Syllabus: Math Alive – MAT 199 – Spring 2009

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 2/3-2/5
• Lab 1
• Help Session 2/11 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 2/12

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)

• Lecture Notes (PDF), covered in class 2/10-2/12
• Lab 2
• Help Session 2/18 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 2/19

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 2/17-2/19
• Lab 1
• Help Session 2/25 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 2/26

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

• Lecture Notes (PDF), covered in class 2/24-2/26
• Lab 2
• Help Session 3/4 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 3/5

Probability & Statistics :

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

• Lecture Notes (PDF), covered in class 3/3-3/5
• Lab 1
• Help Session 3/11 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 3/12

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

• Lecture Notes (PDF), covered in class 3/10-3/12
• Lab 2
• Help Session 3/25 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 3/26

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 3/24-3/26
• Lab 1
• Help Session 4/1 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 4/2

Part 2. Dynamical systems and chaos.

• Lecture Notes (PDF), covered in class 3/31 - 4/2
• Lab 2
• Help Session 4/8 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 4/9

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 4/7 - 4/9
• Lab 1
• Help Session 4/15 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 4/16

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 4/14 - 4/16
• Lab 2
• Help Session 4/22 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 4/23

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 4/21 - 4/23
• Lab 1
• Help Session 4/29 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 4/30

Part 2. Weighted voting systems. Fair division.

• Lecture Notes (PDF), covered in class 4/28 - 4/30
• Lab 2
• Help Session 5/6 Wednesday 8-10pm Fine Hall Room 224
• Problem Set - due 5/7

This document last modified Wednesday, 11-Feb-2009 09:54:29 EST