“Race in Jefferson’s Republic” We in America do not have government by the majority. We have government by the majority who participate. Thomas Jefferson What could be more American than apple pie, mom, and Thomas Jefferson? Like all of us, Jefferson was a person of infinite complexity. He experienced joys, sorrows, disgust, frustrations, uncertainty, and self-doubt. He was one of America’s founding fathers, but also a human being who lived in a rapidly changing world. In the true sense of the word, he was a Renaissance Man, one who excels in a variety of endeavors. He was an inventor, statesman, musician, architect, bibliophile, agronomist, author, diplomat, and president. He was also a husband, father, and slaveholder. Was Jefferson a genius with limited character, or just a wealthy man who was a product of his times? In this learning module, you will investigate this very real person who shaped a revolution that shook the foundation of the world’s political structures. You will: Actively read historian Ronald Takaki’s provocative essay on Jefferson as well as primary sources from Jefferson and others in Hollitz, Chapter 6. Complete a Critical Thinking Analysis with an added paragraph explaining four primary sources, And draw conclusions regarding Jefferson’s life and legacy as well as implications for our lives today! PART III GRAPH THEORY 224 13 Food Webs Author: Robert A. McGuigan, Department of Mathematics, Westfield State College. Prerequisites: The prerequisites for this chapter are basic concepts of graph theory. See Sections 9.1 and 9.2 of Discrete Mathematics and Its Applications. Introduction A food web is a directed graph modeling the predator-prey relationship in an ecological community. We will use this directed graph to study the question of the minimum number of parameters needed to describe ecological competition. For this purpose we will consider how graphs can be represented as intersection graphs of families of sets. We will also investigate the axiomatic description of measures of status in food webs. Competition In an ecological system, the various species of plants and animals occupy niches defined by the availability of resources. The resources might be defined in terms of factors such as temperature, moisture, degree of acidity, amounts of nutrients, 225 226 Applications of Discrete Mathematics and so on. These factors are subject to constraints such as temperature lying in a certain range, pH lying within certain limits, etc. The combination of all these constraints for a species then defines a region in n-dimensional Euclidean space, where n is the number of factors. We can call this region the ecological niche of the species in question. For example, suppose we restrict ourselves to three factors, such as tem- perature, nutrients, and pH. Assume that the temperature must be between t1 and t2 degrees, the amount of nutrients between n1 and n2 and the p ...