Madison Math Circle Abstracts: Difference between revisions

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[[Image:logo.png|right|440px|Click the image to return to the main Madison Math Circle page]]
[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]


== September 14 2015  ==
[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%" | '''David Sondak'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: How to SEE Sound'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Welcome to the Madison Math Circle!'''
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The idea is to give a simple overview of sound waves by introducing sines and cosines and some of their basic anatomy (amplitude and frequency).  We will then have a computational component where the students create their own sound waves by fiddling with parameters in the sines and cosines (again, amplitude, frequency and different superpositions of the sines and cosines). They will actually be able to see plots of their waves AND listen to their waves.  Finally, if time permits, the students will use their own sound waves to make Oobleck dance.  This will bring the exercise full circle in that they will be able to see their very own sound waves in action.
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.
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== September 21 2015 ==
== September 25 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Prof. Uri Andrews'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Betsy Stovall'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Guarding Mona Lias'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Math is a game!'''
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You have gotten a tip that a famous art thief is going to steal something from the Louvre. It is your task to organize a security team that can watch all the works of art. The problem is that the Louvre is really big and has a strange layout. Where do you put your guards? And how many do you need?
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.
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== September 28 2015 ==
== October 2 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Rachel Davis'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Pick's Theorem'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Thinking outside the box'''
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In this talk, we will a very easy formula that allows us to quickly compute the areas of polygons whose vertices are points of a grid, and we will prove that this formula works. (Solutions to the worksheet distributed during the circle can be found [[File:Pick.pdf]].)
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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== October 5 2015 ==
== October 9 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Solly Parenti'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: The Math of Sudoku'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Hackenbush'''
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Have you ever sat next to someone in the airport or airplane who plays sudoku? Have you ever tried to play yourself? When you play, do you have some strategies that help you to complete the puzzle? It turns out that there is some deep mathematics behind this simple game. Come to math circle this week to learn about it, and maybe you can help the person next to you solve his/her sudoku!
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 16 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Mihaela Ifrim'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Escape of the Clones!'''
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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 12 2015 ==
== October 23 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ryan Julian'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ryan Julian'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: The Geometry of Hockeysticks and Eight Dimensional Oranges'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Recursion for Fun and Profit'''
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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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== November 6 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Wanlin Li'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: How to Outsmart a State Test?'''
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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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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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== November 20 2017 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Boomerang Sequences'''
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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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== February 5 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ben Wright'''
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| 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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== 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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== February 19 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Brandon Boggess'''
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| 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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== February 26 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Becky Eastham'''
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| 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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== March 5 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Juliette Bruce'''
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| 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
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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.
 
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== March 12 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Solly Parenti'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Tangled up in Two'''
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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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== March 19 2018 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Edwin Baeza'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: Mathematics and Sound Design'''
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Like most people, I've often considered opening an eight dimensional grocery store. Of course, the main difficulty with this plan is that I'd need some way of neatly stacking all of the eight dimensional fruit that I'd be selling. In this talk, we'll explore a variety of elementary counting problems, discover that nearly all elementary counting problems are really the same problem, and we'll apply these new insights to determine how to stack 8 dimensional fruits into neat 8 dimensional pyramids.
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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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Carrie Chen'''
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| bgcolor="#BDBDBD"  align="center" | '''Help! Important data lost due to ink stains!'''
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| 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'''
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| bgcolor="#BDBDBD"  align="center" | '''Title: TBD'''
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| bgcolor="#BDBDBD"  | 
Abstract
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= Off-Site Meetings =
== October 2 2017 (East High School) ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker TBD'''
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| bgcolor="#BDBDBD"  align="center" | '''Title:  How to make it as a Hackenbush player in the planet Zubenelgenubi 4'''
|-
| 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.
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== October 26 2015 ==
== November 2 2017 (WID) - 1 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Alisha Zacharia'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Aperiodic tilings: Beyond your parents' bathroom floor'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Fractals, Fractions and Fibonnaci.'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
A tiling is a way of covering the plane with geometric shapes such that there are no overlaps or gaps. If you have any tile in your home (maybe in your kitchen or bathroom) that is most likely an example of a tiling. Come learn about the cool math behind tilings and about the coolest tiling of all, the Penrose tiling.
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.


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== November 2 2015 ==
== November 2 2017 (WID) - 2 ==
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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%" | '''Marko Budisic'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Zach Charles'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Mathematics of GPS Satellites'''
| bgcolor="#BDBDBD"  align="center" | '''Title: 1+1 = 10 or "How does my computer do anything?"'''
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|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
GPS is a system of satellites circling the Earth at a height 12,500 miles. That means you could easily fit both Mars and Venus in the distance between your phone and each car-sized satellite hovering in space. Once considered science fiction, GPS is now a part of our everyday life: we can use it through our phones, through our car navigation, and even some watches. Simple math equations lie at the heart of this system, and we will write them down, understand what they mean, and figure out how to solve them.
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.
 
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== November 9 2015 ==
== November 2 2017 (Whitewater) ==
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{| 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"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Tess Anderson'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Juliette Bruce'''
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|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Gold Coins and Goast'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Doodling Daydreams'''
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| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
What do pulling gold coins out of a a hat have to do with the famous Monty Hall "Goat Problem" in which you are a game show contestant trying to pick out the one prize hidden behind one of three doors? Come and find out while savoring some chocolate gold coins. We will also discuss a jailer problem in which an infinite number of jailers try to free an infinite number of prisoners.  If time permits, other fun problems will be discussed.
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.
 
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== November 16 2015 ==
== November 3 2017 (KM Global) ==
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{| 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"
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|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Betsy Stoval'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: To Infinity and Beyond?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Recent discoveries in mathematics'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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.


1, 2, 3,..., infinity? What is infinity? Is infinity plus one bigger than infinity? Beginning by figuring out what we mean when we say to collections of objects have the same number of things we will slowly work our way deep into the world of infinity. This world is often weird and counterintuitive, and we shall explore it!
|}                                                                         
|}                                                                         
</center>
</center>


== November 23 2015 ==
== 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%" | '''Prof. Tullia Dymarz'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Juliette Bruce'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: To Infinity and Beyond?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Is any knot not the unknot'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
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>


TBA
 
== 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>


== February 1 2016 ==
 
 
== 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%" | '''Will Mitchell'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Jordan Ellenberg'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Are these networks the same?'''
| bgcolor="#BDBDBD"  align="center" | '''Title: Is math destroying the right to vote?'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
The question of deciding whether two things are the same comes up in many different places in math.  In this session we'll consider the problem of deciding if two networks or "graphs" are the same.  This leads to some entertaining and challenging puzzles.  We will also learn a bit about how people try to solve similar problems using computers.  This problem has applications in the design of electronic circuits and in searching for organic chemical compounds within large databases.
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>
 
== High School Visits ==
== 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%" | '''Prof. Daniel Erman'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Wanlin Li'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: How to Catch a (Data) Thief'''
| bgcolor="#BDBDBD"  align="center" | '''Title: From Patterns to Functions?'''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
I will discuss some surprising statistical facts that have been used to catch companies that lie about data.
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.


|}                                                                         
|}                                                                         
</center>


== March 1 2018 (WID) - 2 ==
<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: Daniel Erman'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: What does math research look like?'''
|-
| bgcolor="#BDBDBD"  | 
I’ll try to illustrate the type of thinking that goes in math research by having us all dive into a famous historical problem.


|}                                                                       
</center>
== March 5 2018 (JMM High School) ==
<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%" | '''Carolyn Abbott'''
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Speaker: Zach Charles'''
|-
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Donuts and coffee cups: the topology of surfaces'''
| bgcolor="#BDBDBD"  align="center" | '''Title: 1+1 = 10 or "How does my computer do anything?" '''
|-
|-
| bgcolor="#BDBDBD"  |   
| bgcolor="#BDBDBD"  |   
A classic problem in topology is to decide whether one surfaces can be deformed into another, without creating any holes or connecting any new points (stretching and bending is allowed!). If you can do so, such surfaces are considered 'the same.' We will formalize this notion and classify all closed surfaces, along the way answering such questions as whether a coffee cup is the same as a donut.
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>


|}                            
== March 19 2018 (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: Phil Wood'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  The Mathematics of Winning Strategies '''
|-
| bgcolor="#BDBDBD"  | 
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.
|}                                                                       
</center>
 
== April 30 2018 (JMM 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: Juliette Bruce'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title:  From Books to Mars'''
|-
| bgcolor="#BDBDBD"  | 
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.
|}                                                                      
</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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