Syllabus: Math Alive – MAT 199 – Spring 2008

Cryptography : From World War II machines to unbreakable codes

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.

• Lecture Notes (PDF), covered in class 2/5-2/7
• Lab 1
• Help Session 2/13 Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 2/14

Part 2. Modular arithmetic. Modular multiplication. Fermat's little theorem. Public key cryptography. The RSA algorithm.

• Lecture Notes (PDF), covered in class 2/12-2/14
• Lab 2
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 2/21

Error correction & compression :

Part 1. Error detection and error-correcting codes. How a scratched CD can play flawlessly. ASCII Encoding. Hamming Code.

• Lecture Notes (PDF), covered in class 2/19-2/21
• Lab 1
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 2/28

Part 2. The big sqze: lossless compression of texts. Lempel-Ziv algorithm. Image compression.

• Lecture Notes (PDF), covered in class 2/26-2/28
• Lab 2
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 3/6

Probability & Statistics :

Part 1. Probability & statistics. Monty Hall problem. 99% accurate tests that are wrong half the time.

• Lecture Notes (PDF), covered in class 3/4-3/6
• Lab 1
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 3/13

Part 2. Normal distribution. Statistics. Statistical calculations. Confidence interval.

• Lecture Notes (PDF), covered in class 3/11-3/13
• Lab 2
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 3/27

Birth, Growth, Death & Chaos : The Dynamics of Complex Systems

Part 1. Investments and interest. Population growth. Linear models. Nonlinear models.

• Lecture Notes (PDF), covered in class 3/25-3/27
• Lab 1
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 4/3

Part 2. Dynamical systems and chaos.

• Lecture Notes (PDF), covered in class 4/1 - 4/3
• Lab 2
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 4/10

Graph Theory : Bridges, circuits, trees and maps

Part 1. Graphs, degrees, trees, hydrocarbon molecules, Chinese postman problem, Bacon numbers.

• Lecture Notes (PDF), covered in class 4/8 - 4/10
• Lab 1
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 4/17

Part 2. Flow, Street Network, Avoiding Conflicts, Coloring Trees, Complete Graphs, Coloring Polygons, Plato and Euler, map-coloring problem.

• Lecture Notes (PDF), covered in class 4/15 - 4/17
• Lab 2
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 4/25

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.

• Lecture Notes (PDF), covered in class 4/22 - 4/24
• Lab 1
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 5/2

Part 2. Weighted voting systems. Fair division.

• Lecture Notes (PDF), covered in class 4/29 - 5/1
• Lab 2
• Help Session Wednesday 8-10pm Fine Hall Top Floor
• Problem Set - due 5/9

This document last modified Friday, 01-Aug-2008 14:07:33 EDT