April 11: P-adic numbers and SET!

Advanced Series

Title: Better Living Through Infinite Series: The p-Adics

Speaker: Roger Van Peski

Time & Date: 2pm-3pm Saturday April 11

Location: Princeton Public Library, teen room (3rd floor)

Abstract:

We’re going to talk a bit about a somewhat lesser-known cousin of the real numbers: the p-adics. These may be thought of as infinite geometric series of powers of a prime p, where we generously allow these series to retain their identity as independent ‘numbers’ rather than just throwing them away because they (often) diverge to infinity. Far from being a whimsical exercise in pretending things don’t diverge, they are actually extremely important in a wide variety of areas in math. They also have a lot of interesting properties—for instance, if two p-adic discs intersect at any point, one is contained in the other! We’ll define and discuss some of the fascinating ways in which the p-adic integers and p-adic rational numbers behave and their relation to the regular integers and rationals, as well as what being ‘cousin of the real numbers’ actually means in a rigorous sense.

Prerequisites: It will help if you’re comfortable working with infinite series, such as the geometric series you may have seen in precalculus or the variety of series in calculus.

Chili peppers: 3 out of 4.

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Recreational Series

Title: SET

Leader: Roger Van Peski

Time & Date: 3:14pm – 4pm Saturday April 11

Location: Princeton Public Library, teen room (3rd floor)

Abstract:

SET is a fun card game which revolves around fast pattern-searching, but like many seemingly simple games, it has a lot more mathematical subtlety than meets the eye. We’ll play a game or two for fun and to get comfortable with the rules and learn a clever trick to convince your amazed friends that you can count cards! This leads into a discussion of the mathematical life of SET, with connections to combinatorics, modular arithmetic, and finite geometry.