Talk on Saturday (4/8)

 

Mercer County Math Circle will be having a talk this Saturday (4/8) at 2:00 PM in the 3rd floor of Princeton Public Library.
Speaker: Heesu Hwang
Time & Date: 2pm-3pm Saturday April 8
Location: Princeton Public Library, teen room (3rd floor)
Parallelism: Not Just For Geometry.

  • Have you ever had math problems you didn’t want to solve intelligently? A geometry problem or algebra problem for example where it seemed smart to simply coordinate bash or try a ton of factorizations. When deciding to bash or not, the driving factor is always how much computation we must do; the same trade-off exists in computer science. How do we do computation efficiently? One way to make computation faster is parallelism: distributing a task over many processors. What types of tasks can we distribute? How much faster can we solve problems if we can use multiple processors? We will explore the basics of run-time and speed-ups due to parallelism.
A recreational session will follow.
Hope to see all of you there!

Math Circle 2/11: Gaussian Distributions and Probability

Advanced Series

Title: The Law of Large Numbers and the Central Limit Theorem

Speaker: Chris Zhang

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

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

Abstract: The Gaussian or normal distribution is one of the most important models in statistics and is widespread in many fields of science, engineering, social science, and math. First we try to understand probability and prove the Law of Large Numbers. Then we will learn why the normal distribution is so prevalent through the Central Limit Theorem.

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Recreational Series

Title: Normal Distribution Game

Leader: Harini Subrahmanyam Fredrickson

Time & Date: 3:14 PM – 4 PM Saturday February 11

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

Abstract: We will be playing a game to learn more about normal distributions.


May 23: Machine Learning-SVMs for Image Segmentation

Advanced Series

Title: Machine Learning: SVMs for Image Segmentation

Speaker: David Fridovich-Keil

Time & Date: 2pm-3pm Saturday May 23

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

Abstract:

Machine learning is a buzzword these days. You probably already know that machine learning is used for face recognition, but I bet you didn’t know it’s also used for music classification and selection (e.g. Spotify), household thermostats (Nest), stock trading, and robotics. But what is it, exactly? Machine learning is often defined as algorithms that can improve their performance over time and experience. For example, a face recognition algorithm might attain higher accuracy if it has seen more example faces of each person. In this session, we will see one of the most common machine learning tools — the linear Support Vector Machine, or SVM — and try using it to classify pixels in an image as either people or not people.

Chili peppers: 2 out of 4.


May 9: Quaternions and Hyperbolic Paraboloids

Advanced Series

Title: Quaternions-Super complex numbers

Speaker: Heesu Hwang

Time & Date: 2pm-3pm Saturday May 9

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

Abstract:

Complex numbers are made by taking i to be the square root of -1. Well Quaternions instead have THREE elements i, j, and k that all square to -1. Come learn about the numbers that made physics work.

Chili peppers: 2 out of 4.

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Recreational Series

Title: Hyperbolic Paraboloids

Leader: Harini Subrahmanyam Fredrickson

Time & Date: 3:14pm – 4pm Saturday May 9

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

Abstract:

We will be exploring hyperbolic paraboloids through origami and sliceforms.

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.

March 28: Modular Arithmetic and Building a Geodesic Dome

Advanced Series

Title: Modular Arithmetic Part I

Speaker: Gregory Owen

Time & Date: 2pm-3pm Saturday March 28

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

Abstract:

We’ll be discussing modular arithmetic, bases other than 10, and some introductory results in number theory. We’ll cover the basic rules of modular arithmetic and use these rules to establish divisibility tests (by the end of the class, you’ll be able to quickly say which of 321583691 or 321583692 is divisible by 3 and which by 11). This class will also lay the foundation for a second class I’ll teach later this semester, which will get into some really cool topics like base 2i, in which you can represent any complex number using only the digits 0-3.

Chili peppers: 1 out of 4.

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Recreational Series

Title: Building a Geodesic Dome

Leader: Harini Subrahmanyam Fredrickson

Time & Date: 3:14pm – 4pm Saturday March 28

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

Abstract: We will be engaging in a fun hands-on activity by creating a large geodesic dome. These can be found in many places in the world, such as the Epcot Center at Disney World!


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!