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: leibowitz@math.uconn.edu**

**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**

**TOPICS**:

- Chapter 1; Early
number systems and symbols
- Chapter 2;
Mathematics in early civilizations
- Chapter 3; Beginnings
of Greek mathematics
- Chapter 4;
Euclid, Eratosthenes, Archimedes
- Chapter 5; Diophantus, later commentators
- Chapter 6;
Fibonacci
- Chapter 7;
Renaissance, Cardan, cubic and quartic equations
- Chapter 8;
Descartes, Newton, Leibniz and parts of the next two chapters,

focusing on Mersenne, Fermat, Pascal, Euler.

**GRADES**:

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: writingcenter.uconn.edu.

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:
Trigonometric Functions and their names