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.

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Third Mercer County Math Circle: Normal Distributions and Probability

Advanced Series

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

Speaker: Chris Zhang

Time & Date: 2pm-3pm Saturday January 14

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.

Chili Peppers: 3 out of 4.

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Recreational Series

Title: Normal Distribution Game

Leader: Harini Subrahmanyam Fredrickson

Time & Date: 3:14 PM – 4 PM Saturday January 14

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

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


Second Math Circle: Two Player Games

Advanced Series

Title: Two Player Games

Speaker: Fatih Kaleoglu

Time & Date: 2pm-3pm Saturday December 10

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

Abstract: I will introduce the mathematics behind two-player games, touching upon why in every finite game a player has a non-losing strategy. Then I will talk about the game nim, its properties and resemblance to general games.

Chili Peppers: 2 out of 4.

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Recreational Series

Title: Two Player Games

Leader: Harini Subrahmanyam Fredrickson

Time & Date: 3:14 PM – 4 PM Saturday December 10

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

Abstract: We will be trying our hand at some of the games learned during the advanced series.


Kickoff Event: November 12 – Math and Music

Advanced Series

Title: The Mathematics of Sound

Speaker: Philip Etter

Time & Date: 2pm-3pm Saturday November 12

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

Abstract: An informal discussion about the basic mathematics of one of the most fundamental parts of our lives – sound. The basic questions we’ll ask are as follows: what is sound and how do we represent it mathematically? How do we distinguish between different sounds? And, perhaps most importantly, how can we manipulate and analyze sound with a computer? While the talk will be non-technical, the underlying mathematics involved is incredibly deep and powers a staggering amount of technology in our daily lives, from our cell phones to streaming services like YouTube.

Prerequisites: Ability to understand the graph of a function

Chili Peppers: 2 out of 4.
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Recreational Series

Title: Making Musical Instruments using Straws

Leader: Harini Subrahmanyam Fredrickson

Time & Date: 3:14 PM – 4 PM Saturday November 12

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

Abstract: We will be creating our own music by constructing trumpets out of straws. Those who went to the advanced series can see a direct application of the concepts covered!


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.