History of Mathematics
GENERAL EDUCATION: This course does not fulfill a General Education requirement.

CATALOG DESCRIPTION: Intended for those students majoring in Mathematics Education. This class presents historical topics that teachers can use in their math classrooms. This course introduces mathematical ideas and problem solving strategies that have evolved from ancient times to the present. (Winter)
TOPICS: The course will begin with computing techniques used in antiquity and how they have come to influence present day methods. Students will solve quadratic equations and verify algebraic identities using geometric methods developed by Thales and Pythagoras. The Geometry of Euclid will be discussed with special emphasis on how his theory of parallels would centuries later motivate the advent of non-Euclidean Geometries. Problems will be investigated that will establish a distinct contrast between Greek and Hindu Mathematics. The invention of the Calculus in the seventeenth centry will be studied with special attention given to those mathematical results that paved the way for this "new" mathematics that would forever change the modern world. The course will conclude with an investigation into nineteenth and twentieth century mathematics. Emphasis will center on Cantor's set theory, with special attention given to his Axiom of Choice and the turmoil this axiom created in early twenthieth century mathematics. Topology, Logic and David Hilbert's Formalism will be addressed as time allows.
OBJECTIVES: Students will view mathematics as a systematic, organized body of knowledge rooted in algebra, plane geometry, trigonometry and analytic geometry. By tracing the work of ancient mathematicians, students will gain an understanding that many brances of mathematics existing today are natural consequences of thousands of years of human endeavor. Students will leave the course with a greater appreciation for mathematics and for those who have gone before. They will come to understand as did Isaac Newton who said, "If I have been allowed to see farther than others, it is only because I have stood on the shoulders of giants."
REQUIREMENTS: Each student must have the textbook selected for the course.
Assignments will consist of reading from the textbook, working certain mathematical problems listed at the end of the reading sections, and quizzes over the reading and math problems assigned. There will be chapter tests to assess material covered in the textbook. There will be outside reading assignments that supplement the textbook, written assignments relating to individual research, and oral reports.
PREREQUISITES: Math 113 or concurrent enrollment in Math 113 and the consent of the instructor.