For meetings prior to Fall 2017, visit the Circle Archive.
|Advanced||Beginners||Breaking Numbers into Parts||Early Elementary||High School I||High School II||Junior Circle|
|10/8/2017| [Show less]
Today we will learn about the (surprisingly difficult) task of converting the preferences of many individuals into a group preference. We will look at some methods for arriving at a group preference, and discuss some of the underpinning mathematics.
|10/15/2017| [Show less]
Today we will be continuing out study of voting systems. We will also take a look at (and prove) Arrow's impossiblity theorem, which gives us important insights into the nature of voting systems.
|10/22/2017| [Show less]
Over the course of your mathematical career I'm sure that various teachers, friends, or tutors have told you that infinity is not a number. Why is that? And if it isn't, does that mean that mathematics has nothing to say about the infinite? In this class, we will answer these two questions, as well as addressing many more.
|10/29/2017| [Show less]
This week we will continue our tour of the infinite. Using the tools that we developed last week we will find some new bijections, uncover some more surprising results and prove Cantor's theorem, one of the most important, surprising and pradoxical results in modern mathematics.
|11/5/2017| [Show less]
In this week's meeting we will use the tools that we developed over the past two weeks to look at paradoxes. Since time immemorial mathematicians and philosophers have pondered questions about the infinite and mused over their peculiar implications. Now that we have the tools necessary to have these conversations in earnest, we can discuss, appreciate and resolve some of these paradoxes.
|11/12/2017| [Show less]
This week we will be concluding our study of the infinite. In this week, our goal is to get as close as we can to proving the Banach-Tarski paradox. This paradox shows that it is possible, using some very clever cuts, to cut a solid 3d sphere into three distinct parts, and rearrange those parts so that at the end one is left with two spheres identical in every way to the first.
|11/19/2017| [Show less]
With our study of the infinite complete, we are going to talk about generating functions. Sequences are one of the common themes across mathematics, and generating functions give us a different powerful method for answering questions about sequences by looking at them in a different light. We will introduce the idea of generating functions, and use them to solve a variety of problems.
|12/3/2017| [Show less]
This week we'll be finding some surprising connections between three disparate things, an ancient puzzle, counting on other bases, and the famous Sierpinski triangle.
|1/14/2018| [Show less]
Today we are going to take a look at one of the most enduring 'real world' problems which is greatly aided by mathematical study, cryptography. The practice of concealing, decoding, and hiding messages has been around since the dawn of time, but the desire for efficient and unbreakable codes has accelerated in recent years.
|1/21/2018| [Show less]
This week we are going to going to continue our stuck of cryptography and cryptographic schemes. We are going to talk more about symmetric schemes, and in particular we are going to talk about a process that lets two people, who have never spoken before, agree on a common secret shared key.