Proofs from THE BOOK (Winter 2022) is about extremely elegant proofs from many areas of mathematics. We will loosely follow Aigner and Ziegler’s book by the same title, going through the beautiful proofs they present and putting them into a broader mathematical context.
The title of the book and the class comes from the great 20th-century mathematician Paul Erdős, who liked to talk about a deity who had a book of perfect proofs to all theorems. We will glimpse into that book and study those proofs and where they come from, as well as where else the proof techniques lead elsewhere in mathematics.
There are various entirely independent classes we can run based on the material from Proofs from THE BOOK. Here is a small sampling of the topics we will discuss in the Winter 2022 class:
- Suppose we have finitely many points in the plane, not all on a line. Must there exist a line passing through exactly two of them?
- The probabilistic method: How can we use probability to show the existence of an object with a certain property?
- How many times must we shuffle a deck of cards before it becomes well-shuffled?
- What sorts of techniques do we use to prove that numbers are irrational? Transcendental?
The Winter 2022 Proofs from THE BOOK class will be completely independent of previous Proofs from THE BOOK class we have offered: it will not rely on them and will cover entirely different content.