### Mathematics-Science 380 -- History of mathematics

#### Trent University, 2006-2007

**Prerequisite:** MATH 110 and 235H, or MATH 110 and permission of the instructor. Second-year students wishing to take the course must have permission of the instructor.

Exam period office hours:

For 9-24 April, Monday through Thursday 11:00-12:00.

Stefan Bilaniuk

Gzowski College (Symons Campus) 337

*Winter hours:* ~~Mondays 10:00-10:50, and Tuesdays 11:00-11:50, Wednesdays 11:00-11:50, and Thursdays 10:00-10:50~~, or by appointment, or just drop by!

*Winter hours:* To be announced.

*phone:* 748-1011 x7474

*home phone:* 742-7862 -- Do *not* call between 10 p.m. and 8 a.m.

*e-mail:* `sbilaniuk @ trentu.ca`

The Heritage of Thales, by W.S. Anglin & J. Lambeck

Springer Verlag, 1995, ISBN 0-387-94544-X

*Lectures:* Mondays and Thursdays 11:00-11:50 in GCS 110.

*Seminars:* Thursdays 12:00-12:50 in GCS 110.

There will be ~~twelve~~ eleven fortnightly assignments, two term projects, and a take-home final examination. The assignments will be handed out and collected every other week in the Wednesday lectures, the projects will be due at the end of each term, and the final examination will be written during the examination period in April and will be due at its end. The final mark will be calculated as follows:

Best ~~10~~ 9 of ~~12~~ 11 assignments ~~(10 at 4% ea.)~~ (9 at 4.4% ea.) | 40% |

2 Projects (2 at 15% ea.) | 30% |

Final Examination | 30% |

This scheme may be modified for students in *exceptional* circumstances. Any such modification will require the agreement of both the student and the instructor.

*Plagiarism is an extremely serious academic offence and carries penalties varying from failure in an assignment to suspension from the University.* Definitions, penalties and procedures for dealing with plagiarism are set out in Trent University's Academic Dishonesty Policy which is printed in the Calendar. It can also be found online.
For clarity, the following guidelines will apply in MATH 380:
You are permitted and encouraged to work together and ask anyone willing (especially the instructor!) for explanations, hints, and suggestions on the problem sets, and to consult whatever sources you wish, with the exception that **you may not consult anyone who has taken the course before or their work**. However, **all work submitted for credit must be written up entirely by you, giving due credit to all relevant sources of help and information**. The take-home final exam will have more restrictive conditions that will be spelled out on the exam.

We will survey the historical development of some important parts of mathematics. In particular, we will focus on the evolution of proofs and abstraction and the development of algebra. In rough chronological order, we will consider mathematics in:

- Prehistory (
*i.e.* the -- speculative! -- origins)
- Egypt and Mesopotamia
- Classical Greece and Rome
- China, India, and the Islamic world
- Europe from the Middle Ages on
- The world at present

Note that additional material may be covered on the assignments and projects.

View or download in pdf format:

- MATH 380 Course Outline
- Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11
- Fall Projects
- Winter Projects
- Final Exam
- Map of the Near East
- Euclid's Axioms

Euclid's prooof of the Pythagorean Theorem

(Excerpted from Euclid's Elements in Greek by Richard Fitzpatrick.)
- MATH 380 Final Exam from 2004-2005
- Elementary Calculus: An Approach Using Infinitesimals by H. Jerome Keisler
- The Newton Project
- The Euler Archive

Department of Mathematics
Trent University

Maintained by Stefan Bilaniuk. Last updated 2007.04.05.