INSTRUCTOR: Duncan J. Melville, 218 Valentine, Phone: 229-5298
Office Hours: MWF 10:50-11:50
FINAL EXAM TIME: Wednesday, December 14 from 1:30 pm to 4:30 pm in
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 in-class 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 8-10 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.
|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
|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
|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
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.
Introduction to Greek civilization.
Signs of the Zodiac.
Instructions for the paper.
Go to My Home Page.