Notes for the Governor's School Math Lectures

Here are notes for a program of lectures to be given to about 100 high school students attending the New Jersey Governor's School of Engineering and Technology during July, 2002. The notes were initially prepared before the lectures (first posting: 6/30/2002). I am sure 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 material is presented here in two formats, Postscript and PDF. I hope that everyone can read at least one of these.

Remarks about Maple for
Governor's School students 		Homework or "assessment
of instructional efficacy"
Now with answers!

Hot news!

What is it?Page(s)LinksLast changed
Title & table of contents I [Postscript] | [PDF] 7/31/2002
Introduction 0 [Postscript] | [PDF] 7/31/2002
Lecture 0: People and secrets
Lecture 1: Secret sharing
Lecture 2: Modular arithmetic		 1-2
3-6
7-10		 [Postscript] | [PDF] 7/10/2002
Lecture 3: Fermat and Euler 11-14 [Postscript] | [PDF] 6/30/2002
Lecture 4: Public key encryption
Lecture 5: How hard is arithmetic?		 15-19
20-26		 [Postscript] | [PDF] 7/25/2002
Lecture 6: Who owns ideas?
Lecture 7: More encryption
Lecture 8: Perfect cryptography		 27-31
32-34
35-36		 [Postscript] | [PDF] 7/11/2002
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
 37-39
40-44
45-46
47-49
50-51
52-54		 [Postscript] | [PDF] 7/25/2002
Lecture 14½: Intermezzo
BIRTHDAY TIME! 		55 [Postscript] | [PDF] 7/16/2002
Lecture 15: Pigeons and patterns
Lecture 16: Friends, strangers, and coloring graphs
Lecture 17: Ramsey and five		 56-57
58-62
63-66		 [Postscript] | [PDF] 7/16/2002
Lecture 18: Random graphs and real networks
Lecture 19: Coding theory		 67
68		 [Postscript] | [PDF] 7/16/2002

Comments
7/16/2002
Small changes were made in Lecture 5. Major "renovations" have been made in the discussion of networks. Less major but still large changes have been made in Lectures (new numbers!) 15, 16 and 17.
The following is still true: the last two lectures are essentially dummy lectures, with only slight comments and some references. I suspect I won't get up to that material. If I do, I'll need to prepare rapidly.

7/25/2002 I only covered the material up to Lecture 14 in class. Minor changes were posted today in some of the earlier material.
I thank the students for their patience.
8/3/2002 Today I posted answers to homework problems.
8/6/2002 And now a minor addition to the answers.
8/9/2002 The Hot news! was posted.
11/5/2002 The picture was added to this page.

Maintained by greenfie@math.rutgers.edu and last modified 8/9/2002.