|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.
|1/28/2018| [Show less]
This week we will be concluding our discussion of cryptographic schemes by talking about one of the most exciting developments in cryptography over the last century, public key cryptography. One scheme of this kind if the celebrated RSA algorithm. Using RSA, two parties who have never met can exchange messages in public with total knowledge that their messages are secret.
|2/4/2018| [Show less]
This week in the LAMC we will be rolling dice and taking chances in our survey of probability. We will cover some of the basic rules for those who have no background, and will build up to understanding Bayes rule. this rule is extremely important rule in probability and statistics, and moreover is a rule which can change the way that you think about live, probably.
|2/11/2018| [Show less]
This week we will have a special guest, who will present on information theory. Information theory is the mathematics that gives meaning to randomess, and is responsible for letting people talk over the phone, use YouTube, and many more.
|2/25/2018| [Show less]
This week we will finish up our work in information theory, With our expertise of entropy in tow, we will use it to analyize some more problems in probability. Finally we will learn about optimal codes.
|3/4/2018| [Show less]
This week we will talk about the core of programming and computers, the idea of an algorithm. Algorithms are not only extremely common in real life (they are used every time you use anything electronic) but they are also quite interesting mathematically on their own. Today we will start talking about algorithms, agree on a definitions, and come up with lots and lots of examples of algorithms. Note, zero programming experience is required. We will not be programming in a particular language, but we will be talking about programs.
|3/11/2018| [Show less]
Today we are going to continue our discussion of algorithms, but instead of trying to try and write algorithms to do specific things, we are going to try and talk about algorithms themselves. Despite having obvious applications to computer science, algorithms were originally studied within mathematical Logic. Today we will talk about trying to write programs to analyze programs, and come up against one of the most famous hard problems, the so called Halting problem.
|3/18/2018| [Show less]
As we have done at the end of every quarter, this Sunday we'll be having a competition style class. You will be broken up into teams, and you will together compete to see who can answer the most questions with the fewest mistakes.
|4/8/2018| [Show less]
Nim, an example of a take-away game, is very old indeed. Since time immemorial those who know how to win at Nim have confounded friends, baffled enemies, and won numerous bar bets. Today we will letting you in on the secret, so that you too might be able to exercise that same power, if not entertain your friends for a little while. Although we will motivate the discussion with Nim, we will continue to talk about other mathematical games, and find and prove some surprising results.
|4/15/2018| [Show less]
This weekend we will be returning to the roots of mathematics, and study some problems that were solved a very, very long time ago. We are going to be studying plane, and in particular we will by studying what are called cyclic quadrilaterals, quadrilaterals which can be circumscribed by a circle.
|4/22/2018| [Show less]
This week we'll be studying a bit of game theory, the branch of mathematics that explains why we interact with each other the way that we do, and what we can do about it.
There is something that I would like you to do before class this weekend. Please find a half of an hour or so to play the game at the following URL. It frames the discussion that we'll be having, and is a very well developed, interactive tool. Plus, it's kind of fun!
You should be able to play it in browser on any desktop/laptop.