Madison Math Circle Abstracts

August 6 2016

Science Saturday

Title: Game Busters

The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.) Solutions for Chomp Solutions for Nim Solutions for Set.

September 12 2016

Jean-Luc Thiffeault

Title: Why do my earbuds keep getting entangled?

I'll discuss the mathematics of random entanglements. Why is it that it's so easy for wires to get entangled, but so hard for them to detangle?

September 19 2016

DJ Bruce

Title: Is Any Knot Not the Unknot?

You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.

September 26 2016

Megan Maguire

Title: Coloring Maps

Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.

October 3 2016

Zach Charles

Title: 1 + 1 = 10, or How does my smartphone do anything?

Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.

October 10 2016

Keith Rush

Title: Randomness, determinism and approximation: a historical question

If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.

October 17 2016

Philip Wood

Title: The game of Criss-Cross

Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.

October 24 2016

Ethan Beihl

Title: A Chocolate Bar for Every Real Number

By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?

October 31 2016

No Meeting This Week

Title: N/A

Enjoy Halloween.

November 7 2016

Polly Yu

Title: Are we there yet?

When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.

November 14 2016

Micky Soule Steinberg

Title: Circles and Triangles

We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!

November 21 2016

Benedek Valko

Title: Fun with hats

We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy.

February 6 2017

Cullen McDonald

Title: Building a 4-dimensional house

I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond.

February 13 2017

Dima Arinkin

Title: Solve it with colors

How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!) We will look at problems that can be solved by a clever coloring design.

February 20 2017

Reese Johnston

Title: Knights and Knaves

An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.

February 27 2017

Jessica Lin

Title: The Mathematics Behind Sound

We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."

March 6 2017

Becky Eastham

Title: How to Win a Brand New Car and Escape Execution with Probability

We'll learn about some famous paradoxes in probability. Come and have your brain teased by the Monty Hall Problem (will you win a goat or a car?) and the 100 Prisoners Problem (can you and your fellow prisoners come up with a clever strategy to save your lives?). We'll solve these problems and more!

March 13 2017

Jim Brunner

Title: You and your clones predict the future

We are going to talk about how to predict the future based on the present! Often, we know only things about the probability of the very near future, like which city we are going to be in next week. Luckily, there is a way to use that information to figure not just where we’ll be in two or three weeks, but also what the probability is that we are in some city in a very long time from now. The tool we need is called a Markov Chain. I’ll talk about how a Markov Chain can help us figure out the probability of different events in the future, and how we can clone ourselves in order to figure out how a Markov Chain behaves.

March 27 2017

John Wiltshire-Gordon

Title: What if seven is zero?

We take as axiomatic the usual laws of arithmetic, along with a new law: 7=0. Evidently, this new law challenges certain widespread intuitions about numbers. Will all of mathematics crumble?

High School Meetings

October 17 2016 (JMM)

Daniel Erman

Title: What does math research look like?

Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.

October 24 2016 (West)

DJ Bruce

Title: Shhh, This Message is Secret

gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.

October 31 2016 (East)

DJ Bruce

Title: Shhh, This Message Is Secret

gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.

December 5 2016 (JMM)

Philip Matchett Wood

Title: The game of Criss-Cross

Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.

December 5 2016 (East)

Uri Andrews

Title: How to split an apartment

So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.

February 13 2017 (East)

Eva Elduque

Title: Pick's Theorem

In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!

February 20 2017 (JMM)

Megan Maguire

Title: Coloring Maps

Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.

March 20 2017 (East)

DJ Bruce

Title: Doodling Daydreams

As a high schooler I occasionally got bored, would zone out, and would doodle on my paper. Often repeatedly tracing around something on my paper creating doodles like this: In this bored state my mind would often wander, and I would wonder about important things like "Will I have a date for prom?" or "What is the cafeteria serving for lunch?", but germane to this talk were my wonderings about, "What’s happening to the shape of this doodle?" It turns out that these idle daydreams and doodles provide a good taste for how mathematicians "do" math. We will start by doodling and asking questions, and then we'll see where these lead us mathematically.

April 3 2017 (JMM)

Polly Yu

Title: Are we there yet?

When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.