Notes for the Governor's School Math Lectures

Here are notes for a program of lectures which were given to about 100 high school students attending the New Jersey Governor's School of Engineering and Technology during July, 2004. The notes were initially prepared before the lectures (first posting: 6/21/2004). Almost surely there will be changes. Comments are welcome: please advise me (greenfie@math.rutgers.edu) of errors or bad writing. Later versions were posted as shown.

At this time it is difficult to write mathematical formulas and notation using standard HTML. Therefore most material is presented here in PDF format, since PDF (Adobe) readers now are part of most browsers.

Remarks about Maple for
Governor's School students
Last modified 6/21/2004 		Some serious homework
problems for the students
All done, with student solutions.
Last modified 7/28/2004

 
Links about the topics

What is it?Page(s)LinksLast changed
Title, introduction, and table of contents i-iii [PDF link] 6/21/2004
Lecture 0: People and secrets
Lecture 1: Secret sharing
Lecture 2: Modular arithmetic		 1-2
3-6
7-10		 [PDF link] 6/21/2004
Lecture 3: Fermat and Euler 11-14 [PDF link] 6/21/2004
Monday, July 13 The Euclidean algorithm and its application to multiplicative inverses mod primes. This should be in the notes around page 12 but isn't.
[HTML link] 7/13/2004
Wednesday, July 14 A Maple program to create RSA pairs and {en|de}cryption exponents. Also displayed is Maple notation for efficient modular exponentiation.
[HTML link] 7/14/2004
Lecture 4: Public key encryption
Lecture 5: How hard is arithmetic?		 15-19
20-27		 [PDF link] 6/21/2004
Lecture 6: Who owns ideas?
Lecture 7: More encryption
Lecture 8: Perfect cryptography		 28-32
33-35
36-37		 [PDF link] 6/21/2004
Lecture 9: Probably ...
Lecture 10: Gambling
Lecture 11: The transmission network
Lecture 12: Broadcasting-statement and heuristics
Lecture 13: Broadcasting-problem analysis
Lecture 14: Broadcasting-solution and discussion
 38-40
41-45
46-47
48-50
51-52
53-55		 [PDF link] 6/21/2004
Lecture 14½: Intermezzo
BIRTHDAY TIME! 		56 [PDF link] 6/21/2004
Lecture 15: Pigeons and patterns
Lecture 16: Friends, strangers, and coloring graphs
Lecture 17: Ramsey and five		 57-58
59-63
64-67		 [PDF link] 6/21/2004
Lecture 18: Random graphs and real networks
Lecture 19: Coding theory		 68-69
70		 [PDF link] 6/21/2004

Maintained by greenfie@math.rutgers.edu and last modified 7/28/2004.