Madison Math Circle Abstracts: Difference between revisions

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[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]
[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]


== August 6 2016  ==
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle Main Math Circle Page]
 
 
 
== September 18 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Game Busters'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Welcome to the Madison Math Circle!'''
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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.)
Abstract:  At the Madison Math Circle, we aim to give a flavor for the creative type of thinking that goes into mathematical research. In this week's interactive activity, students will explore questions related to Mobius strips, developing their own conjectures.
<ul>
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li>
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li>
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li>
</ul>
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== September 12 2016 ==
== September 25 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Betsy Stovall'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Why do my earbuds keep getting entangled?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Math is a game!'''
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I'll discuss the mathematics of random entanglements.  Why is it that
When mathematicians are working to solve a theoretical problem, it often helps to imagine that we are playing a game:  What could our opponent do to make our job as difficult as possible, and what is our strategy to defeat them no matter what move they make?  In this session, we will try this out by playing several games and trying to come up with winning strategies. 
it's so easy for wires to get entangled, but so hard for them to
detangle?
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== September 19 2016 ==
== October 2 2017 ==
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|-
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Rachel Davis'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Is Any Knot Not the Unknot?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Thinking outside the box'''
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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.
Abstract: We will try some geometric puzzles related to area, volume, and dimension using techniques such as drawing diagrams, looking at special cases, using symmetry, and changing perspective.
 
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== September 26 2016 ==
== October 9 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Solly Parenti'''
|-
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| bgcolor="#BDBDBD"  align="center" | '''Title: Coloring Maps'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Hackenbush'''
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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.
Abstract: I come from an alien world where we spend all of our time playing a game called hackenbush.  I'd like to introduce y'all to this game so you don't embarass yourself if you come visit my planet.
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== October 3 2016 ==
== October 16 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Mihaela Ifrim'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Escape of the Clones!'''
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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.
Abstract: We wish to find an invariant (an invariant is a quantity that doesn't change no matter how the process plays out). By playing couple of games will help us find some! The main game we will play is Escape of the Clones! Promise you will like it!
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== October 10 2016 ==
== October 23 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ryan Julian'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Randomness, determinism and approximation: a historical question'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Recursion for Fun and Profit'''
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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.
Abstract: Beginning with the classic Towers of Hanoi puzzle, we'll explore several puzzles whose solutions can often be found by thinking recursively.  We'll also discover how recursion and related methods of simplifying problems can be used to create efficient algorithms to solve a variety of practical problems.
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== October 30 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Euler Characteristic'''
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Abstract: The most important invariant associated to a collection of featureless points is their number, which can be found using a process called "counting".  We explain a generalization of counting that works for other, more interesting shapes.  For example, we will count a circle and a sphere.  We recall typical counting arguments, and try to apply them to shapes.
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== October 17 2016 ==
== November 6 2017 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Wanlin Li'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: The game of Criss-Cross'''
| bgcolor="#BDBDBD"  align="center" | '''Title: How to Outsmart a State Test?'''
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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.
Abstract: A common problem in a state test is given a sequence of numbers like 4, 9, 16, 25, 36... ask what the next number to expect. I used to dislike these problems up until a teacher taught me a cool trick.  In this talk, I want to share this trick and discuss the math behind this.
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== November 13 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
|-Jean-Luc Thiffeault
| bgcolor="#BDBDBD"  align="center" | '''Title: Goldbug Variations'''
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| bgcolor="#BDBDBD"  | 
Abstract
I'll discuss the motion of little mathematical bugs: they hop around the positive integers, flipping direction arrows as they go.  How many such bugs drop off the line at -1, and how many escape to infinity?  Next, we tackle a similar problem in the plane, and discover beautiful geometrical patterns, known as Propp Circles.
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== October 24 2016 ==
== November 20 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: A Chocolate Bar for Every Real Number'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Boomerang Sequences'''
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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?
I don't know what will happen in this talk. No, I don't mean that in the sense that math teachers often use, where they say "I don't know, why don't you try it!" but really secretly they know what's going to happen. I mean that in the most literal sense. I will introduce sequences of numbers that (sometimes) bounce back, and you will explore them, and I might learn something, because I don't know what will happen. We'll have a blast, and maybe we'll discover something that no-one ever has before.
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== October 31 2016 ==
 
== February 5 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ben Wright'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: N/A'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Mobius Band Magic'''
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If you fold a loop of paper in half and cut it down the middle, how many loops of paper do you end up with? 2? Would you believe me if I said 1? How is this possible? A magician would never reveal the secret, but a mathematician will. We will learn to draw & construct loops & Mobius bands and explore their intrinsic & extrinsic properties.
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Enjoy Halloween.
== February 12 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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Abstract
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== November 7 2016 ==
== February 19 2018 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Brandon Boggess'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Are we there yet?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Towers of Hanoi'''
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An old legend tells of a mysterious temple located in Hanoi, Vietnam containing three pegs and 64 golden disks. Since the beginning of the world, priests have been moving these disks across the pegs according to rules handed down by an ancient prophecy. The legend states that when the final disk is placed, the world will come to an end. We will examine these rules and decide whether we should be worried by this legend.
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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.
== February 26 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Becky Eastham'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: No Pigeons Will Be Harmed During This Talk'''
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| bgcolor="#BDBDBD"  | 
The Pigeonhole Principle is the statement that if you have if you have (n) pigeonholes, and you want to stuff (n+1) pigeons into these holes, then one of the holes will have at least two pigeons in it (why mathematicians want to stuff pigeons into holes at all is a excellent question for another time).  While the Pigeonhole Principle might seem obvious, it can be used to prove things that are not at all obvious with relative ease!  We’ll explore how to use this simple fact to solve a variety of problems.
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== November 14 2016 ==
== March 5 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Juliette Bruce'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Circles and Triangles'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Doodling Dreams'''
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As a high schooler I occasionally got bored, would zone out, and doodle on my paper. Often repeatedly tracing around something on my paper creating doodles like this:
<gallery widths=300px heights=150px mode="packed">
File:doodle.jpg
</gallery>
In this bored state my mind would often wandered, 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.


We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!
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== November 21 2016 ==
== March 12 2018 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Solly Parenti'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Fun with hats'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Tangled up in Two'''
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|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
Every tangled cord you have ever encountered is secretly a number.  Once you learn how to count these cords, cleaning your room will be as easy as 1-2-3.
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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.  
== March 19 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Edwin Baeza'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Mathematics and Sound Design'''
|-
| bgcolor="#BDBDBD"  | 
We'll learn about sound waves by hearing and seeing them in action. We'll start by seeing a different way to think about sound and how to manipulate it. With this new knowledge we can explore some elements of modern sound design.
 
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== April 2 2018 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Carrie Chen'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Help! Important data lost due to ink stains!'''
|-
| bgcolor="#BDBDBD"  | 
John and Mary have a [https://www.math.wisc.edu/wiki/images/Ledger.pdf ledger card] for office supplies, however their cat broke the ink bottle and got the card stained. Let’s help them recover those numbers with Chinese Remainder theorem!
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== April 9 2018 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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| bgcolor="#BDBDBD"  | 
Abstract
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== February 6 2017 ==
 
= Off-Site Meetings =
== October 2 2017 (East High School) ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker TBD'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Building a 4-dimensional house'''
| bgcolor="#BDBDBD"  align="center" | '''Title: How to make it as a Hackenbush player in the planet Zubenelgenubi 4'''
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|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
Abstract: In the distant planet of Zubenelgenubi 4, we live our life without numbers. I know, how do we pass our time if we can't construct a smartphone without numbers? The answer is that we have invented an extremely violent sport about chopping down trees called Hackenbush, and playing this game is an essential social skill in Zubenelgenubi 4. I will teach you how to play the pen and paper version of Hackenbush, and hint at how learning this game leads to a kind of math that is highly illegal in 254,233 planetary systems.


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.
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== February 13 2017 ==
== November 2 2017 (WID) - 1 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Alisha Zacharia'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Solve it with colors'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Fractals, Fractions and Fibonnaci.'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
Abstract: Let’s go on a history tour! We’ll visit some math objects that intrigued generations of mathematicians and explore connections between them. We'll observe something that happens a lot in modern mathematics: discovering connections among seemingly unrelated things! Through this talk I hope to introduce you to how vital it is for mathematicians today to be able to effectively communicate with and teach each other even if they work in very different branches of mathematics.


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.
|}
</center>
</center>


 
== November 2 2017 (WID) - 2 ==
== February 20 2017 ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Zach Charles'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Knights and Knaves'''
| bgcolor="#BDBDBD"  align="center" | '''Title: 1+1 = 10 or "How does my computer do anything?"'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
Abstract: Computers perform all sorts of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Even weirder, 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.


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.
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|}
</center>
</center>


== February 27 2017 ==
== November 2 2017 (Whitewater) ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Juliette Bruce'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: The Mathematics Behind Sound'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Doodling Daydreams'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
Abstract: As a high schooler I occasionally got bored, would zone out, and doodle on my paper. Often repeatedly tracing around something on my paper creating doodles like this:
<gallery widths=300px heights=150px mode="packed">
File:doodle.jpg
</gallery>
In this bored state my mind would often wandered, 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.


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."
|}                                                                      
|}
</center>
</center>


= High School Meetings =
== November 3 2017 (KM Global) ==
== October 17 2016 (JMM) ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Betsy Stoval'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  What does math research look like?'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  Recent discoveries in mathematics'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.
Abstract: So much wonderful and useful mathematics was discovered centuries ago that it can seem as though we must know everything by now.  To the contrary, thousands of research mathematicians around the world are working to develop new mathematical theories every day.  I will talk about some exciting recent discoveries in math and some tantalizing unsolved problems.  To make matters more concrete, students will develop a solution to the Erdős Discrepancy Problem, which was only completely solved in 2015, in a simple case.


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|}                                                                         
</center>
</center>


== October 24 2016 (West) ==
== November 27 2017 (JMM High School) ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Juliette Bruce'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  Shhh, This Message is Secret'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  Is any knot not the unknot'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.  
Abstract:
You're walking home from school, and you pull your headphones out 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.
|}                                                                       
</center>


== December 11 2017 (East High School) ==
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: John Wiltshire-Gordon'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  What if seven is zero?'''
|-
| bgcolor="#BDBDBD"  | 
Abstract: 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?
|}                                                                         
|}                                                                         
</center>
</center>


== October 31 2016 (East)==
 
 
== February 19 2018 (East High School) ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Jordan Ellenberg'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  Shhh, This Message Is Secret'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  Is math destroying the right to vote?'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.
Abstract: The Supreme Court is deciding whether or not Wisconsin’s way of electing the State Assembly violates the Constitution by depriving Wisconsinites of their right to representation.  The key issues in this case are really about math, and how legislators armed with powerful algorithms can design electoral districts so that they choose the voters, rather than the voters choosing them. On the other hand, we can use math to find unfairness in maps and suggest better ones — I’ll talk a little bit about how.
|}                                                                         
|}                                                                         
</center>
</center>


== December 5 2016 (JMM) ==
== March 1 2018 (WID) - 1 ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Wanlin Li'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  The game of Criss-Cross'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  From Patterns to Functions?'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.
What is a pattern? What's the next number in the sequence 1,2,3,4,5? What about 1,4,9,16,25? Why that number? In this talk we'll talk about how to find the next number in many sequences, and where it comes from. In addition we'll consider the relations between functions an patterns.


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|}                                                                         
</center>
</center>


== December 5 2016 (East) ==
== March 1 2018 (WID) - 2 ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Daniel Erman'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: How to split an apartment'''
| bgcolor="#BDBDBD"  align="center" | '''Title: What does math research look like?'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.
I’ll try to illustrate the type of thinking that goes in math research by having us all dive into a famous historical problem.


|}                                                                         
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</center>
</center>


== February 13 2017 (East) ==
== March 5 2018 (JMM High School) ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Zach Charles'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  Pick's Theorem'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  1+1 = 10 or "How does my computer do anything?" '''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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!
Computers perform all sorts of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Even weirder, 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.
 
|}                                                                         
|}                                                                         
</center>
</center>


== February 20 2017 (JMM) ==
== March 19 2018 (East High School) ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Phil Wood'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  Coloring Maps'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  The Mathematics of Winning Strategies '''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.
Strategies are everywhere: how a business decides to deploy resources, how a school district decides on a curriculum plan, how a student decides which material to study for a test.  In this Math Circle, we will discuss how mathematical ideas can inform strategies, focusing on simple games where perfect analysis of strategies is possible.
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</center>
</center>


== April 3 2017 (JMM) ==
== April 30 2018 (JMM High School) ==
<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Juliette Bruce'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  Are we there yet?'''
| bgcolor="#BDBDBD"  align="center" | '''Title:  From Books to Mars'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.
I will discuss ways to cleverly send a message so that even if part of the message is lost, the entire message can be recovered.
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</center>
</center>

Latest revision as of 18:48, 26 April 2018

Logo.png

Main Math Circle Page


September 18 2017

Daniel Erman
Title: Welcome to the Madison Math Circle!

Abstract: At the Madison Math Circle, we aim to give a flavor for the creative type of thinking that goes into mathematical research. In this week's interactive activity, students will explore questions related to Mobius strips, developing their own conjectures.

September 25 2017

Betsy Stovall
Title: Math is a game!

When mathematicians are working to solve a theoretical problem, it often helps to imagine that we are playing a game: What could our opponent do to make our job as difficult as possible, and what is our strategy to defeat them no matter what move they make? In this session, we will try this out by playing several games and trying to come up with winning strategies.

October 2 2017

Rachel Davis
Title: Thinking outside the box

Abstract: We will try some geometric puzzles related to area, volume, and dimension using techniques such as drawing diagrams, looking at special cases, using symmetry, and changing perspective.

October 9 2017

Solly Parenti
Title: Hackenbush

Abstract: I come from an alien world where we spend all of our time playing a game called hackenbush. I'd like to introduce y'all to this game so you don't embarass yourself if you come visit my planet.

October 16 2017

Mihaela Ifrim
Title: Escape of the Clones!

Abstract: We wish to find an invariant (an invariant is a quantity that doesn't change no matter how the process plays out). By playing couple of games will help us find some! The main game we will play is Escape of the Clones! Promise you will like it!

October 23 2017

Ryan Julian
Title: Recursion for Fun and Profit

Abstract: Beginning with the classic Towers of Hanoi puzzle, we'll explore several puzzles whose solutions can often be found by thinking recursively. We'll also discover how recursion and related methods of simplifying problems can be used to create efficient algorithms to solve a variety of practical problems.

October 30 2017

John Wiltshire-Gordon
Title: Euler Characteristic

Abstract: The most important invariant associated to a collection of featureless points is their number, which can be found using a process called "counting". We explain a generalization of counting that works for other, more interesting shapes. For example, we will count a circle and a sphere. We recall typical counting arguments, and try to apply them to shapes.

November 6 2017

Wanlin Li
Title: How to Outsmart a State Test?

Abstract: A common problem in a state test is given a sequence of numbers like 4, 9, 16, 25, 36... ask what the next number to expect. I used to dislike these problems up until a teacher taught me a cool trick. In this talk, I want to share this trick and discuss the math behind this.

November 13 2017

Speaker
Title: Goldbug Variations

Abstract 

I'll discuss the motion of little mathematical bugs: they hop around the positive integers, flipping direction arrows as they go.  How many such bugs drop off the line at -1, and how many escape to infinity?  Next, we tackle a similar problem in the plane, and discover beautiful geometrical patterns, known as Propp Circles.

November 20 2017

Ethan Beihl
Title: Boomerang Sequences

I don't know what will happen in this talk. No, I don't mean that in the sense that math teachers often use, where they say "I don't know, why don't you try it!" but really secretly they know what's going to happen. I mean that in the most literal sense. I will introduce sequences of numbers that (sometimes) bounce back, and you will explore them, and I might learn something, because I don't know what will happen. We'll have a blast, and maybe we'll discover something that no-one ever has before.


February 5 2018

Ben Wright
Title: Mobius Band Magic

If you fold a loop of paper in half and cut it down the middle, how many loops of paper do you end up with? 2? Would you believe me if I said 1? How is this possible? A magician would never reveal the secret, but a mathematician will. We will learn to draw & construct loops & Mobius bands and explore their intrinsic & extrinsic properties.

February 12 2018

Speaker
Title: TBD

Abstract

February 19 2018

Brandon Boggess
Title: Towers of Hanoi

An old legend tells of a mysterious temple located in Hanoi, Vietnam containing three pegs and 64 golden disks. Since the beginning of the world, priests have been moving these disks across the pegs according to rules handed down by an ancient prophecy. The legend states that when the final disk is placed, the world will come to an end. We will examine these rules and decide whether we should be worried by this legend.

February 26 2018

Becky Eastham
Title: No Pigeons Will Be Harmed During This Talk

The Pigeonhole Principle is the statement that if you have if you have (n) pigeonholes, and you want to stuff (n+1) pigeons into these holes, then one of the holes will have at least two pigeons in it (why mathematicians want to stuff pigeons into holes at all is a excellent question for another time). While the Pigeonhole Principle might seem obvious, it can be used to prove things that are not at all obvious with relative ease! We’ll explore how to use this simple fact to solve a variety of problems.

March 5 2018

Juliette Bruce
Title: Doodling Dreams

As a high schooler I occasionally got bored, would zone out, and doodle on my paper. Often repeatedly tracing around something on my paper creating doodles like this:

  • Doodle.jpg

In this bored state my mind would often wandered, 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.

March 12 2018

Solly Parenti
Title: Tangled up in Two

Every tangled cord you have ever encountered is secretly a number. Once you learn how to count these cords, cleaning your room will be as easy as 1-2-3.

March 19 2018

Edwin Baeza
Title: Mathematics and Sound Design

We'll learn about sound waves by hearing and seeing them in action. We'll start by seeing a different way to think about sound and how to manipulate it. With this new knowledge we can explore some elements of modern sound design.

April 2 2018

Carrie Chen
Help! Important data lost due to ink stains!

John and Mary have a ledger card for office supplies, however their cat broke the ink bottle and got the card stained. Let’s help them recover those numbers with Chinese Remainder theorem!

April 9 2018

Speaker
Title: TBD

Abstract


Off-Site Meetings

October 2 2017 (East High School)

Speaker TBD
Title: How to make it as a Hackenbush player in the planet Zubenelgenubi 4

Abstract: In the distant planet of Zubenelgenubi 4, we live our life without numbers. I know, how do we pass our time if we can't construct a smartphone without numbers? The answer is that we have invented an extremely violent sport about chopping down trees called Hackenbush, and playing this game is an essential social skill in Zubenelgenubi 4. I will teach you how to play the pen and paper version of Hackenbush, and hint at how learning this game leads to a kind of math that is highly illegal in 254,233 planetary systems.

November 2 2017 (WID) - 1

Speaker: Alisha Zacharia
Title: Fractals, Fractions and Fibonnaci.

Abstract: Let’s go on a history tour! We’ll visit some math objects that intrigued generations of mathematicians and explore connections between them. We'll observe something that happens a lot in modern mathematics: discovering connections among seemingly unrelated things! Through this talk I hope to introduce you to how vital it is for mathematicians today to be able to effectively communicate with and teach each other even if they work in very different branches of mathematics.

November 2 2017 (WID) - 2

Speaker: Zach Charles
Title: 1+1 = 10 or "How does my computer do anything?"

Abstract: Computers perform all sorts of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Even weirder, 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.

November 2 2017 (Whitewater)

Speaker: Juliette Bruce
Title: Doodling Daydreams

Abstract: As a high schooler I occasionally got bored, would zone out, and doodle on my paper. Often repeatedly tracing around something on my paper creating doodles like this:

  • Doodle.jpg

In this bored state my mind would often wandered, 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.

November 3 2017 (KM Global)

Speaker: Betsy Stoval
Title: Recent discoveries in mathematics

Abstract: So much wonderful and useful mathematics was discovered centuries ago that it can seem as though we must know everything by now. To the contrary, thousands of research mathematicians around the world are working to develop new mathematical theories every day. I will talk about some exciting recent discoveries in math and some tantalizing unsolved problems. To make matters more concrete, students will develop a solution to the Erdős Discrepancy Problem, which was only completely solved in 2015, in a simple case.

November 27 2017 (JMM High School)

Speaker: Juliette Bruce
Title: Is any knot not the unknot

Abstract: You're walking home from school, and you pull your headphones out 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.


December 11 2017 (East High School)

Speaker: John Wiltshire-Gordon
Title: What if seven is zero?

Abstract: 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?


February 19 2018 (East High School)

Speaker: Jordan Ellenberg
Title: Is math destroying the right to vote?

Abstract: The Supreme Court is deciding whether or not Wisconsin’s way of electing the State Assembly violates the Constitution by depriving Wisconsinites of their right to representation. The key issues in this case are really about math, and how legislators armed with powerful algorithms can design electoral districts so that they choose the voters, rather than the voters choosing them. On the other hand, we can use math to find unfairness in maps and suggest better ones — I’ll talk a little bit about how.

March 1 2018 (WID) - 1

Speaker: Wanlin Li
Title: From Patterns to Functions?

What is a pattern? What's the next number in the sequence 1,2,3,4,5? What about 1,4,9,16,25? Why that number? In this talk we'll talk about how to find the next number in many sequences, and where it comes from. In addition we'll consider the relations between functions an patterns.

March 1 2018 (WID) - 2

Speaker: Daniel Erman
Title: What does math research look like?

I’ll try to illustrate the type of thinking that goes in math research by having us all dive into a famous historical problem.

March 5 2018 (JMM High School)

Speaker: Zach Charles
Title: 1+1 = 10 or "How does my computer do anything?"

Computers perform all sorts of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Even weirder, 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.

March 19 2018 (East High School)

Speaker: Phil Wood
Title: The Mathematics of Winning Strategies

Strategies are everywhere: how a business decides to deploy resources, how a school district decides on a curriculum plan, how a student decides which material to study for a test. In this Math Circle, we will discuss how mathematical ideas can inform strategies, focusing on simple games where perfect analysis of strategies is possible.

April 30 2018 (JMM High School)

Speaker: Juliette Bruce
Title: From Books to Mars

I will discuss ways to cleverly send a message so that even if part of the message is lost, the entire message can be recovered.

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