Difference between revisions of "Madison Math Circle"

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(New page: =What is it?= The UW-Madison math department organizes a series of talks aimed at high school students throughout the semester. Our goal is to present fun talks that give students a taste ...)
 
 
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=What is it?=
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[[Image:logo.png|right|600px]]
The UW-Madison math department organizes a series of talks aimed at high school students throughout the semester. Our goal is to present fun talks that give students a taste of interesting ideas in math and science. In the past we've had talks about plasma and weather in outer space, the way images are shaded in video games, and how credit card numbers are securely transmitted over the internet.  
 
  
'''Important:''' After each talk we'll have '''pizza''' provided by the department, and students will have an opportunity to mingle and chat with the speaker to ask questions about college, careers in science, etc.
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For the site in Spanish, visit [[Math Circle de Madison]]
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=COVID-19 Update=
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We will moving back to in-person talks for the remainder of the semester.  
  
=Alright, I want to come!=
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As is the university's policy, all participants must wear masks. We will make every effort to maintain social distancing where possible.
Great! If you're a high school teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in Van Vleck Hall on the UW campus). '''We'd also appreciate if you [mailto:math-night@math.wisc.edu email] us the dates that your group will be attending''', so we can purchase the appropriate amount of pizza.
 
  
If you're a high school student, speak with your high school teacher about organizing a car pool to the math night (and tell us how many people are coming!)
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=What is a Math Circle?=
 +
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department.  Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption.  In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion.  The talks are independent of one another, so new students are welcome at any point.
  
=Questions?=
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The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.
If you have any questions, suggestions for topics, or so on, just email the Math Night organizers: [mailto:math-night@math.wisc.edu math-night@math.wisc.edu].
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[[Image: MathCircle_2.jpg|550px]] [[Image: MathCircle_4.jpg|550px]]
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After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.
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'''The Madison Math Circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!
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=All right, I want to come!=
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Our in person talks will be at, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year, and the link for our virtual talks will be available through our mailing list and on the schedule below. New students are welcome at any point!  There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:
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[https://docs.google.com/forms/d/e/1FAIpQLSe_cKMfdjMQlmJc9uZg5bZ-sjKZ2q5SV9wLb1gSddrvB1Tk1A/viewform '''Math Circle Registration Form''']
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All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle.
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If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).
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==Spring Enhancement Workshop==
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Our aim is to offer an opportunity for students to not only explore various fields of math through our weekly talks, but also give them the opportunity to hone the various skills involved in higher mathematics. To this end, starting this spring, we are beginning a first in a semesterly series of workshops aimed at developing these skills for middle school students. The workshop, titled the Math Circle Spring Enhancement Workshop (SEP) will be held in May, on every Monday from 6:00pm - 7:00pm from May 2nd to May 30th at the UW-Madison campus. Please see our schedule below for details. 
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The topics for this workshop will cover an introduction to constructing mathematical arguments and proofs, understanding how to generalise simple mathematical ideas, and learn how to discover math for one's self. We will build these skills through collaborative problem solving sessions while learning about graph theory, game theory, and other cool areas of mathematics.
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The 2022 SEP is being organised by the Math Circle team in collaboration with Dr. Peter Juhasz, an instructor at the Budapest Semester in Math Education, a world renowned program in training talented students in math education from across the globe. Peter will be the main speaker and facilitator for the spring and has extensive experience teaching mathematics to secondary students and is the chief organizer of various mathematics camps in Hungary. He also directs the Joy of Thinking Foundation, whose aim is to promote mathematics education of gifted students in Hungary.
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We want to invite any middle school students curious about math to join! If you are interested, please register using the form below. As always, this workshop is free and only requires your curiosity and participation!
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  [https://forms.gle/ZwcTcMrAAc6UfjnP9 '''Math Circle SEP Registration Form''']
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All your information is kept private, and is only used by the Madison Math Circle organiser to help run the Circle.
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We hope to see you there!
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<center>
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{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
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|-
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! colspan="4" style="background: #e8b2b2;" align="center" | SEP Schedule
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|-
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! Date !! Location and Room
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|-
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| May 2nd || 3255 Helen C White Library
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|-
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| May 9th || 3255 Helen C White Library
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|-
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| May 16th || B107 Van Vleck Hall
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|-
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| May 23rd || B115 Van Vleck Hall
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|-
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| May 30th || B115 Van Vleck Hall
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|}
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</center>
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==Meetings for Spring 2022==
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<center>
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{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
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|-
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! colspan="4" style="background: #e8b2b2;" align="center" | Spring 2022
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|-
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! Date !! Speaker !! Topic
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|-
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| February 7th || Aleksandra Cecylia Sobieska || <strong>Mathematical Auction</strong>
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We will play a game called “Mathematical Auction,” where teams have the opportunity to solve and steal problems for points by presenting solutions that build on one another.
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|-
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| February 14th || Jake Fiedler || <strong>Fractals in Math and Nature</strong>
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If you've ever had to clean up branches after a storm, you may notice that the branches look surprisingly like the whole tree they fell from, just at a smaller scale. Similarly, lightning bolts during that storm probably had numerous "arms", each appearing similar to the entire bolt. In this talk, we'll investigate this behavior more closely through objects called fractals. We'll see how fractals are made, where they appear in the real world, and then you'll get a chance to build your own.
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|-
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| February 21st || Mikhail Ivanov || <strong>Elevator with just 2 buttons.</strong>
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There are two buttons inside an elevator in a building with twenty floors. The elevator goes 7 floors up when the first button is pressed, and 9 floors down when the second one is pressed (a button will not function if there are not enough floors to go up or down).
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Can we use such elevator? We'll play with this elevator found math behind it.
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|-
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| February 28th || Michael Jesurum || <strong>Bubbling Cauldrons</strong>
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Place our numbers into the cauldrons in ascending order – you can choose which cauldron each one goes in. However, if two numbers in one cauldron add up to a third number in that same cauldron, they bubble up and cause an explosion! This means that all the numbers leave the cauldrons, and you must start all over again. Our goal is to find the largest number we can place in our cauldrons without them exploding… do you think you’re up for this daunting task?
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|-
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| March 7th || Erika Pirnes || <strong>Reconstructing Graphs</strong>
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A graph is a "picture" with dots (called vertices) and lines (called edges). From a graph, we can extract information called the deck. In this talk, we will explore the connection between a graph and its deck, and how we can move from one to the other. We will do a lot of examples! There is a famous conjecture (unproven result) that stays that a graph can always be reconstructed (recovered) from its deck. This is called the reconstruction conjecture. (There are some small restrictions on what the graph can be)
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|-
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| March 14th || SPRING BREAK || <strong>NA</strong>
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NA
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|-
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| March 21st || Ian Seong || <strong>Center of a triangle? But which center?</strong>
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It is easy to locate the center of a circle, or regular polygons. How do we define the center for an arbitrary triangle?
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In fact, for each triangle, there are many points that can be entitled the "center". We will investigate a few of them (classic examples are circumcenter and incenter) and learn how they are constructed.
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|-
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| March 28th || Caitlin Davis || <strong>Math and voting: Can math help us make decisions more fairly?</strong>
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We are often faced with decisions we must make as a group.  For example, a city might need to decide on a new mayor, or you and your friends might need to decide on a movie to watch or a type of pizza to share.  We often use voting to try to make a fair choice. The voting method which you’re probably used to is called “plurality,” but it turns out there are many other possible voting methods. Could one of them be more fair than plurality?  We’ll talk about how math can be used to study questions like this.
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|-
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| April 4th || BREAK || <strong>NA</strong>
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|-
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| April 11th || Aleksander Skenderi || <strong>Happy Numbers</strong>
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In many areas of mathematics, we look for patterns to describe or model a particular problem. However, sometimes these patterns occur in some late stage of some process, and sometimes not at all! For instance, if a particle of gas is moving around in a container, it may be that, after some time, the gas particle follows an easily described trajectory. It may also be, depending on the initial trajectory, that the gas particle moves totally randomly. In this talk, we'll describe a class of numbers called "happy numbers," and explore some of their properties and patterns.
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|-
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| April 18th || John Cobb || <strong>Chip-Firing Games on Graphs</strong>
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We will play a game called the dollar game, where we will try to clear out debt among a group of people in a funny way. Then, we’ll investigate ways to see when this is possible and how to do it, leading to some unexpected conclusions and a look into a very active area of math called tropical geometry.
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|-
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| April 25th || Chengxi Wu || <strong>Non integer bases and Paths on colored graphs</strong>
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We can count in base 10 (decimals) or base 2 (binary), but how about counting in base 5/3, or the golden ratio? We will investigate that via the question of finding possible paths on a graph with colored vertices, and also look at some of the interesting self similar patterns we can get from it!
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|}
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</center>
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==Meetings for Fall 2021==
  
==Talks this semester==
 
More details about each talk to follow. All talks are at 7pm in Van Vleck Hall B231.
 
  
 
<center>
 
<center>
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{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
 
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
 
|-
 
|-
! Date !! Speaker !! Talk (click for more info)
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! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2021
 
|-
 
|-
| February 17th, 2011 '''still being held''' || Andrew Bridy || [[#Cryptography|Cryptography]]
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! Date !! Speaker !! Topic
 
|-
 
|-
| March 10th, 2011 || Ed Dewey || [[#The 0.5th Dimension|The 0.5th Dimension]]
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| September 20th || Daniel Erman || <strong>Number Games</strong>
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We’ll play some math-based games and then try to understand some of the patterns we observe.
 
|-
 
|-
| March 24th, 2011 || Lalit Jain || [[#Cutting & Pasting|Cutting & Pasting]]
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| September 27th || Evan Sorensen || <strong> The fastest way to travel between two points </strong>
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Given two points, we know the shortest distance between the points is a straight line. But is that always true? We will talk about how to build the best track for a toy car to travel between two points.  We’ll start by trying a few different options together and having a race. We’ll then talk about how two brothers thought about how to solve this problem using interesting examples from physics.
 
|-
 
|-
| April 7th, 2011 || Balazs Strenner || [[#Tilings|Tilings]]
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| October 4th || Yandi Wu || <strong> Do you wanna build a donut?  </strong>
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Topology is a field of math that deals with studying spaces. This math circle talk is an introduction to a concept in topology called “cut-and-paste” topology, which is named that way because we will build spaces out of cutting and gluing pieces of paper.
 
|-
 
|-
| April 28th, 2011 || Prof. Nigel Boston || [[#Face Recognition|Face Recognition]]
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| October 11th || Ivan Aidun || <strong> Words, Words, Words </strong>
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We'll play a game where you have to guess a secret word that I choose.  We'll figure out how to use logic to improve our guesses.  Then, we'll explore some questions like: is there a best way to guess? or, what happens when I change the rules slightly?
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|-
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| October 18th || Allison Byars || <strong> Sheep and Wolves </strong>
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In this math circle talk, we'll look at placing sheep and wolves on a grid so that none of the sheep get eaten.  We'll find different arrangements and try to figure out the maximum number which can be placed on a board of given size and generalize it for an arbitrary board.  We will also discuss how this relates to a field of mathematics called combinatorics.
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|-
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| October 25th || Jacob C Denson || <strong>Proofs in Three Bits or Less</strong>
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How many questions does it take to beat someone at Guess Who? How long should it take for you to figure out how to get to this math talk from your house? How many questions do you have to ask your classmate before you know they're telling the truth to you? Let's eat some pizza, and talk about how mathematicians might reason about these problems.
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|-
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| November 1st || Qin Li || <strong> How do we describe the world? </strong>
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The physical world consists of everything from small systems of a few atoms to large systems of billions of billions of molecules. Mathematicians use different languages and equations to describe large and small systems. Question is: How does mother nature use different languages for different systems and scales? Let us see what these languages look like, talk about their connections and differences, and see how they are reflected in our day-to-day life.
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|-
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| November 8th || John Yin ||  <strong> River Crossings </strong>
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Here's a classic puzzle: A farmer needs to move a wolf, a sheep, and a box of cabbages across a river. He has a boat that can fit only one object other than himself. However, when left alone, the wolf will eat the sheep, and the sheep will eat the cabbages. How can the farmer move the wolf, the sheep, and the box of cabbages across the river without anything being eaten? I will discuss this problem by connecting it to graph theory, then give a generalization.
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|-
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| November 15th || Erik Bates || <strong> How big is a cartographer’s crayon box? </strong>
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Have a look at a world map.  If you are looking at one with borders and colors, notice that no border has the same color on both sides.  That is, no neighboring countries are colored the same. So how many different colors are needed to make this possible?  Does the answer change for a map of the U.S., when we try to color its fifty states?  What about a map of Wisconsin with its 72 counties?  We will explore these questions---and uncover some very deep mathematics---by doing the simplest and most soothing activity: coloring.
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|-
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| November 22nd || Robert Walker || <strong>Lagrange's Four Square Sum Theorem</strong>
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How many perfect squares are needed to represent each nonnegative integer n as a sum of perfect squares? This talk will answer that precise question -- students will get to the bottom of this.
 
|}
 
|}
  
 
</center>
 
</center>
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===Cryptography===
 
<span style="background:#00FF00">February 17th, 2011</span> '''Update 2/16/11: still being held'''
 
  
'''The science of code making and code breaking'''
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==Directions and parking==
  
Sending information securely over the internet is an enormous practical problem.  How can you be sure that no one is reading your email, or worse, stealing your credit card number when you buy something online?  Cryptography is the art of encoding a message so it looks like a string of random letters or numbers, and decoding it on the other side to get the original message back. In this talk I'll show you some simple ways you can use math to encode and decode information, and how the same techniques can be used to attack codes and try to break them.  The branch of math used is called number theory, and the problems that come up are very simple to state and very hard to solve, leading right to current research that mathematicians are working on today.
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Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.
  
====Speaker: [http://www.math.wisc.edu/~bridy Andrew Bridy]====
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<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">
Andrew is a third year math Ph. D. student studying algebra and computer science. Before coming to graduate school, he taught high school math for a year and was deployed with the Peace Corps to Honduras. Andrew is an avid video game fan - you should ask him to tell you about his favorite PC video games of the late 1990's.
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[[File: Helencwhitemap.png|400px]]</div>
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===The 0.5th Dimension===
 
<span style="background:#00FF00">March 10th, 2011</span>
 
  
'''A Harrowing Journey to the 0.5th Dimension'''
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'''Parking.''' Parking on campus is rather limited.  Here is as list of some options:
  
We frequently think about two dimensional spaces, like a map of a country, or three dimensional spaces, like the Holodeck from Star Trek. But what exactly is "dimension", anyway? This turns out to be a surprisingly deep question, without a unique answerBut asking it is still useful, and leads us to the strange and beautiful notion of Hassdorf dimension, one of the fndamentals of fractal geometry, which gives a meaning to non-integer dimensions. We will discuss Haussdorf dimension and its motivation, and see an application to psychology.  
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*There is a parking garage in the basement of Helen C. White, with an hourly rate.  Enter from Park Street.
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*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].
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*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34].   
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*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].
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*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .
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*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].
  
====Speaker: [http://www.math.wisc.edu/~dewey Ed Dewey]====
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==Email list==
Ed is a first year Ph. D. student in mathematics. He used to be in a ska band. 
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The best way to keep up to date with the what is going is by signing up for our email list. Please add your email in the form:
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[https://docs.google.com/forms/d/e/1FAIpQLSe_cKMfdjMQlmJc9uZg5bZ-sjKZ2q5SV9wLb1gSddrvB1Tk1A/viewform '''Join Email List''']
  
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==Contact the organizers==
===Cutting & Pasting===
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The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@g-groups.wisc.edu here]. We are always interested in feedback!
<span style="background:#00FF00">March 24th, 2011</span>
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<center>
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<gallery widths=500px heights=300px mode="packed">
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<!--File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]-->
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<!--File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]-->
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File:Uri.jpg|[https://www.math.wisc.edu/~andrews/ Prof. Uri Andrews]
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File: Omer.jpg|[https://www.math.wisc.edu/~omer/ Dr. Omer Mermelstein]
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</gallery>
  
  
The Bolyai-Gerwein theorem says that any two polygons of the same area have an "equi-dissection". In other words, there is a way to cut up one of the polygons into pieces (using straight line cuts) that can be rearranged to form the other. This deep theorem is surprisingly recent compared to much of classical geometry and has many interesting generalizations. During this weeks talk we will prove the theorem as a group using little more then argument by "scissors and glue."
 
  
Here are some fun applets to see this in action:
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<gallery widths=500px heights=250px mode="packed">
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File: Karan.jpeg|[https://karansrivastava.com/ Karan Srivastava]
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File: Colin.jpg|[https://sites.google.com/view/colincrowley/home Colin Crowley]
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File: Allison.jpg|[https://sites.google.com/wisc.edu/allisonbyars/ Allison Byars]
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</gallery>
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</center>
  
http://demonstrations.wolfram.com/AnExampleOfTheBolyaiGerwienTheorem/
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and [https://math.wisc.edu/graduate-students/ Caitlin Davis] and  [https://math.wisc.edu/graduate-students/ Ivan Aidun].
  
http://www.cut-the-knot.org/Curriculum/Geometry/TwoRectangles.shtml
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==Donations==
 +
Please consider donating to the Madison Math Circle. Our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from private donors. The easiest way to donate is to go to the link:
  
 +
[http://www.math.wisc.edu/donate Online Donation Link]
  
An example of dissecting a square into pieces that form a triangle of the same area.
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There are instructions on that page for donating to the Math Department.  <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b>  The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.
[[Image:TriangleSquare.jpg|200px]]
 
  
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Alternately, you can bring a check to one of the Math Circle Meetings.  If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. 
  
====Speaker: [http://www.math.wisc.edu/~jain Lalit Jain]====
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Or you can make donations in cash, and we'll give you a receipt.
Lalit is a first year Ph. D. student in mathematics interested in number theory and computer science. Before coming to graduate school, Lalit was a high school math teacher with [http://en.wikipedia.org/wiki/Teach_for_america Teach For America] in San Francisco. You should ask Lalit about who shot Frances in the video game Left 4 Dead.
 
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===Tilings===
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==Help us grow!==
<span style="background:#00FF00">April 7th, 2011</span>
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If you like Math Circle, please help us continue to grow!  Students, parents, and teachers can help by:
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* Like our [https://facebook.com/madisonmathcircle '''Facebook Page'''] and share our events with others!
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* Posting our [https://www.math.wisc.edu/wiki/images/Math_Circle_Flyer_2021.pdf '''flyer'''] at schools or anywhere that might have interested students.
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* Discussing the Math Circle with students, parents, teachers, administrators, and others.
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* Making an announcement about Math Circle at PTO meetings.
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* Donating to Math Circle.
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Contact the organizers if you have questions or your own ideas about how to help out.
  
'''Tilings'''
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=Useful Resources=
 +
<!--==Annual Reports==
 +
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf  2013-2014 Annual Report]-->
  
Tilings in the mathematical sense mean non-overlapping, gap-free coverings of the plane by certain shapes. For instance, one can take (infinitely many) squares and place them on the infinite plane as they are on a chessboard, nicely fitting next to each other. This is maybe the simplest example. But if one takes regular pentagons, it is impossible to form a tiling using only them.
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== Archived Abstracts ==
  
The first class of interesting tilings we will discuss are the Penrose tilings. These involve two different shapes, the "kite" and the "dart". Not only it is fun to play with them and to try to make different arrangements, but these tilings have really interesting mathematical properties. Just to mention one of these: the ratio of the number of kites and darts - which I'll make precise - in all the possible arrangements is always the same, and it is the golden ratio!
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2020-2021 2020 - 2021 Abstracts]
  
Tilings have an artistic nature as well. The Dutch graphic artist M. C. Escher is famous for his math-connected drawings, and in fact many of these are tilings with funny shapes, birds for example. Another series of masterpieces by him are the woodcuts Circle Limit I-IV which picture hyperbolic tilings of the disk using funny graphics again. We will talk about their mathematical background, and also about how to write a program that makes a hyperbolic tiling out of an arbitrary image file.
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2019-2020 2019 - 2020 Abstracts]
  
[[Image:LW434.jpg]]
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]
[[Image:LW361A.jpg]]
 
[[Image:kite and dart.gif]]
 
  
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]
  
====Speaker: [http://www.math.wisc.edu/~strenner/balazs/Home.html Balazs Strenner]====
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]
Balazs is a first year PhD student originally from Hungary, land of [http://en.wikipedia.org/wiki/Paul_Erd%C5%91s many] [http://en.wikipedia.org/wiki/Leo_Szilard fantastic] [http://en.wikipedia.org/wiki/John_von_Neumann mathematicians and scientists]. Balazs is quite merciless as the Deputy Sheriff in the card game [http://en.wikipedia.org/wiki/Bang! Bang!]
 
  
----
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[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]
  
===Face Recognition===
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]
<span style="background:#00FF00">April 28th, 2011</span>
 
  
'''Invariant-Based Face Recognition'''
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[https://www.math.wisc.edu/wiki/index.php/Archived_Math_Circle_Material The way-back archives]
  
I shall describe the main difficulties with automated face recognition and how our team of mathematicians, engineers, and computer scientists overcame some of them by using mathematical invariants.  
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==Link for presenters (in progress)==
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[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations  Advice For Math Circle Presenters]
  
What are invariants? Invariants are features that do not change under 3D rotation and translation. An example is the curvatures at the tip of the nose. These curvatures do not change, regardless of what angle you look at the face from. The problem though in practice is that curvatures are very sensitive to small changes in the measurements used to compute them, so that simply rounding of the measurements can lead to very different, not invariant numbers.
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[http://www.geometer.org/mathcircles/ Sample Talk Ideas/Problems from Tom Davis]
  
For this reason, invariants have been rejected in the past for recognizing faces because they were not robust to measurement error, and so we decided to come up with a new family of robust invariants. I shall report how our implementation of this won us 2nd place in the 3D section of the national Face Recognition Grand Challenge.
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[https://www.mathcircles.org/activities Sample Talks from the National Association of Math Circles]
  
====Speaker: [http://www.math.wisc.edu/~boston Professor Nigel Boston]====
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[https://epdf.pub/circle-in-a-box715623b97664e247f2118ddf7bec4bfa35437.html "Circle in a Box"]
Nigel Boston is a Professor in the Departments of Mathematics and Electrical & Computer Engineering at UW-Madison. Nigel works in many interesting areas, including applying research from algebra and number theory to real world problems in engineering.
 

Latest revision as of 12:51, 13 May 2022

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For the site in Spanish, visit Math Circle de Madison

COVID-19 Update

We will moving back to in-person talks for the remainder of the semester.

As is the university's policy, all participants must wear masks. We will make every effort to maintain social distancing where possible.

What is a Math Circle?

The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.

The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.


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After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.

The Madison Math Circle was featured in Wisconsin State Journal: check it out!

All right, I want to come!

Our in person talks will be at, Monday at 6pm in 3255 Helen C White Library, during the school year, and the link for our virtual talks will be available through our mailing list and on the schedule below. New students are welcome at any point! There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:

Math Circle Registration Form

All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle.

If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).

Spring Enhancement Workshop

Our aim is to offer an opportunity for students to not only explore various fields of math through our weekly talks, but also give them the opportunity to hone the various skills involved in higher mathematics. To this end, starting this spring, we are beginning a first in a semesterly series of workshops aimed at developing these skills for middle school students. The workshop, titled the Math Circle Spring Enhancement Workshop (SEP) will be held in May, on every Monday from 6:00pm - 7:00pm from May 2nd to May 30th at the UW-Madison campus. Please see our schedule below for details.

The topics for this workshop will cover an introduction to constructing mathematical arguments and proofs, understanding how to generalise simple mathematical ideas, and learn how to discover math for one's self. We will build these skills through collaborative problem solving sessions while learning about graph theory, game theory, and other cool areas of mathematics.

The 2022 SEP is being organised by the Math Circle team in collaboration with Dr. Peter Juhasz, an instructor at the Budapest Semester in Math Education, a world renowned program in training talented students in math education from across the globe. Peter will be the main speaker and facilitator for the spring and has extensive experience teaching mathematics to secondary students and is the chief organizer of various mathematics camps in Hungary. He also directs the Joy of Thinking Foundation, whose aim is to promote mathematics education of gifted students in Hungary.

We want to invite any middle school students curious about math to join! If you are interested, please register using the form below. As always, this workshop is free and only requires your curiosity and participation!

  Math Circle SEP Registration Form

All your information is kept private, and is only used by the Madison Math Circle organiser to help run the Circle.


We hope to see you there!

SEP Schedule
Date Location and Room
May 2nd 3255 Helen C White Library
May 9th 3255 Helen C White Library
May 16th B107 Van Vleck Hall
May 23rd B115 Van Vleck Hall
May 30th B115 Van Vleck Hall




Meetings for Spring 2022

Spring 2022
Date Speaker Topic
February 7th Aleksandra Cecylia Sobieska Mathematical Auction

We will play a game called “Mathematical Auction,” where teams have the opportunity to solve and steal problems for points by presenting solutions that build on one another.

February 14th Jake Fiedler Fractals in Math and Nature

If you've ever had to clean up branches after a storm, you may notice that the branches look surprisingly like the whole tree they fell from, just at a smaller scale. Similarly, lightning bolts during that storm probably had numerous "arms", each appearing similar to the entire bolt. In this talk, we'll investigate this behavior more closely through objects called fractals. We'll see how fractals are made, where they appear in the real world, and then you'll get a chance to build your own.

February 21st Mikhail Ivanov Elevator with just 2 buttons.

There are two buttons inside an elevator in a building with twenty floors. The elevator goes 7 floors up when the first button is pressed, and 9 floors down when the second one is pressed (a button will not function if there are not enough floors to go up or down).

Can we use such elevator? We'll play with this elevator found math behind it.

February 28th Michael Jesurum Bubbling Cauldrons

Place our numbers into the cauldrons in ascending order – you can choose which cauldron each one goes in. However, if two numbers in one cauldron add up to a third number in that same cauldron, they bubble up and cause an explosion! This means that all the numbers leave the cauldrons, and you must start all over again. Our goal is to find the largest number we can place in our cauldrons without them exploding… do you think you’re up for this daunting task?

March 7th Erika Pirnes Reconstructing Graphs

A graph is a "picture" with dots (called vertices) and lines (called edges). From a graph, we can extract information called the deck. In this talk, we will explore the connection between a graph and its deck, and how we can move from one to the other. We will do a lot of examples! There is a famous conjecture (unproven result) that stays that a graph can always be reconstructed (recovered) from its deck. This is called the reconstruction conjecture. (There are some small restrictions on what the graph can be)

March 14th SPRING BREAK NA

NA

March 21st Ian Seong Center of a triangle? But which center?

It is easy to locate the center of a circle, or regular polygons. How do we define the center for an arbitrary triangle?

In fact, for each triangle, there are many points that can be entitled the "center". We will investigate a few of them (classic examples are circumcenter and incenter) and learn how they are constructed.

March 28th Caitlin Davis Math and voting: Can math help us make decisions more fairly?

We are often faced with decisions we must make as a group. For example, a city might need to decide on a new mayor, or you and your friends might need to decide on a movie to watch or a type of pizza to share. We often use voting to try to make a fair choice. The voting method which you’re probably used to is called “plurality,” but it turns out there are many other possible voting methods. Could one of them be more fair than plurality? We’ll talk about how math can be used to study questions like this.

April 4th BREAK NA
April 11th Aleksander Skenderi Happy Numbers

In many areas of mathematics, we look for patterns to describe or model a particular problem. However, sometimes these patterns occur in some late stage of some process, and sometimes not at all! For instance, if a particle of gas is moving around in a container, it may be that, after some time, the gas particle follows an easily described trajectory. It may also be, depending on the initial trajectory, that the gas particle moves totally randomly. In this talk, we'll describe a class of numbers called "happy numbers," and explore some of their properties and patterns.

April 18th John Cobb Chip-Firing Games on Graphs

We will play a game called the dollar game, where we will try to clear out debt among a group of people in a funny way. Then, we’ll investigate ways to see when this is possible and how to do it, leading to some unexpected conclusions and a look into a very active area of math called tropical geometry.

April 25th Chengxi Wu Non integer bases and Paths on colored graphs

We can count in base 10 (decimals) or base 2 (binary), but how about counting in base 5/3, or the golden ratio? We will investigate that via the question of finding possible paths on a graph with colored vertices, and also look at some of the interesting self similar patterns we can get from it!

Meetings for Fall 2021

Fall 2021
Date Speaker Topic
September 20th Daniel Erman Number Games

We’ll play some math-based games and then try to understand some of the patterns we observe.

September 27th Evan Sorensen The fastest way to travel between two points

Given two points, we know the shortest distance between the points is a straight line. But is that always true? We will talk about how to build the best track for a toy car to travel between two points. We’ll start by trying a few different options together and having a race. We’ll then talk about how two brothers thought about how to solve this problem using interesting examples from physics.

October 4th Yandi Wu Do you wanna build a donut?

Topology is a field of math that deals with studying spaces. This math circle talk is an introduction to a concept in topology called “cut-and-paste” topology, which is named that way because we will build spaces out of cutting and gluing pieces of paper.

October 11th Ivan Aidun Words, Words, Words

We'll play a game where you have to guess a secret word that I choose. We'll figure out how to use logic to improve our guesses. Then, we'll explore some questions like: is there a best way to guess? or, what happens when I change the rules slightly?

October 18th Allison Byars Sheep and Wolves

In this math circle talk, we'll look at placing sheep and wolves on a grid so that none of the sheep get eaten. We'll find different arrangements and try to figure out the maximum number which can be placed on a board of given size and generalize it for an arbitrary board. We will also discuss how this relates to a field of mathematics called combinatorics.

October 25th Jacob C Denson Proofs in Three Bits or Less

How many questions does it take to beat someone at Guess Who? How long should it take for you to figure out how to get to this math talk from your house? How many questions do you have to ask your classmate before you know they're telling the truth to you? Let's eat some pizza, and talk about how mathematicians might reason about these problems.

November 1st Qin Li How do we describe the world?

The physical world consists of everything from small systems of a few atoms to large systems of billions of billions of molecules. Mathematicians use different languages and equations to describe large and small systems. Question is: How does mother nature use different languages for different systems and scales? Let us see what these languages look like, talk about their connections and differences, and see how they are reflected in our day-to-day life.

November 8th John Yin River Crossings

Here's a classic puzzle: A farmer needs to move a wolf, a sheep, and a box of cabbages across a river. He has a boat that can fit only one object other than himself. However, when left alone, the wolf will eat the sheep, and the sheep will eat the cabbages. How can the farmer move the wolf, the sheep, and the box of cabbages across the river without anything being eaten? I will discuss this problem by connecting it to graph theory, then give a generalization.

November 15th Erik Bates How big is a cartographer’s crayon box?

Have a look at a world map. If you are looking at one with borders and colors, notice that no border has the same color on both sides. That is, no neighboring countries are colored the same. So how many different colors are needed to make this possible? Does the answer change for a map of the U.S., when we try to color its fifty states? What about a map of Wisconsin with its 72 counties? We will explore these questions---and uncover some very deep mathematics---by doing the simplest and most soothing activity: coloring.

November 22nd Robert Walker Lagrange's Four Square Sum Theorem

How many perfect squares are needed to represent each nonnegative integer n as a sum of perfect squares? This talk will answer that precise question -- students will get to the bottom of this.

Directions and parking

Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.

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Parking. Parking on campus is rather limited. Here is as list of some options:

Email list

The best way to keep up to date with the what is going is by signing up for our email list. Please add your email in the form: Join Email List

Contact the organizers

The Madison Math Circle is organized by a group of professors and graduate students from the Department of Mathematics at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the organizers here. We are always interested in feedback!


and Caitlin Davis and Ivan Aidun.

Donations

Please consider donating to the Madison Math Circle. Our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from private donors. The easiest way to donate is to go to the link:

Online Donation Link

There are instructions on that page for donating to the Math Department. Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"! The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.

Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check.

Or you can make donations in cash, and we'll give you a receipt.

Help us grow!

If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:

  • Like our Facebook Page and share our events with others!
  • Posting our flyer at schools or anywhere that might have interested students.
  • Discussing the Math Circle with students, parents, teachers, administrators, and others.
  • Making an announcement about Math Circle at PTO meetings.
  • Donating to Math Circle.

Contact the organizers if you have questions or your own ideas about how to help out.

Useful Resources

Archived Abstracts

2020 - 2021 Abstracts

2019 - 2020 Abstracts

2016 - 2017 Math Circle Page

2016 - 2017 Abstracts

2015 - 2016 Math Circle Page

2015 - 2016 Math Circle Page (Spanish)

2015 - 2015 Abstracts

The way-back archives

Link for presenters (in progress)

Advice For Math Circle Presenters

Sample Talk Ideas/Problems from Tom Davis

Sample Talks from the National Association of Math Circles

"Circle in a Box"