Lecture Notes

Notes are in PDF format.

Cryptography : From World War II machines to unbreakable codes
PDF Part 1: The Hagelin Cryptograph - One of the most popular cryptographs in the 1940's and 1950's. Binary Numbers. Binary Addition. Parity Addition. HBO - Transmission of encrypted password.
PDF Part 2: Modular arithmetic. Modular multiplication. Fermat's little theorem. Public key cryptography. The RSA algorithm.
PDF Addendum to Part Two with Updates on RSA Challenge and Largest Known Prime (as of Feb. 1, 2009)

Error correction & compression :
PDF Part 1: Error detection and error-correcting codes. How a scratched CD can play flawlessly. ASCII Encoding. Hamming Code.
PDF Part 2: The big sqze: lossless compression of texts. Lempel-Ziv algorithm. Image compression.

Probability & Statistics :
PDF Part 1: Probability & statistics. Monty Hall problem. 99% accurate tests that are wrong half the time.
PDF Part 2: Normal distribution. Statistics. Statistical calculations. Confidence interval.

Birth, Growth, Death & Chaos : The Dynamics of Complex Systems
PDF Part 1: Investments and interest. Population growth. Linear models. Nonlinear models.
PDF Part 2: Dynamical systems and chaos.

Graph Theory : Bridges, circuits, trees and maps
PDF Part 1: Graphs, degrees, trees, hydrocarbon molecules, Chinese postman problem, Bacon numbers.
PDF Part 2: Flow, Street Network, Avoiding Conflicts, Coloring Trees, Complete Graphs, Coloring Polygons, Plato and Euler, map-coloring problem.

Voting & Social Choice :
PDF Part 1: The mathematics of voting, power and sharing. Fairness in politics: the impossible dream? Voting systems, distribution of power in conventions. Plurality method. Plurality with Runoff. Sequential Runoff. Borda Count. Condorcet Method.
PDF Part 2: Weighted voting systems. Fair division.