INSTRUCTOR: Duncan J. Melville, 218 Valentine, Phone: 2295298
Office Hours: MWF 10:5011:50
FINAL EXAM TIME: Wednesday, December 14 from 1:30 pm to 4:30 pm in
VAL 104.
This time and date will not change.
TEXT: There is no required text. Instead you will have a selection of readings from both primary and secondary sources for each class period.
OBJECTIVES: This course is intended to introduce you to the mathematics of the ancient and classical worlds. We will be concerned with both the development of certain mathematical ideas and the roles mathematics has played in the historical cultures and societies we study. That is, we will be interested in the mathematicians who created the mathematics, the teachers who communicated the mathematics, the students who learned the mathematics and the people who paid for it all. We will seek to understand their motivations, desires, interests and requirements.
Thousands of years of mathematical work has left a vast and complex history, rather more than can be covered in one semester. We will make no pretense of completeness, but will uncover the general outlines of the world of mathematics throughout ancient history, and will swoop down on illustrative or interesting episodes in more detail.
FORMAT: History of mathematics combines the methodologies of both history and mathematics. This means you will be expected to read (a lot), write (a lot) and talk (a lot) about mathematics, as well as learn a lot of mathematics. Readings and homework will be assigned in each class. You will have both general assignments (the same for everyone in the class) and specific ones (each individual will have different assignments). You will be expected to participate in discussions on your general assignments and be discussion leader on your personal topics. Classroom participation is important, and will be worth around 15% of your grade over the semester.
Various short mathematical and writing assignments will be given during the semester; these will add up to about 40% of the grade. There will be two inclass exams. One will cover the mathematics of Mesopotamia and Egypt, the other will cover Classical and Hellenistic mathematics. Tentative dates are October 10 and November 30. Together, these exams will be worth about 30% of your grade. Towards teh end of the semester you will write a paper of 810 pages and give an accompanying presentation during our finals time. I will give you more details and a timeline later. The term paper will be worth 15% of your grade.
STUDY HABITS: In order to do well in this class, you will need to work regularly (at least 5 days a week) and plan on spending an average of about 10 hours a week on the course outside of class time. Most of that time is going to be reading Reserve material or handouts. Figure out where this time is going to come from in your schedule. Read assigned material a couple of times: first, skim it to get the general idea of what the topics and main points are, then go through again in more detail. Read with a pencil. Take notes. Think about what you will say in class. Think about questions others may have. Think about your responses to these questions. For most people it is probably best to do the reading on your own, and somewhere quiet with few distractions. You will then often find it much easier to refine your thinking on various topics by talking to other people in the class. Most people are nervous about talking in class, asking questions, and writing on the board. Practice.
I expect and encourage you to work together. I also expect you to understand that plagiarism and all forms of cheating are serious crimes. Poor documentation deserves poor grades.
Expect to work very hard in this course. Expect no reward for effort. Expect appropriate reward for performance. Expect to have fun.
Class 
Date 
Topics 

Day 1  August 29 
Introduction; Archaic mathematics 

Day 2  August 31 
Third millennium mathematics  
Day 3  September 5  Cuneiform arithmetic  
Day 4  September 7  Old Babylonian algorithms  
Day 5  September 12  OB Problem Texts  
Day 6  September 14  More on OB problems 

Day 7  September 19  Mesopotamian mathematical environment  
Day 8  September 21  Introduction to Egypt; Hieroglyphic and hieratic numbers  
Day 9  September 26  Pyramids: construction and logistics  
Day 10  September 28  Egyptian arithmetic, RMP  
Day 11  October 3  RMP and Egyptian geometry  
Day 12  October 5  Egyptian metrological problems 

Day 13  October 10  Exam 1  
Day 14  October 12  Introduction to Greece; Pythagoreans  


Day 15  October 17  Greek numbers and arithmetic  
Day 16  October 19  Platonic mathematical philosophy and education  
Day 17  October 24  4th century Greek mathematics  
Day 18  October 26  Hellenistic world, Alexandria, introduction to Euclid  
Day 19  October 31 
Elements I  
Day 20  November 2  Elements XIII  
Day 21  November 7  Elements VII  
Day 22  November 9  Archimedes  
Day 23  November 14  Archimedes  
Day 24  November 16  Apollonius  


Day 25  November 28 
Apollonius  
Day 26  November 30  Exam 2  
Day 27  December 5  Late classical mathematics  
Day 28  December 7  Look back in wonder 
For more details and the readings, follow the links to the daily
schedules. The daily schedules give a more detailed breakdown for each
class meeting. There will typically be three components to each
day's meeting: preliminary reading you do before class, analysis of the
readings in class, and homework based upon the class topic. This
means that between any two classes, you will need to do homework from
the class before and reading for the
class ahead. In the schedule below, readings and homework are
attached
to the discussion day. There is a lot of reading. Plan on
spending a great deal of time in the library this semester.
The main history of mathematics Web sites are:
The MacTutor History of
Mathematics Archive contains brief biographies of many
mathematicians and short
topical articles on many subjects.
The sites or pages listed below are more specialized in their coverage. They are listed in roughly the order we will encounter the material to which they refer.
My Mesopotamian Mathematics site. Includes pages on several Mesopotamian mathematical topics, images of tablets, bibliographies, journal links, and links to some related sites.
Egypt from the Exploring Ancient World Cultures site. Has a more detailed chronology than I am likely to give you and has links to many images.
Abzu's Egypt page has links to a huge number of sites you may be interested in.
The Perseus Project is hard to use, but has a huge amount of information on Ancient Greece. In particular, you should look at:
These are links to the subsidiary pages we access on particular days. There are links from the relevant days, but I have gathered them here as well to save you hunting around for which particular day we did something.
Cuneiform arithmetic exercises.
Egyptian Chronology.
Egyptian Metrology.
Introduction to Greek civilization.
Signs of the Zodiac.
Instructions for the paper.
Go to My Home
Page.