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
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.