Saturday May 24: Markov Chains, Martingale Construction, and Halving Fun

Advanced Series

Title: Markov Chains and Martingale Construction

Speaker: Ryan Peng

Time & Date: 2pm-3pm, Saturday May 24

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

Abstract: We will take a quick tour of Markov chains and their applications to some probability puzzles. A Markov chain is a mathematical process that undergoes well defined random transitions in order to take on varying random values throughout time. In this session, we will focus on fun applications & creative problem solving rather than the mathematical details & proofs. Time-permitting, we will also explore martingales and how they can reduce complicated probability problems to sets of simple algebraic equations.

Chili peppers: 2.5 out of 4

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Recreational Series

Title: Halving Fun

Leader: Justin Lanier

Time & Date: 3:14pm-4pm, Saturday May 24

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

Abstract: Join us as we “halve” some fun while creating some art and solving some puzzles that involve breaking shapes in half. What’s the most beautiful way you could cut a square into two equal pieces? Is it always possible to cut a funky shape in half through a specified point? Whether on grids or with free-form shapes, halving tasks provide many fruitful mathematical opportunities. Come explore and these questions and more!

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Saturday May 10: Euler Characteristic, the 5 Platonic Solids, and Cryptography

Advanced Series

Title: The Euler Characteristic and the 5 Platonic Solids

Speaker: Professor Gyan Bhanot

Time & Date: 2pm-3pm, Saturday May 10

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

Abstract: For any planar figure made from any combination of polygons, there is a seemingly mysterious relationship between the number of edges (E), the number is vertices (V) and the number of faces (F), namely that X = V+F-E = 1. The quantity X = V+F-E is called the Euler Characteristic of any surface of polyhedra. We will give an elementary proof that X = 1 in 2-dimensions and X = 2 in 3-dimensions.

A “Platonic Solid” is a convex 3-d object made from regular polygons with the same number of faces meeting at each vertex. We will use the result X = 2 in 3-d to prove that there are only five “Platonic Solids”: the Cube, the Tetrahedron, the Octahedron, the Dodecahedron and the Icosahedron, which are shown in the figure.

Figure: Platonic_Solids

Chili peppers: 1 out of 4

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Recreational Series

Topic: Cryptography

Leader: Harini Subrahmanyam Fredrickson

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

Time & Date: 3:14pm-4:14pm, Saturday May 10

Description: The description is a secret for now (it’s encrypted!); stay tuned for us to update the website with one, or come to the talk to find out what cryptography is about!