Lecture 1 - Mesopotomian and Egyptian Mathematics.

- For a more historical viewpoint, see also Math 629, in particular this chapter.

Lecture 2 - Greek Mathematics

- See also Boas&Geller pages 57-65, for a discussion on what kinds of numbers can be constructed via a straightedge and compass.

Lecture 3 - Axiomatic Systems

- See also Boas&Geller Pages 73-78

Lecture 4 - Axiomatic Systems (cont'd)

Goedel's Incompleteness Theorem, Boas & Geller page 78.

- Sketch of a proof via Cantor's diagonalization process.

Lecture 5 - Limits, part I.

- Dealing with infinity. Discussion of early concepts of limits (geometrical, philosophical).

- Making limits precise.

- Geometrical Examples
- Recursion
- Iterated Functions
- Dynamical Systems

- Classical epsilon-delta

Lecture 8 - Functions, part I.

- Notation and historical comments
- some historical problems and questions

Lecture 9 - Functions, part II.

- limits of sequences of functions
- unusual functions
- dimension matters

Lecture 10 - Geometry, part I.

- Euclidean geometry,
- Algebraic geometry,
- Analytic Geometry

Lecture 11 - Geometry, part II.

- Curvature

Lecture 12 - Geometry, part III.

- Geometer's Sketchpad
- Non Euclidean Applet

Lecture 13 - Applications of Geometry [Summary]

Lecture 14 - Calculus of Variations, part I.

Lecture 15 - Calculus of Variations, part II.

Lecture 16 - Optimization.

Lecture 17 - Complex Arithmetic

See Chapter 12 of Boas & Geller

Lecture 18 - Computer Graphics, using Complex Numbers and Quaternions

Lecture 19 - Survey of Historically important problems. Ideas for projects.

Lecture 20 - More Historically important problems.

Lecture 21 - (Very) recent results concerning the distribution of primes.

Lecture 22 - Proof of Fermat's (Little) Theorem

Lecture 23 - Cryptography, Prime Factorizations, and Public Key encryption

Lecture 24 - Problems and Puzzles involving primes