## Day 13: Exam 1

### Coverage

This exam will cover the semester so far.  That is, the mathematics of Mesopotamia and Egypt.  In slightly more detail, this means you will need to be able to:
• find where and when Mesopotamia and ancient Egypt were;
• discuss the development of mathematical technology from tokens to writing;
• recognize and explain the content of archaic tablets;
• explain some of the archaic metrological systems;
• understand the development of mathematics during the third millennium;
• perform or check computations in Fara-period or Sargonic mathematics (with suitable metrological charts);
• describe the sexagesimal place value system and explain how it arose from the archaic systems;
• demonstrate a wizardry with cuneiform arithmetic;
• be able to follow, describe, explain and do Old Babylonian word problems (in translation);
• find reciprocals using either of the two procedures we discussed;
• explain the importance of algorithmic procedures in Mesopotamian and Egyptian mathematics;
• explain Hoyrup's cut and paste geometry approach to 'quadratic' problems;
• discuss the algebraic and geometric views of Old Babylonian mathematics;
• discuss the role of tables and lists in Mesopotamian mathematics;
• explain the role of the scribe in Mesopotamia in different periods;
• explain scribal training in Mesopotamia in different periods;
• illustrate the hieroglyphic and hieratic numeration systems of Egypt and explain their uses;
• explain and perform arithmetic in the 'Egyptian style';
• understand and explain Egyptian word problems such as those from RMP;
• explain pyramid construction techniques and logistics;
• explain methods of orienting pyramids and constructing right angles;
• discuss and compare sources of our knowledge of Egyptian and Mesopotamian mathematics;
• recognize Egyptian and Mesopotamian mathematical artifacts;
• guess what I forgot to put on this list.
I will supply you with metrological tables, a reciprocal table and a 2x reciprocal table.  You will be permitted to use a calculator to check your workings if necessary.

### Format

Some fun arithmetical questions.  These will be similar to the arithmetical homework questions and allows you to demonstrate your skills with the various computational techniques we have covered.

Some problems.  I will give you a couple of word problems similar to the ones you have studied and expect you to work through them and discuss their relationship to the rest of the corpus.  Another possibility is to give a 'variant' of an example using different data but the same algorithm.

A selection of IDs and definitions.  Given an artifact or topic, identify and describe as fully as possible, including location, date, contents and significance.
Examples: Identify this image, this image, this image, or this image.
Terminology: hekat, khar, sila, kush, nindan, ban, sar.
Topics: reciprocal tables, edubba literature, sexagesimal system.
Some short answer questions.  These will be short discussion questions, often focussing on development of an idea or topic, or comparison of ideas.
Examples: Discuss the development of the sexagesimal place value system.
Compare the numeration systems of Egypt and Mesopotamia in the second millennium.
Discuss the role of the scribe in Mesopotamia.
Discuss the role of the scribe in Egypt.
Discuss the types of mathematics needed for planning and constructing a pyramid.
Discuss the role of tables in Old Babylonian mathematics.
Compare the characteristics of Old Babylonian mathematical problems with those in the RMP.
Discuss the ideology of scribal training in Ur III.
Give an analysis of a particular problem from Mesopotamia or Egypt in terms of the ideas we have discussed.

On to Day 14.

Up to Ancient and Classical Mathematics