Problem Sets

Problem sets are made available on the web as the course progresses.

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

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

Birth, Growth, Death & Chaos
Part 1. Investments and interest. Population growth. Linear models. Nonlinear models.
Part 2. Dynamical systems and chaos.

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

Voting & Social Choice
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.
Part 2. Weighted voting systems. Fair division.