Prerequisites: 2 years of college-preparatory mathematics and satisfactory performance on a placement test. A survey of contemporary topics in mathematics, centering on applications and projects. Topics include measurements, rates of growth, basic statistics, the mathematics of political power, the geometry of the solar system, and computer arithmetic.

Course Introduction

This course examines a series of topics that illustrate the practical applications of mathematics. It is project-oriented and requires you to make connections between real-world problems and the mathematics necessary to solve them.

Course Outline

• Producing Data
• Describing Data
• Probability—The Mathematics of Chance
• Statistical Inference
• Social Choice—The Impossible Dream
• Weighted Voting Systems
• Fair Division
• Apportionment
• Growth and Form
• Geometric Growth
• Inaccessible Distances
• Reflecting the Universe
• New Geometries for a New Universe
• Symmetries and Rigid Motions

Goals/Objectives

After completing this course, you should be able to:

• cite elements of good statistical design, undertake elementary statistical analysis, and recognize and explain the shortcomings of unsound methods of statistical analysis
• mathematically analyze situations involving the weighting of power in various voting structures and implement apportionment of power strategies
• use the Pythagorean theorem and properties of similar triangles to calculate sizes of and distance between objects, including astronomical objects

Course Materials

Required Texts

COMAP. (1997). For all practical purposes: Introduction to contemporary mathematics, 4^th ed. New York: Freeman.

Huff, D. (1994). How to lie with statistics. New York: Horton.

University of Maryland University College. Instructor’s notes—Math 105: Mathematics—Contemporary topics and applications, 2d ed. College Park, MD: UMUC, 1997.

Guide to Writing and Research. College Park, MD: UMUC, 1995.

Video Series

A video series supplements this course. The videos reinforce and enhance the material presented in your textbook.

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