# Saturday March 22, 2014 – Recurrence Relations and Celtic Knots

Title: Recurrence Relations

Lecture Notes: Recurrence_relations

Speaker: Andy Loo

Abstract: In counting problems, sometimes it is hard to count the total number of configurations directly, but if we look at the problem from a different angle, we may be able to find connections with the number of configurations in smaller cases. The question then is how to get the total number from these recurrence relations. Let’s find out this weekend!

Chili peppers: 2 out of 4
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Title: The Math of Celtic Knots

Leaders: Justin Lanier & Harini Subrahmanyam Fredrickson

Time & Date: 3:14pm-4pm, Saturday March 22

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

Abstract: It’s St. Patrick’s Day this week! We’ll look at some ornate Celtic knots, observe and explain some patterns, and make some knot drawings of our own. We’ll also discuss the difference between knots and links, ways to identify each, and some other basic topological ideas. Come shamrock some great math with us!

# Saturday March 8, 2014: Discrete Calculus and Security Systems

Title: Discrete Calculus and its Applications
Lecture Notes: discrete-calculus-and-its-applications
Speaker: Alexander Payne
Time & Date: 2pm-3pm, Saturday March 8
Abstract: Have you ever wondered if there is a unified way to compute the sum of a sequence, like the sum of k^2 from k=1 to n? We will present discrete calculus, an elegant approach to the change and summation of a sequence, to solve problems such as these. Then, we will cover applications of this fascinating analog of traditional calculus by examining the Newton forward difference equation, a way to approximate certain smooth functions with the operations of discrete calculus. No calculus background is necessary.
Chili Peppers: 3 out of 4

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Title: Guarding a GalleryLeader: Justin Lanier

Time & Date: 3:14pm-4pm, Saturday March 8Location: Princeton Public Library, teen room (3rd floor)

Abstract: Imagine you needed to set up a security system at an art gallery, based on its 2D floor plan. You’d want to make sure that the cameras you installed would be able to see every part of the gallery, but you wouldn’t want to buy more cameras than you had to. Depending on the shape of the gallery, how many cameras would you need? We’ll explore this problem and variations on it.