Math 4850/6850 Syllabus (Spring 2003)

Topic: History of Mathematics Room: Grad Studies 302
Call Number: 4850: 96-545 7th Period: 2:30-3:20 PM
6850: 06-546

Instructor: Dr. Robert Rumely E-mail: rr@math.uga.edu
Office: 437 Grad Studies (706) 542-2630
Home: 1081 Twin Lakes Road, Athens, Ga. 30606 (706) 543-0443

Office Hours: 3rd Period (10:05-11:00) MWF; other times by appointment, gladly.

Text: Katz: A History of Mathematics, 2nd edition

Purpose: The main goal of this course is to give you an idea of the sweep of mathematical thought,
from Babylonian and Egyptian times to the present. We will focus on the development
of ideas, on the relation between mathematical history and secular world history, and on
the people who created mathematics. This is a "writing-intensive course", and another goal is to teach you to write expository mathematics.

Assignments and Grades:
Readings will be assigned daily, and occasionally mathematical problems. There will
also be weekly short writing assignments, related to the course material. There will be
takehome midterm and finals.

4850: There will be two 6-page papers required for the course, one on a biography of a
mathematician, and one on the development of a mathematical topic. A list of important
mathematicians and a list of suggested topics will be handed out. A third required
project will be to complete a mathematical timeline covering 1500 to the present.
There will be two exams during the course, a mid-term and a comprehensive final.

6850/honors: In place of one of the papers above, read a biography of a mathematician
from a list of suggested books, or a book on the development of a topic, and write an
10-page paper on it.

Your grade will be determined using the weights:

HW/Short Writing Assignments 15%
Paper 1 20%
Paper 2 20%
Midterm 15%
Timeline 15%
Final 15%

Final Exam Due: Wednesday, May 7, 12:00 noon

Attendance: Attendance will be taken sporadically, starting Wednesday, January 17.
Students with more than 3 unexcused absences may be withdrawn from the class.

Readings: Reading assignments will be assigned daily, and it is essential that you do all
reading before the next. Readings cover material from class in greater depth, and will
also contain material that cannot be covered in class. You will be responsible for the
readings, as well as class notes, on tests.

Course Outline:
Overview: 1 day
Babylonian and Egyptian Mathematics: 1 day
Greek Mathematics: 9 days
Hindu and Arab Mathematics: 2 days
History of Numeration, Symbols, and Pi: 2 days
Renaissance Mathematics: 8 days
Origins of the Calculus: 3 days
Mathematics of the 1700's: 4 days
Mathematics of the 1800's: 7 days
Mathematics of the 20th Century: 6 days

Important Dates:
Biography paper due: Friday, September 28
MIDTERM EXAM: Friday, October 5
Mathematical topic paper due: Friday, November 9
Timeline due: Friday, November 30
FINAL EXAM: Friday, December 14

Expected Course Schedule:
Week: Monday Wednesday Thursday Friday
08/13-08/17 Intro
08/20-08/24 Babylonia, Egypt Greek schools 3 Classic Greek Problems
08/27-08/ Euclid's Elements Euclid's Elements Apollonius, Conics
09/03-09/07 (Labor Day) Archimedes Archimedes
09/10-09/34 Ptolemy, Trigonometry Diophantus, Arithmetic Hindus, Arabs
09/17-09/21 Al-Khowarazmi History of numbers & symbols History of Pi
09/24-09/28 Bacon, Galileo, Kepler Cardano, Cubic Equation Napier, Logarithms
10/01-10/05 Art, Projective Geometry Fibonacci, Mercator MIDTERM EXAM
10/08-10/12 Descartes, Coordinate Geometry Fermat, Number Theory Precursors to Calculus
10/15-10/19 Newton, Principia Leibniz Bernoulli's
10/22-10/26 Euler: Achievements Euler: Lack of rigor (Fall Break)
10/29-11/02 Berkeley, d'Alembert: limits Lagrange, Laplace Gauss
11/05-11/09 Abel, Galois Fourier Non-Euclidean Geometry
11/12-11/16 Cauchy, Weierstrass: Rigor Dedekind, Cantor Quaternions, Vectors
11/19-11/23 Einstein: Relativity (Thanksgiving) (Thanksgiving)
11/26-11/30 Paradoxes in Set Theory Responses Computers
12/03-12/07 Public Key Cryptography Wiles: Fermat's Last Theorem (Reading Day)
12/10-12/14 FINAL EXAM