Mathematics 2720W Syllabus
Fall 2012

Meeting times: Tuesday and Thursday, 2:00-3:15 PM
Instructor: Professor Gerald M. Leibowitz
Office: MSB 419B   Campus phone: (860) 486-8380
E-Mail address:
Office hours Fall 2012: Tu Th 1-2 PM and by arrangement

Text: The History of Mathematics: An Introduction (latest Edition) by David M. Burton




15%   Mathematical homework exercises using methods or notation of historical periods.
See below for links to many of the homework assignments.

10%   Three page paper [approximately 750 words not including bibliography] concerning mathematics in ancient Egypt and Mesopotamia.
First draft due in class on Tuesday, September 25, 2012.  I will read the drafts and make suggestions for improvements.
Final version due Tuesday October 16, 2012.
Please read the file Short Paper for more about this paper.

15%   Midterm examination. Thursday, October 18, 2012. Students may use the textbook and two two-sided handwritten 8.5x11 inch sheets of notes at the midterm. Please write in pencil, not in ink.   Topics guide to the Midterm Exam.

20%   Longer paper on the historical development of a mathematical topic or the mathematics of a certain time period and place.
[The topic of the short paper may not be used. A paper about the history of actuarial science is acceptable but a paper about the history of actuarial societies is not.]
First draft due at my office mailbox 3PM, Friday October 26, 2012.
Final draft due in class November 13, 2012.

How Long is a Long Paper?
The University Senate Guidelines for W-courses say that the total writing required should be a minimum of "15 typed double-spaced, finished pages (approximately 400 words of text exclusive of footnotes, bibliography, diagrams, etc.)." So papers 2 and 3 should be at least 6 double spaced pages (about 1500 words each) plus bibliographies.

20%  A biographical paper (six double spaced pages plus bibliography) about a mathematician or mathematical scientist. Due the last Tuesday of the semester, December 4, 2012. Write about both the person's life and his or her mathematical achievements.

Please choose someone from the following list, unless you can convince me that someone else is an acceptable topic: Niels H. Abel, Archimedes, Aristarchus of Samos, George Boole, Jerome Cardan, René Descartes, Leonhardt Euler, Pierre de Fermat, Fibonacci (Leonardo of Pisa), Galileo Galilei, Évariste Galois, Carl F. Gauss, Sophie Germain, David Hilbert, Christiaan Huygens, Felix Klein, G.W. Leibniz, Isaac Newton, A. Emmy Noether, Claudius Ptolemy, Pythagoras, Julia Robinson, John von Neumann, Karl W. Weierstrass, Grace Chisolm Young.

20%  Final examination. Tuesday, December 11, 2012, 1:00-3:00 PM.
Students are required to be available for their exams during that time. (Please note: vacations, previously purchased tickets or reservations, weddings (unless part of the wedding party), and other large or small scale social events, are not permissible excuses for missing a final exam.)
At our final exam, students may use their textbooks and three two-sided handwritten 8.5x11 inch sheets of notes.
Here is a link to a Guide to the Final Examination.

NOTE: If you need to polish your writing skills in English, you may find the University Writing Center to be helpful. Reference:
Since this is a "W" course, one cannot pass the course without passing the writing part.

The three themes of this course are mathematics, history, and biography. We shall focus in particular on mathematics in the ancient Middle East, geometry and algebra in classical Greece, the preservation of the knowledge of antiquity outside of Europe in medieval times, progress in number theory and the solution of polynomial and diophantine equations, and the development of differential and integral calculus in the seventeenth century. Often, the lectures will concentrate on the mathematics while the text presents the history, but sometimes these roles will be reversed.

Homework set 1. Egyptian hieroglyphic and Attic Greek numerals
Homework set 2. Mesopotamian cuneiform, Chinese rod, and Mayan priestly numerals
Homework set 3. Sexagesimal fractions. Ancient Egyptian linear equations
Homework set 3A asks that you write your name in hieroglyphics. It will be distributed in class.
Homework set 4. Due Thursday September 20. More Mathematics in ancient Egypt
Homework set 5. Due Tuesday October 9. Pythagorean Number Theory
Homework set 6. Due Tuesday October 16. Greek Algebra, Geometry, and Number Theory
Homework set 7. Due Thursday October 25. Greek Constructions
Homework set 8. Due Thursday November 1. Archimedes
Homework set 9. Due Thursday November 8. Ptolemy and Diophantus
Homework set 10. Due Thursday November 15. Will be distributed in class.
Topic: Exercises from Indian Mathematics Books from Long Ago
Homework set 11. Due Thursday December 6. The Chinese Remainder Theorem

Deciphering Egyptian hieroglyphics, brief history

The Rhind Mathematical Papyrus

Link to a New York Times article about the Egyptian mathematical papyrus texts

Handouts on Greek Mathematics after Euclid
Notes on Alexandrian Greek mathematics.

Notes on Archimedes of Syracuse.
Notes on Apollonius of Perga.

Notes on Hellenistic Astronomers and the origins of trigonometry.

Notes on Heron of Alexandria, a Greek mathematician
who was influenced by the legacies of the Egyptians and the Babylonians.

Notes about Diophantus and his mathematics.
Diophantus' contributions to algebra, and the sum of squares identities.
Some examples of problems treated by Diophantus.
Problem II.28.

Notes: Mathematics in the Arab and Persian World in the Middle Ages. Thabit ibn Qorra and Omar Khayyam.

Notes: Trigonometric Functions and their names

Last edited on August 27, 2012