Textbook: Howard Eves, An Introduction to the History of Mathematics, 6^{th} edition, Brooks/Cole, Thomson Learning, Inc.
Instructor: Leo Goldmakher
Telephone: 4162072783
Email: leo.goldmakher at utoronto dot ca
Office hours: Mondays 12:001:15 pm and Thursdays 4:306:00; additional office hours by appointment.
DATE  LECTURE SUMMARY 
ASSIGNMENT (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 post300 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, nonexamples, 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. 
Assignment 2
Figure 2.1 
Prove that the only regular polyhedra are the five Platonic solids.  
Oct. 25 
Corrected definition of regular polyhedron Intellectual Athens. 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 306090 triangle with unit hypotenuse. (No trigonometry allowed!)  
Nov. 1 
Euclid's Elements. Rules for divisibility 
Assignment 3
Figure 3.4 
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? Diophantine equations: 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. 
Assignment 4 
Why does
1 +
^{1}⁄_{4} +
^{1}⁄_{42} +
^{1}⁄_{43} +
^{1}⁄_{44} + ... =
^{4}⁄_{3}?
(`The formula' is not an acceptable answer.) 

Nov. 22 
Chinese mathematics:
Indian Mathematics: AlKhwarizmi 
Read Chapter 7 of Eves 
A person has a number of eggs.


Nov. 29  Student Presentations.  Final project  
Dec. 6  Student Presentations.  Assignment 5 