Mathematics 446 - Fall 2005

The history of mathematics

  • Instructor: Bill Casselman
  • Class times: MWF 1:00 - 2:00
  • Class location: Biology 2449
  • Office hours: by appointment only.
  • Email address: I usually respond to email within a few hours.
  • Office: Mathematics 215

The main topic will be the history of numbers (as opposed to algebra or geometry). The course will be basically a series of snapshots of different developments. We'll begin with very early ways of representing numbers, sooner or later looking also at Euclid's treatment of both magnitudes and integers, as well as Dedekind's treatise on real numbers, the ultimate development of Euclid's treatment.

References will be scattered - some in libraries, many on the Internet. All students will be expected to read and digest original sources (translated into English). They will also be expected to do independent projects, mostly involving an essay explaining what they find in an original source. Class notes will appear on this site from time to time. Some idea of what the course will be like can be seen at the course web pages for spring, 2003 and spring, 2005.

Every student taking this course must have a total of 27 credits in mathematics or computer science courses. Courses taken concurrently (i.e. this term, the fall of 2005) can be counted. If the credits are in computer science they must be approved by me explicitly.

Grading will be based on (1) roughly weekly assignments; (2) exams - a mid-term examination, a final examination, and numerous quizzes; (3) a final essay project. As a rule, every day on which an assignment is due there will be a short quiz on the same material. Exams and quizzes will be graded proportionally to duration. I have not yet decided how the three different components will be weighted. Some information about the essay projects can be found below, and more will probably be posted here later on.

In order not to get a grade of 0 on a quiz or examination, a student must present a valid medical excuse within 2 days of the missed exam, or arrange the absence, and have it approved by the instructor, at least 2 days in advance.

Some references used last year

Homework assignments

  • The first assignment is due next class! It is to prove the theorem stated in class today about representation of positive integers in base B > 1.
  • Second assignment due Monday, September 19.
  • Sixth assignment due Monday, November 7.

The projects

Every student is required to hand in a project at the end of the term. These will normally be essays of some kind explaining something about mathematics and history. All project topics must be approved by the instructor. An essay should normally be about 20-30 pages in length, and done by computer word-processing. Illustrations are encouraged. All sources - all illustrations and text not produced entirely by you - must be acknowledged. Grades will be based on:
  • Mathematical content
  • Historical content
  • Relevance to course material
  • Difficulty
  • Interest
  • Originality
  • Clarity
  • Accuracy
Project topics must be selected by about 3 weeks before the end of term.