce students to difference equations by showing their unique application to computer science. HiMAP Module 2.Hi...

### Student Generations (HiMAP)

Introduces functions and strategies (heuristics) for students to generate and solve their own problems. HiMAP Module ...

### The Apportionment Problem: The Search for the Perfect Democracy (HiMAP)

A look at the apportionment of the House of Representatives, and how many representatives from each state are sent to...

### Fair Divisions: Getting Your Fair Share (HiMAP)

Demonstrates how mathematics can be used to divide objects fairly, such as the equitable distribution of an item that...

### A Mathematical Look at the Calendar (HiMAP)

This unit demonstrates mathematical techniques for finding the day of the week on a given date, finding mathematical ...

### Spheres and Satellites (HiMAP)

Students use graphing calculators to discover amazing geometric facts about our backyards, our world, and beyond. HiM...

### The Mathematician's Coloring Book (HiMAP)

The four-color theorem is introduced through maps, pictures, and worksheets, which explore the branch of mathematics ...

### Decision Making & Math Models (HiMAP)

This unit discusses the mathematical models that help solve three common management problems. The unit works well wit...

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COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.

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