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=Weekly Meeting=
[[Image:logo.png|right|600px]]
We have a weekly meeting, <b>Monday at 6pm in 120 Ingraham Hall</b>, during the school year.  <b>New students are welcome at any point! </b> There is no required registration, no fee, and the talks are independent of one another, so you can just show up any week.  See below for directions. 
 
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 [http://goo.gl/maps/6k5IA Ingraham Hall] room 120, on the UW-Madison campus).


For the site in Spanish, visit [[Math Circle de Madison]]
=What is a Math Circle?=
=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 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.
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[[Image: MathCircle_2.jpg|500px]]  
[[Image: MathCircle_2.jpg|550px]] [[Image: MathCircle_4.jpg|550px]]  
 
[[Image: MathCircle_4.jpg|500px]]  




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.
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:''' 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
'''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]!


=All right, I want to come!=
=All right, I want to come!=
==Directions and parking==
Meetings are held in 120 Ingraham Hall.
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">
[[File: Ingraham_Map.jpg|400px]]</div>
'''Parking.''' Parking on campus is rather limited.  Here is as list of some options:
*Directly in front of Ingraham hall, 2 metered spots (25 minute max) in [http://goo.gl/maps/HhFUm Lot 11 off of Observatory Drive].
*A 0.2 mile walk to Ingraham Hall via [http://goo.gl/maps/3IFaw these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].
*A 0.3 mile walk to Ingraham Hall via [http://goo.gl/maps/yFwNr these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. 
*A 0.2 mile walk to Ingraham Hall via [http://goo.gl/maps/9NNNm these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].
*A 0.3 mile walk to Ingraham Hall via [http://goo.gl/maps/P156B these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].
==Email list==
Sign up for our email list: https://lists.math.wisc.edu/listinfo/math-circle
==Contact the organizers==
If you have any questions, suggestions for topics, or so on, just email the '''organizers''' (Carolyn Abbott, Gheorghe Craciun, Daniel Erman, Lalit Jain, Ryan Julian, and Philip Matchett Wood): [mailto:math-circle-organizers@math.wisc.edu math-circle-organizers@math.wisc.edu].  We are always interested in feedback!
==Report on Math Circle in 2013-14==
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf Annual Report]
==Donations==
Please consider donating to the Madison Math Circle.  As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers.  Our costs have been covered so far by donations from the UW Math Department plus generous gifts from a private donor.  But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year.  In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.
So please consider donating to support your math circle!  The easiest way to donate is to go to the link:


[http://www.math.wisc.edu/donate Donation Link]
Our in person talks will be at, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. New students are welcome at any point!  There is no fee and the talks are independent of one another. You can just show up any week, but we ask all participants to take a moment to register by following the link below:


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.
[https://forms.gle/5QRTkHngWf43nmCC9 '''Math Circle Registration Form''']


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 "University of Wisconsin Math Department" and add the note "Math Circle Donation" on the check.
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle.  


==Flyer==
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).
Please feel free to distribute our flyer! 
[https://www.math.wisc.edu/wiki/images/Flyer_MMSD.pdf Flyer]


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


=Meetings for Fall 2014 and Spring 2015=


== Fall Schedule ==
<center>
<center>
All talks are at '''6pm in [http://goo.gl/maps/6k5IA Ingraham Hall] room 120''', unless otherwise noted.


{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
|-
|-
! colspan="4" style="background: #ffdead;" align="center" | Fall 2014
! colspan="4" style="background: #e8b2b2;" align="center" | Fall Schedule
|-
|-
! Date and RSVP links!! Speaker !! Topic !! Link for more info
! Date !! Location and Room || Speaker || Title
|-
|-
| September 8, 2014 || Philip Matchett Wood || [[#Philip Matchett Wood | Pictures and Puzzles]] ||
| Oct 7 || 3255 College Library || Caitlin Davis || How to Cut a Cake (Fairly)
|-
|-
| September 15, 2014 || Jen Beichman || [[#TBA | Playing with geometric sums]] ||
| Oct 14 || 3255 College Library || Uri Andrews || Math, Philosophy, Psychology, and Artificial Intelligence
|-
|-
| September 22, 2014 || DJ Bruce || [[#TBA | Is any knot the unknot?]] ||
| Oct 21 || 3255 College Library || Sam Craig || Fractal geometry and the problem of measuring coastlines
|-
|-
| September 29, 2014 || Uri Andrews || [[#TBA | The games of Criss Cross and Brussels Sprouts]] ||
| Oct 28 || 3255 College Library || Cancelled || Cancelled
|-
|-
| October 6, 2014 || David Sondak || [[#David Sondak | Fluids, Math, and Oobleck!]] ||
| Nov 4 || 3255 College Library || Sam Craig || Proofs of the Pythagorean theorem, new and old.
|-
|-
| October 13, 2014 || George Craciun || [[#George Craciun | Proofs without words (but with plenty of pictures)]] ||
| Nov 11 || 3255 College Library || Chenxi Wu || Heron’s method for approximating square roots
|-
|-
| October 20, 2014 || Scott Hottovy || [[#TBA | Coming soon!]] ||
| Nov 18 || 3255 College Library || Diego Rojas || Non-Transitive Dice: The Math That Doesn’t Play Fair
|-
|-
| October 27, 2014 || Daniel Hast || [[#Hast | Clock arithmetic and perfect squares: a "Golden Theorem" of reciprocity]] ||
| Nov 25 || 3255 College Library || Kaiyi Huang || A geometric investigation into a space shuttle failure
|-
|-
| November 3, 2014 || Alisha Zachariah || [[#TBA | Infinity]] ||
| Dec 2 || 3255 College Library || TBA || TBA
|-
|-
| November 10, 2014 || Marko Budisic || [[#Marko Budisic | Mathematics of epidemics ]] ||
| Dec 9 || 3255 College Library || TBA || TBA
|-
|-
| November 17, 2014 || Nigel Boston || [[#Nigel Boston | Same bad channel]] ||
| Dec 16 || 3255 College Library || TBA || TBA
|-
|-
| <strike>November 24, 2014</strike> || <strike>Daniel Erman</strike> || [[#TBA | <strike>How to catch a (data) thief </strike> Cancelled or weather]] ||
|}
 
</center>
 
= Fall Abstracts =
 
=== Abstract 10/7 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| December 1, 2014 || Daniel Erman || [[#TBA | How to catch a (data) thief]] ||
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Caitlin Davis'''
|-
|-
! colspan="4" style="background: #ffdead;" align="center" | Spring 2015
| bgcolor="#BDBDBD" align="center" | '''Title: How to Cut a Cake (Fairly)'''
|-
|-
| <strike>January 26, 2015 </strike> || TBA || [[#TBA | Coming soon!]] ||
| bgcolor="#BDBDBD"  | 
Imagine you and a friend are sharing a cupcake.  How can you cut the cupcake so that each of you gets your fair share?  If you've ever shared a cupcake (or some other treat) with a friend, you might have an answer!  Now what if you're sharing a cake with several friends?  Can we use the same strategy to cut the cake fairly? We'll talk about how math can be used to study questions like this.
|}                                                                       
</center>
 
=== Abstract 10/14 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| February 2, 2015 || Soledad Benguria || [[#TBA | Exploring Palindromes]] ||
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''
|-
|-
| February 9, 2015 || Jeff Linderoth|| [[#TBA | Coming soon!]] ||
| bgcolor="#BDBDBD"  align="center" | '''Title: Math, Philosophy, Psychology, and Artificial Intelligence'''
|-
|-
| February 16, 2015 || Simon Marshall || [[#Simon Marshall | The Ant Walk]] ||
| bgcolor="#BDBDBD"  |  
People come to understand the truth via a process of arguing. This could be a philosophical debate. This could be an internal dialogue. This could be in a courtroom. This could be deciding with your family where to go for dinner. These are all different forms of argumentation, with different rules for when you are convinced. In a courtroom, you have to be convinced beyond a reasonable doubt, whereas when deciding where to go for dinner, you might just have to look hungriest to win. These processes can be mathematically modeled. Moreover, this is important for the modern goal of teaching a computer how to think and how to understand human reasoning (Artificial Intelligence).
|}                                                                       
</center>
 
 
=== Abstract 10/21 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| February 23, 2015 || Uri Andrews || [[#TBA | Coming soon!]] ||
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Sam Craig'''
|-
|-
| March 2, 2015 || Jordan Ellenberg|| [[#TBA | Coming soon!]] ||
| bgcolor="#BDBDBD"  align="center" | '''Title: Fractal geometry and the problem of measuring coastlines'''
|-
|-
| March 9, 2015 || Ali Lynch || [[#TBA | Mathematical Games and Winning Strategies]] ||
| bgcolor="#BDBDBD"  |  
A fractal is a shape which looks about the same when you look closely as when you look far away. I will show some examples of fractals that arise in math (like the Sierpinski triangle) and in nature (like the coastline of an island) and discuss the difficulties in determining what the length of a fractal means.
|}                                                                       
</center>
 
=== Abstract 11/4 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
|-
| March 16, 2015 || Daniel Schultheis || [[#TBA | Picture Hanging and Secret Algebra]] ||
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Sam Craig'''
|-
|-
| March 23, 2015 || Betsy Stovall|| [[#Ches | Divisibility Cheats]] ||
| bgcolor="#BDBDBD" align="center" | '''Title: Proofs of the Pythagorean theorem, new and old.'''
|-
|-
| March 30, 2015 || No meeting|| [[#TBA | UW Spring Break]] ||
| bgcolor="#BDBDBD" |
The Pythagorean theorem has been known for thousands of years and over that time, people have found a number of different ways to prove the theorem. We will talk about a proof given by Pythagoras, a proof by US President Andrew Garfield, and a very recent proof (that you might have heard of in the news) by Calcea Johnson and Ne'Kiya Jackson.
|}
</center>
 
=== Abstract 11/11 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
|-
| April 6, 2015 || Julie Mitchell || [[#Julie Mitchell | Protein Folding and Robot Dances: Understanding the Basics of Kinematic Motion]] ||
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Chenxi Wu'''
|-
|-
| April 13, 2015 || Jessica Lin ||[[#TBA | Coming soon!]] ||
| bgcolor="#BDBDBD" align="center" | '''Title:Heron’s method for approximating square roots.'''
|-
|-
| April 20, 2015 || DJ Bruce ||[[#TBA | Coming soon!]] ||
| bgcolor="#BDBDBD" |
We will talk about Heron's method for approximating square roots. This will lead us on a journey through approximation methods including Newton's method, through algebraic concepts like the p-adic numbers, and Hensel's Lemma.
|}
</center>
 
=== Abstract 11/18 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
|-
| April 27, 2015 || David Anderson ||[[#TBA | Coming soon!]] ||
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Diego Rojas'''
|-
|-
| May 4, 2015 || Daniel Ross ||[[#TBA |Last meeting of semester!]] ||
| bgcolor="#BDBDBD" align="center" | '''Title:Non-Transitive Dice: The Math That Doesn’t Play Fair.'''
|-
|-
| bgcolor="#BDBDBD" |
What if I told you there’s a set of dice where winning doesn’t follow the rules you expect? In this talk, we’ll explore the strange and surprising world of non-transitive dice, where the usual logic of “if A is better than B, and B is better than C, then A must be better than C” simply falls apart. Using math, probability, and a little imagination, we’ll uncover why these dice defy intuition and how they challenge our understanding of competition and strategy. Get ready to think about games—and math—in a whole new way!
|}
|}
</center>


=== Abstract 11/25 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Kaiyi Huang'''
|-
| bgcolor="#BDBDBD" align="center" | '''Title:A geometric investigation into a space shuttle failure'''
|-
| bgcolor="#BDBDBD" |
We know that a circle has the same width in every direction, but is it the only object that has this property? NASA engineers assumed so, which, together with a string of other mistakes, might have led to the tragic failure of their space shuttle launch. Let’s look further into this problem so that we won’t make the same mistake again!
|}
</center>
</center>


== Abstracts ==
==Directions and parking==
 
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.
 
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">
[[File: Helencwhitemap.png|400px]]</div>
 
'''Parking.''' Parking on campus is rather limited.  Here is as list of some options:


===Philip Matchett Wood===
*There is a parking garage in the basement of Helen C. White, with an hourly rate.  Enter from Park Street.
''Pictures and Puzzles''
*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].
*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]. 
*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].
*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] .
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].


When does a simple picture solve a tricky puzzle?  Come and learn about how line-and-dot drawing can solve complex puzzles, and create some new puzzles besides!
==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:
[https://docs.google.com/forms/d/e/1FAIpQLSe_cKMfdjMQlmJc9uZg5bZ-sjKZ2q5SV9wLb1gSddrvB1Tk1A/viewform '''Join Email List''']


===DJ Bruce===
==Contact the organizers==
''Is any knot the unknot?
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!
<center>
<gallery widths="500" heights="300" mode="packed">
File:Uri.jpg|[https://www.math.wisc.edu/~andrews/ Prof. Uri Andrews]
</gallery>


Abstract: You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.
<gallery widths="500" heights="250" mode="packed">
</gallery>
</center>


===David Sondak===
==Donations==
''Fluids, Math and Oobleck!''
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:


We will explore the magical world of fluids and their relationship to mathematics. As an example of fluids and math in the real world, we will make the living fluid oobleck and discuss some of its mathematical properties.
[http://www.math.wisc.edu/donate Online Donation Link]


=== George Craciun===
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.
''Proofs without words (but with plenty of pictures)''


We will discuss mathematical proofs that can be done using only pictures or figures. If you want to see many such examples you can check out the book "Proofs without Words: Exercises in Visual Thinking" by  Roger B. Nelsen. For more information also look at the wikipedia page http://en.wikipedia.org/wiki/Proof_without_words , where you can find links to Java Applets that show animations of proofs without words, such as http://usamts.org/Gallery/G_Gallery.php .
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.


=== Daniel Hast===
==Help us grow!==
''Clock arithmetic and perfect squares: a "Golden Theorem" of reciprocity''
If you like Math Circle, please help us continue to grow!  Students, parents, and teachers can help by:
* Like our [https://facebook.com/madisonmathcircle '''Facebook Page'''] and share our events with others!
* Posting our [https://www.math.wisc.edu/wiki/images/Math_Circle_Flyer_2021.pdf '''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.


We'll explore systems of arithmetic where numbers loop back around to zero (like the hours on a clock!), called "modular arithmetic". Which numbers are perfect squares in such systems? Gauss, one of the greatest mathematicians in history, called the remarkable answer the "golden theorem".
=Useful Resources=


=== Alisha Zachariah===
''What is infinity anyway''


Infinity has a long history of having confounded and fascinated thinkers. We will take a look at some fundamental problems that early mathematicians grappled with and see some ways to understand infinity that have contributed to how we do math today.


===Marko Budisic===
== Archived Abstracts ==
''Mathematics of epidemics''


Infectious diseases in our communities often make it into daily conversation: "There's a nasty cold going around.", "It's the flu season, get your shots.", and even, "There are news of a zombie outbreak!" Come hear how math gets applied to something as messy as spread of disease. We will use our wits, pencils, and computers to understand the progress of headaches, common cold, zombie outbreaks, and even ebola, a disease that is currently making the news.
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2023-2024 2023 - 2024 Abstracts]


===Nigel Boston===
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2022-2023 2022 - 2023 Abstracts]
''Same bad channel''


How do we get such clear photos of the comet in the news?
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2021-2022 2021 - 2022 Abstracts]
A 20 watt transmitter sends signals 500 million km through space to
us and yet amazingly they survive this ordeal error-free. What's
behind this is error-correcting codes. I'll give some of the basics,
some related puzzles, and some challenges.


===Soledad Benguria===
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2020-2021 2020 - 2021 Abstracts]
''Exploring Palindromes''


A Palindrome is a word or a number that reads the same forward and backwards. For example, Hannah, radar and civic are palindromic words, and 34743, 6446 are palindromic numbers. We will explore some curious properties of palindromes, and talk about what makes the number 196 special.  
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2019-2020 2019 - 2020 Abstracts]


===Simon Marshall===
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]
''The Ant Walk''


An ant is walking on a grid in the plane, but it can only move north or east. How many ways are there for it to get from one square to another?  The numbers that appear when we answer this question have a wealth of interesting properties.
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]


[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]


[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]


===Betsy Stovall===
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]
''Divisibility Cheats''


We will discuss simple ways to determine whether one number is evenly divisible by a smaller one and also how to prove these facts. If time permits, we will also look at divisibility rules in bases other than 10.  
[https://www.math.wisc.edu/wiki/index.php/Archived_Math_Circle_Material The way-back archives]


===Julie Mitchell===
==Link for presenters (in progress)==
''Protein Folding and Robot Dances: Understanding the Basics of Kinematic Motion''
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations  Advice For Math Circle Presenters]


We will learn about motion subject to constraints. Mathematics based on these principles helps us build robots, explains human motion, and helps us model the shape of proteins like enzymes and antibodies.  
[http://www.geometer.org/mathcircles/ Sample Talk Ideas/Problems from Tom Davis]


==[[Archived Math Circle Material]]==
[https://www.mathcircles.org/activities Sample Talks from the National Association of Math Circles]
[[Archived Math Circle Material]]


=Link for presenters (in progress)=
[https://epdf.pub/circle-in-a-box715623b97664e247f2118ddf7bec4bfa35437.html "Circle in a Box"]
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations  https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations]

Latest revision as of 15:58, 25 November 2024

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For the site in Spanish, visit Math Circle de Madison

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. New students are welcome at any point! There is no fee and the talks are independent of one another. 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).


Fall Schedule

Fall Schedule
Date Location and Room Speaker Title
Oct 7 3255 College Library Caitlin Davis How to Cut a Cake (Fairly)
Oct 14 3255 College Library Uri Andrews Math, Philosophy, Psychology, and Artificial Intelligence
Oct 21 3255 College Library Sam Craig Fractal geometry and the problem of measuring coastlines
Oct 28 3255 College Library Cancelled Cancelled
Nov 4 3255 College Library Sam Craig Proofs of the Pythagorean theorem, new and old.
Nov 11 3255 College Library Chenxi Wu Heron’s method for approximating square roots
Nov 18 3255 College Library Diego Rojas Non-Transitive Dice: The Math That Doesn’t Play Fair
Nov 25 3255 College Library Kaiyi Huang A geometric investigation into a space shuttle failure
Dec 2 3255 College Library TBA TBA
Dec 9 3255 College Library TBA TBA
Dec 16 3255 College Library TBA TBA

Fall Abstracts

Abstract 10/7

Caitlin Davis
Title: How to Cut a Cake (Fairly)

Imagine you and a friend are sharing a cupcake. How can you cut the cupcake so that each of you gets your fair share? If you've ever shared a cupcake (or some other treat) with a friend, you might have an answer! Now what if you're sharing a cake with several friends? Can we use the same strategy to cut the cake fairly? We'll talk about how math can be used to study questions like this.

Abstract 10/14

Uri Andrews
Title: Math, Philosophy, Psychology, and Artificial Intelligence

People come to understand the truth via a process of arguing. This could be a philosophical debate. This could be an internal dialogue. This could be in a courtroom. This could be deciding with your family where to go for dinner. These are all different forms of argumentation, with different rules for when you are convinced. In a courtroom, you have to be convinced beyond a reasonable doubt, whereas when deciding where to go for dinner, you might just have to look hungriest to win. These processes can be mathematically modeled. Moreover, this is important for the modern goal of teaching a computer how to think and how to understand human reasoning (Artificial Intelligence).


Abstract 10/21

Sam Craig
Title: Fractal geometry and the problem of measuring coastlines

A fractal is a shape which looks about the same when you look closely as when you look far away. I will show some examples of fractals that arise in math (like the Sierpinski triangle) and in nature (like the coastline of an island) and discuss the difficulties in determining what the length of a fractal means.

Abstract 11/4

Sam Craig
Title: Proofs of the Pythagorean theorem, new and old.

The Pythagorean theorem has been known for thousands of years and over that time, people have found a number of different ways to prove the theorem. We will talk about a proof given by Pythagoras, a proof by US President Andrew Garfield, and a very recent proof (that you might have heard of in the news) by Calcea Johnson and Ne'Kiya Jackson.

Abstract 11/11

Chenxi Wu
Title:Heron’s method for approximating square roots.

We will talk about Heron's method for approximating square roots. This will lead us on a journey through approximation methods including Newton's method, through algebraic concepts like the p-adic numbers, and Hensel's Lemma.

Abstract 11/18

Diego Rojas
Title:Non-Transitive Dice: The Math That Doesn’t Play Fair.

What if I told you there’s a set of dice where winning doesn’t follow the rules you expect? In this talk, we’ll explore the strange and surprising world of non-transitive dice, where the usual logic of “if A is better than B, and B is better than C, then A must be better than C” simply falls apart. Using math, probability, and a little imagination, we’ll uncover why these dice defy intuition and how they challenge our understanding of competition and strategy. Get ready to think about games—and math—in a whole new way!


Abstract 11/25

Kaiyi Huang
Title:A geometric investigation into a space shuttle failure

We know that a circle has the same width in every direction, but is it the only object that has this property? NASA engineers assumed so, which, together with a string of other mistakes, might have led to the tragic failure of their space shuttle launch. Let’s look further into this problem so that we won’t make the same mistake again!

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!

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

2023 - 2024 Abstracts

2022 - 2023 Abstracts

2021 - 2022 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"

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