Madison Math Circle
For the site in Spanish, visit Math Circle de Madison
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.
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).
Meetings for Spring 2022
|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
|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 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
|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.
Parking. Parking on campus is rather limited. Here is as list of some options:
- There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.
- A 0.5 mile walk to Helen C. White Hall via these directions, many spots (free starting 4:30pm) in Lot 26 along Observatory Drive.
- A 0.3 mile walk to Helen C. White Hall via these directions, many spots (free starting 4:30pm) in Lot 34.
- A 0.3 mile walk to Helen C. White Hall via these directions, 2 metered spots (25 minute max) in front of Lathrop Hall.
- A 0.2 mile walk to Helen C. White Hall via these directions 6 metered spots (25 minute max) around the loop in front of Chadbourne Hall .
- For more information, see the UW-Madison Parking Info website.
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.
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:
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.
2015 - 2016 Math Circle Page (Spanish)
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