Professor Simonson History of Math Ingenuity

Fall 1997 MA 149

All readings are from Journey Through Genius. The other text, Puzzles, Mazes and Numbers should be used as a starting point for your projects. You should read through it completely by the 4th week of the course, making note of which problems and topics interest your group. Then you and your group should make an appointment with me to define a specific project based on your interests.

Week 1: Introduction: What is mathematics? Why do it? What are theorems and

proofs? Examples of mathematical discovery: guessing and experimenting.

Reading: Pages 1-11. Class Handout.

Week 2: Number systems and arithmetic from ancient Egypt, Babylonia, Greece and

Medieval Europe.

Week 3: Square roots and Quadratic equations. Egyptian, Babylonian and Chinese

methods. Medieval methods and the solution of the Cubic Equation.

Reading: Chapter 6.

Weeks 4-5: Geometry and The Pythagorean Theorem. Babylonian tablets of

Pythagorean triples. Euclid's Geometry and the

Definition/Postulate/Theorem/Proof style of mathematics.

Reading: Chapter 2.

Week 6: Number Theory: Prime numbers, Greatest common divisors, Euclid's proofs and

algorithms, Chinese remainder theorem and medieval equivalents.

Reading: Chapter 3.

Weeks 7-8: Areas and ¹. Biblical references and the commentary of Levi ben Gershon

on the biblical value for ¹, and the area of a circle. Hindu methods for

approximating ¹ by Geometry. Archimedes methods for approximating ¹.

Modern computers and summations.

Reading: Chapter 4.

Week 9: Graph Theory - Regular Polyhedra of Plato and Euclid, Euler's Theorem

and the Koenigsburg Bridge Problem, Coloring.

Week 10: Sums and series. The sums of Levi ben Gershom and mathematical

induction. Convergence of geometric series and Zenos paradoxes,

Divergence of harmonic series.

Reading: Chapter 8.

Week 11: Infinity and Countability, Galileo's paradoxes, Cantor's set theory.

Reading: Chapters 11-12.

Weeks 12-15 Group Projects and Discussions.