Math 323: Ancient and Classical Mathematics

Fall 2005 Course information for Dr. Melville's Math 323A

Basic course information

MEETS: MW 1:40-3:10 in VAL 104.

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 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 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.

Course Outline

Details are subject to change as we move through the semester.  Check often.




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
October Break

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
Thanksgiving Break

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 attached to the discussion day.  There is a lot of reading.  Plan on spending a great deal of time in the library this semester.

Reserve and reference materials

There is no text for this class.  Instead, there are a large number of reserve and reference materials that you will need to use during the semester.  A list is here. Reserves are kept behind the circulation desk in the Science Library.

General Web Links

Below are some links to sites that will be helpful to you in this course.

The main history of mathematics Web sites are:

These two sites contain much that is useful at any point in the course. You should take some time to explore them and find out what they have to offer you.

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.

While you're surfing the net, don't forget the library.

Local links

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.

Last modified: 22 August 2005
Duncan J. Melville

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