Series and Games: From Paradox to Paradox (UMAP)

Zeno's paradox of Achilles and the turtle was an early encounter between the human mind and the notion of infinite series. A brief study of series - finite and infinite, leads to a resolution of this paradox and provides a basis for disucssing expected value in games of chance. One example of a game of chance described by D. Bernoulli in 1738 yields a second paradox called the Saint Petersburg Paradox.

Table of Contents:

1. ZENO'S PARADOX

2. FINITE SERIES

3. INFINITE SERIES OF POSITIVE NUMBERS

4. GAMES OF CHANCE

5. THE ST. PETERSBURG PARADOX

6. ANSWERS TO EXERCISES