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.
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.