Mathematics 3010, Summer 2009: Paper Requirements

Length: Seven to ten pages, double spaced. Longer if there are extensive figures.

Topics:: Paper 1: A topic from Ancient or Greek Mathematics. Paper 2: A topic from Islamic or (Modern) European Mathematics.

For one of your two papers, you may choose to do a book or movie review. Your topic should not be one covered in some detail in class.

Writing: The paper must have a title. Use appropriate mathematical notation - variables are in italics, superscripts and subscripts are appropriate. The Symbol font allows easy use of Greek letters. If your paper includes geometric figures, try to use the computer to produce them; hand-drawn figures are acceptable, however. Use a straight edge to make all straight lines. If you do not know how properly to compile a bibliography and cite references, check a style manual. You may use any style you like; Chicago style is somewhat standard for technical papers; MLS style is fine. Just be consistent. There should be some mathematical content in the paper as well, not just history. Check with me if you are worried that you did not use enough math.

Mathematical content and figures must be made your own. Recopy figures you find online or in books and write mathematical arguments in your own words.

If you use Internet references, they must also be cited properly. I would recommend chasing down original references. I consider the MacTutor History of Mathematics Archive as a scholarly source. Wikipedia is great for getting ideas, but not a scholarly source. At least two references in the paper must be from printed sources.

Grading: 50 points for content, 25 points for writing correctness and style. Five points deducted for each day (not class period) late. You may certainly turn in your paper early.

Some good resources:

• Bell, E.T. Men of Mathematics. Be aware that this is not an extremely well-respected source.
• Burton, David. The History of Mathematics: An Introduction
• Boyer, Carl. A History of Mathematics.
• Gullberg, J. Mathematics: From the Birth of Numbers.
• Eves, Howard. An Introduction to the History of Mathematics.
• Eves, Howard. A History of Geometry.
• Kline, Morris. Mathematics and Western Culture.
• Kline, Morris. Mathematical Thought from Ancient to Modern Times.
• Struik, D.J. A Concise History of Mathematics.
• Struik, D.J. A Source Book in Mathematics: 1200-1800.
• The History of Mathematics: A Reader. ed. J. Fauvel and J. Gray.
• Classics of Mathematics. ed. R. Calinger.

Some topics for paper 1:

• Eudoxus and the method of exhaustion
• Advanced Greek geometric constructions
• Three classical geometric construction problems
• The parallel postulate (Euclid's fifth)
• Archimedes methods of determining area and volume
• Greek astronomy
• Babylonian astronomy
• Chinese story problems
• Pappus of Alexandria
• Mayan numbers and astronomy
• The abacus and counting board
• Diophantine equations
• Qin Jiushao