• General description. We will explore some major themes in mathematics--calculation, number, geometry, algebra, infinity, formalism--and their historical development in various civilizations, ranging from the antiquity of Babylonia and Egypt through classical Greece, the Middle and Far East, and on to modern Europe. We will see how the earlier civilizations influenced or failed to influence later ones and how the concepts evolved in these various civilizations.

  The earliest civilizations have left only archaeological and limited historical evidence that requires substantial interpretation. We have many mathematical treatises from the later civilizations, but these are usually in a completed form which leave out the development of the concepts and the purposes for which the mathematics was developed. Thus, we will have to analyze the arguments given by historians of mathematics for their objectivity and completeness.

  See also Clark's Academic Catalog

• Prerequisites. The prerequisite for this course is an intense interest in mathematics. There are no other prerequisites for it other than a familiarity with plane geometry and algebra. Our study will reach just to the beginnings of calculus since we won't have time in one semester for more.
• Course goals.
  • Content goals:
    • follow the development of mathematics from early number systems to the invention of calculus
    • read and understand some historical mathematics
    • survey the development and use of methods of computation, some of which involve tools such as the abacus
    • study the mathematics of various different civilizations, their conception and use of mathematics, and how the historical conditions of those civilizations affected and were affected by mathematics
  • Historical perspective goals:
    • develop your capacity to understand the contemporary world in the larger framework of tradition and history
    • focus on the problems of interpreting the past and can also deal with the relationship between past and present
    • introduce students to the ways scholars think critically about the past, present and future
  • Other goals:
    • Develop your ability to present mathematics and history in spoken and written forms
    • Help you practice research skills
    • Satisfy, in part, your curiosity of how mathematics developed and how it fits into culture
• Course objectives.
  When you have finished this course you should be able to:
  • describe the development of various areas of mathematics within and across various civilizations
  • describe the changing character of mathematics over time and recognize the distinction between formal and intuitive mathematics
  • give examples of significant applications of mathematics to commerce, science, and general life, past and present
  • understand that history includes the interpretion the past, not just facts
  • better research historical questions and present your conclusions to others
• Brief syllabus, Detailed syllabus
• Textbook. The text for the course is A History of Mathematics, an Introduction by Victor J. Katz, Addison-Wesley, second edition, 1998. ISBN: 0-321-01618-1. Web page. (There may be a third edition out by fall, and, if so, we'll use it.) Supplementary material will be included for those subjects of primary interest.
• Course Hours.
• Office hours. Semester schedule. Humor in mathematics.
• Assignments, tests, and presentation/paper. You will do assignments every week or two from the text, and you'll take three tests, each test covering about 1/3 of the course. You will select, research, and present a topic of your choice. Your presentation will be a 15 to 20 minute class presentation accompanied by a 5 to 15 page paper.
• Course grade. 1/5 for assignments, 1/5 for each test, 1/5 for the presentation/paper.

Class notes, quizzes, tests, homework assignments

1. Wednesday, Aug 27. Welcome and survey of the course.

This page is located on the web at

http://aleph0.clarku.edu/~djoyce/ma105/

David E. Joyce,