April 11: The p-Adic Numbers and The Card Game SET
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MercerCounty MathCircle
Apr 8, 2015, 9:47:33 PM4/8/15
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Hi All!
Sorry for the late update but there will be math circle this Saturday, held by Princeton student Roger Van Peski. For the advanced series, he will be talking about the p-adic numbers. Then afterwards, for the recreational series, he will be teaching us about the card game SET. Please find details and the abstracts below or on the website here! Hope to see you all this weekend!
Sincerely,
Roy Zhao
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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.
--
Mercer County Math Circle
mercercountymathcircle.wordpress.com
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.
--------------------------------------------------------------------
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.
--
Mercer County Math Circle
mercercountymathcircle.wordpress.com
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