I gave some lectures during the second week (Monday, July 17, to Friday, July 21) of the Rutgers Young Scholars Program in Discrete Mathematics. It was fun. Many students seemed to be intelligent and listening. Good questions were asked, pushing me to explain perhaps better and to be more honest. This is good. Students seemed to learn some of the material. Their own presentations were generally good. Some comments are here. Most of what was presented followed material previously discussed several times in the Governor's School. Notes are available through the link indicated and more specific references are below.
| Day | Topics | Questions and remarks | References |
|---|---|---|---|
| 1 | Introducing probability | The questions and some comments | Any elementary probability book has information about this. (Dover reprints are cheap!) See also pages 38-45 of these notes, which have additional references. |
| 2 | Digression about set theory and some of its interesting "paradoxes" | The questions and some comments | I don't have any specific reference of my own -- maybe I'll try to write something "some time". Any basic book on set theory (and many other math and theoretical computer science books) will have much of this material. (Dover reprints are cheap!) |
| 3 | Analysis of the transmission (a long unbranched tree) and broadcasting (a binary tree) models | The questions and some comments | Any elementary probability book has information about this. See also pages 46-55 of these notes, which have additional references. |
| 4 | The birthday "paradox", the pigeonhole principle, introduction to Ramsey numbers, and their overestimation via a greedy algorithm (sort of!) | The questions (including one which relies on day 5's presentation) and some comments |
See page 56 here, followed
by these notes on the other
material. The notes have additional references.
There are more drawings of pigeons and information about Google pagerank here. |
| 5 | The probabilistic method applied to underestimation of Ramsey numbers and random algorithms |
Maintained by greenfie@math.rutgers.edu and last modified 7/20/2006.