Textbook: Howard Eves, An Introduction to the History of Mathematics, 6th edition, Brooks/Cole, Thomson Learning, Inc.
Instructor: Leo Goldmakher
Email: leo.goldmakher at utoronto dot ca
Office hours: Mondays 12:00--1:15 pm and Thursdays 4:30--6:00; additional office hours by appointment.
(due on date listed)
|PROBLEM OF THE DAY||DOCUMENTS|| || || || || ||Sept. 13||
Introductions and policies.
What is history?
What is mathematics?
Introduction to Egyptian mathematics:
| || ||Course syllabus||Sept. 20||
Further discussion of Egyptian fractions:
More from the Rhind papyrus:
A bit about the Moscow papyrus:
|Read Chapters 1 and 2 of Eves.||
Does Egyptian multiplication always work?
In particular, can one write any positive
integer as the sum of distinct powers of 2?
| ||Sept. 27||
Brief history of Mesopotamia;
The exploits of Darius, including Pheidippides and the battle of Marathon
The exploits of Xerxes, including the battle of Thermopylae.
The history of cuneiform and its interpretation(s)
The Babylonian number system, pre- and post-300 BC.
|Assignment 1||Write 1⁄7 in Babylonian numerals.|| ||Oct. 4||
Continued discussing the Babylonian number system.
Discussed expanding fractions in different bases:
An example of a Babylonian algebra problem (solved using geometry).
The difference between a theory and a theorem.
The Pythagorean theorem (two statments, not 1!).
Pythagorean triples (examples, non-examples, primitive vs imprimitive).
Plimpton 322, and three interpretations.
|Read Chapter 3 of Eves||Prove the irrationality of √2|| ||Oct. 11||NO CLASS -- THANKSGIVING|| ||Not overeating.|| ||Oct. 18||
Discussed some Greek history and legacy.
Discussion of mathematics and the concept of "proof".
Plato, Socrates, and a problem from the Meno.
Polyhedra and the Platonic solids.
|Prove that the only regular polyhedra are the five Platonic solids.|| ||Oct. 25||
Corrected definition of regular polyhedron
Thales and the notion of proof.
Pythagoras and the Pythagoreans.
Three famous (and unsolvable!) Greek problems.
Introduction to Euclid's Elements.
| ||Determine the area of a 30-60-90 triangle with unit hypotenuse. (No trigonometry allowed!)|| ||Nov. 1||
Rules for divisibility
|A number is divisible by 3 if and only if the sum of its digits is. Why?|| ||Nov. 8||
Twin primes, Sophie Germain primes; are there infinitely many?
Wrapping strings around the equator, and our poor geometric intuition
The difficulty of defining π.
Approximating circles by polygons.
The formula for the area of a circle.
|Read Chapters 4 and 5 of Eves.||
A farmer buys exactly 100 animals, using exactly $100. The animals
he buys are chickens, cows, or pigs, and he buys at least one of each.
If chickens cost $0.50 each, cows cost $10 each, and pigs cost $3
each, how many of each did he buy?
| ||Nov. 15||
Some more discussion of π:
More about Archimedes:
Early Chinese history, and Pinyin.
1⁄44 + ... =
(`The formula' is not an acceptable answer.)
| ||Nov. 22||
|Read Chapter 7 of Eves||
A person has a number of eggs.
|| ||Nov. 29||Student Presentations.||Final project|| || ||Dec. 6||Student Presentations.||Assignment 5|| || |