Madison Math Circle: Difference between revisions

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=What is it?=
[[Image:logo.png|right|600px]]
The UW-Madison math department organizes a series of talks aimed at interested middle school and 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.  


For more information about Math Circles see http://www.mathcircles.org/
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.


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 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.


'''The Madison Math circle was recently 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
[[Image: MathCircle_2.jpg|550px]] [[Image: MathCircle_4.jpg|550px]]


=Alright, I want to come!=
Great! 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 (and tell us how many people are coming so we can purchase the appropriate amount of pizza!)


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 Van Vleck Hall room B223, on the UW-Madison campus). '''We'd also appreciate if you [mailto:math-circle@math.wisc.edu email] us the dates that your group will be attending'''.
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.


'''Parking''' on campus is free at most (but not all) outdoor parking lots after 4:30pm. Parking lots #25 (Elizabeth Waters) and #26 (Observatory Hill) may be the most convenient. These parking lots are on Observatory Drive just west of the intersection with Charter Street. If you park there, then walk east along Observatory Drive to the top of Bascom Hill, then turn right to Van Vleck Hall. See also the map at http://www.map.wisc.edu/?keyword=public%20parking
'''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]!


=Questions?=
=All right, I want to come!=
If you have any questions, suggestions for topics, or so on, just email the '''organizers''' (Ed Dewey, David Dynerman, Nathan Clement, Lalit Jain, Kevin Zamzow, and Gheorghe Craciun): [mailto:math-circle@math.wisc.edu math-circle@math.wisc.edu].


==Talks this semester, Fall 2012==
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:
More details about each talk to follow soon. All talks are at '''6pm in Van Vleck Hall, room B223''', unless otherwise noted.


<center>
[https://forms.gle/5QRTkHngWf43nmCC9 '''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.


{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
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).
|-
! Date !! Speaker !! Talk (click for more info)
|-
| Starting first week of October 2012 || TBA || [[#TBA | TBA]]
|-
| More TBA || 
|}


</center>


==Previous Talks ==
More details about each talk to follow soon. All talks are at '''6pm in Van Vleck Hall, room B223''', unless otherwise noted.


== Fall Schedule ==
<center>
<center>


{| 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)
! colspan="4" style="background: #e8b2b2;" align="center" | 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.
|-
|-
| February 13, 2012 || Patrick LaVictoire || [[#Transforms: Pictures in Disguise | Transforms: Pictures in Disguise]]
| Nov 11 || 3255 College Library || Chenxi Wu || Heron’s method for approximating square roots
|-
|-
| February 20, 2012 || Uri Andrews || [[#Hercules and the Hydra|Hercules and the Hydra]]
| Nov 18 || 3255 College Library || Diego Rojas || Non-Transitive Dice: The Math That Doesn’t Play Fair
|-
|-
| February 27, 2012 || Peter Orlik || [[#Madison Math Circles|Madison Math Circles]]
| Nov 25 || 3255 College Library || TBA || TBA
|-
|-
| March 5, 2012 || Jean-Luc Thiffeault || [[#The hagfish: the slimiest fish in the sea|The hagfish: the slimiest fish in the sea]]
| Dec 2 || 3255 College Library || TBA || TBA
|-
|-
| March 12, 2012 || Cathi Shaughnessy || [[#Archimedes' method | Archimedes' method]]
| Dec 9 || 3255 College Library || TBA || TBA
|-
|-
| March 19, 2012 || Andrei Caldararu || [[#Games with the binary number system | Games with the binary number system]]
| Dec 16 || 3255 College Library || TBA || TBA
|-
|-
| March 26, 2012 || Laurentiu Maxim || [[#How many pentagons and hexagons does it take to make a soccer ball? | How many pentagons and hexagons does it take to make a soccer ball?]]
''' This was the last meeting this semester. '''
''' We hope to see you again in September! '''
|}
|}


</center>
</center>


= Fall Abstracts =


----
=== Abstract 10/7 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Caitlin Davis'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: How to Cut a Cake (Fairly)'''
|-
| 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"
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Math, Philosophy, Psychology, and Artificial Intelligence'''
|-
| 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"
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Sam Craig'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Fractal geometry and the problem of measuring coastlines'''
|-
| 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>


=== Transforms: Pictures in Disguise ===
=== Abstract 11/4 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Sam Craig'''
|-
| bgcolor="#BDBDBD" align="center" | '''Title: Proofs of the Pythagorean theorem, new and old.'''
|-
| 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>


<span style="background:#00FF00">February 13th, 2012, '''6pm''', Van Vleck Hall room B223, UW-Madison campus</span>
=== Abstract 11/11 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Chenxi Wu'''
|-
| bgcolor="#BDBDBD" align="center" | '''Title:Heron’s method for approximating square roots.'''
|-
| 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>


'''Presenter: Patrick LaVictoire.''' How are [http://en.wikipedia.org/wiki/Computer_graphics computer graphics] like a massive game of Sudoku? How does a [http://en.wikipedia.org/wiki/X-ray_computed_tomography CAT scan] get a 3D picture from a bunch of 2D X-ray images? How can you make the [http://cvcl.mit.edu/hybrid_gallery/monroe_einstein.html same image] look like different people when viewed from close up and far away? I'll discuss all these and more, with some neat illustrations and quick games.
=== Abstract 11/18 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Diego Rojas'''
|-
| 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>
==Directions and parking==


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


=== Hercules and the Hydra ===
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">
[[File: Helencwhitemap.png|400px]]</div>


<span style="background:#00FF00">February 20th, 2012, '''6pm''', Van Vleck Hall room B223, UW-Madison campus</span>
'''Parking.''' Parking on campus is rather limited.  Here is as list of some options:


'''Presenter: Uri Andrews.''' We will talk about important techniques of self-defense
*There is a parking garage in the basement of Helen C. White, with an hourly rate.  Enter from Park Street.
against an invading Hydra. The following, from Pausanias (Description
*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].
of Greece, 2.37.4) describes the beginning of the battle of Hercules
*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]. 
against the Lernaean hydra:
*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].


"As a second labour he ordered him to kill the Lernaean hydra.
==Email list==
That creature, bred in the swamp of Lerna,
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:
used to go forth into the plain
[https://docs.google.com/forms/d/e/1FAIpQLSe_cKMfdjMQlmJc9uZg5bZ-sjKZ2q5SV9wLb1gSddrvB1Tk1A/viewform '''Join Email List''']
and ravage both the cattle and the country.
Now the hydra had a huge body, with nine heads,
eight mortal, but the middle one immortal. . . .
By pelting it with fiery shafts he forced it to come out,
and in the act of doing so he seized and held it fast.
But the hydra wound itself about one of his feet and clung to him.
Nor could he effect anything by smashing its heads with his club,
for as fast as one head was smashed there grew up two..."


For more information on some of the conjectures discussed during this talk see http://en.wikipedia.org/wiki/Collatz_conjecture and http://mathworld.wolfram.com/CollatzProblem.html
==Contact the organizers==
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>


<gallery widths="500" heights="250" mode="packed">
</gallery>
</center>


=== Madison Math Circles ===
==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:
<span style="background:#00FF00">February 27th, 2012, '''6pm''', Van Vleck Hall room B223, UW-Madison campus</span>


'''Presenter: Peter Orlik.''' A short introduction to elementary and middle school activities in Madison like Mathematical Olympiad and Mathcounts will be followed by some challenging problems. Please bring your favorite pencils and be prepared to work!
[http://www.math.wisc.edu/donate Online Donation Link]


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.


=== The hagfish: the slimiest fish in the sea ===
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. 


<span style="background:#00FF00">March 5th, 2012, '''6pm''', Van Vleck Hall room B223, UW-Madison campus</span>
Or you can make donations in cash, and we'll give you a receipt.


'''Presenter: Jean-Luc Thiffeault.''' The hagfish is a bottom-dwelling, scavenger fish that resembles an
==Help us grow!==
eel.  It has some interesting peculiarities: first, it sometimes
If you like Math Circle, please help us continue to grow!  Students, parents, and teachers can help by:
willingly ties itself in a knot.  Second, it secretes a spectacular
* Like our [https://facebook.com/madisonmathcircle '''Facebook Page'''] and share our events with others!
amount of slime, which is used in the cosmetics industry. For a long
* Posting our [https://www.math.wisc.edu/wiki/images/Math_Circle_Flyer_2021.pdf '''flyer'''] at schools or anywhere that might have interested students.
time the purpose of this slime was unknown, but recently scientists
* Discussing the Math Circle with students, parents, teachers, administrators, and others.
have filmed live hagfish using it. (I'll keep this purpose a secret
* Making an announcement about Math Circle at PTO meetings.
until the talk...)  I'll then discuss how we can apply mathematical
* Donating to Math Circle.
tools to study hagfish slime.
Contact the organizers if you have questions or your own ideas about how to help out.


=Useful Resources=




=== Archimedes' method ===


<span style="background:#00FF00">March 12th, 2012, '''6pm''', Van Vleck Hall room B223, UW-Madison campus</span>
== Archived Abstracts ==


'''Presenter: Cathi Shaughnessy.''' Students will use Archimedes' classical method to determine bounds for the value of the number pi. Please BRING A CALCULATOR with you for this presentation. The presenter will provide compass, protractor, straightedge and worksheet for each student.  
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2023-2024 2023 - 2024 Abstracts]


----
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2022-2023 2022 - 2023 Abstracts]


[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2021-2022 2021 - 2022 Abstracts]


[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2020-2021 2020 - 2021 Abstracts]


=== Games with the binary number system ===
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2019-2020 2019 - 2020 Abstracts]


<span style="background:#00FF00">March 19th, 2012, '''6pm''', Van Vleck Hall room B223, UW-Madison campus</span>
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]


'''Presenter: Andrei Caldararu.''' I will present a few games and tricks which use the binary number system. For more information about binary numbers please see http://en.wikipedia.org/wiki/Binary_numeral_system
[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)]


[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]


=== How many pentagons and hexagons does it take to make a soccer ball? ===
[https://www.math.wisc.edu/wiki/index.php/Archived_Math_Circle_Material The way-back archives]


<span style="background:#00FF00">March 26th, 2012, '''6:30pm (note special time!!!)''', Van Vleck Hall room B223, UW-Madison campus</span>
==Link for presenters (in progress)==
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations  Advice For Math Circle Presenters]


'''Presenter: Laurentiu Maxim.''' I will first introduce the concept of Euler characteristic of a polyhedral surface. As an application, I will show how one can find the number of pentagons on a soccer ball without actually counting them.
[http://www.geometer.org/mathcircles/ Sample Talk Ideas/Problems from Tom Davis]


----
[https://www.mathcircles.org/activities Sample Talks from the National Association of Math Circles]


''' This was the last meeting this semester.   We hope to see you again in September! '''
[https://epdf.pub/circle-in-a-box715623b97664e247f2118ddf7bec4bfa35437.html "Circle in a Box"]

Latest revision as of 15:39, 18 November 2024

Logo.png

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.


MathCircle 2.jpg MathCircle 4.jpg


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 TBA TBA
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!

Directions and parking

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

Helencwhitemap.png

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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