Madison Math Circle Abstracts

September 14 2015

David Sondak

Title: How to SEE Sound

The idea is to give a simple overview of sound waves by introducing sines and cosines and some of their basic anatomy (amplitude and frequency). We will then have a computational component where the students create their own sound waves by fiddling with parameters in the sines and cosines (again, amplitude, frequency and different superpositions of the sines and cosines). They will actually be able to see plots of their waves AND listen to their waves. Finally, if time permits, the students will use their own sound waves to make Oobleck dance. This will bring the exercise full circle in that they will be able to see their very own sound waves in action.

September 21 2015

Prof. Uri Andrews

Title: Guarding Mona Lias

You have gotten a tip that a famous art thief is going to steal something from the Louvre. It is your task to organize a security team that can watch all the works of art. The problem is that the Louvre is really big and has a strange layout. Where do you put your guards? And how many do you need?

September 28 2015

Eva Elduque

Title: Pick's Theorem

In this talk, we will a very easy formula that allows us to quickly compute the areas of polygons whose vertices are points of a grid, and we will prove that this formula works. (Solutions to the worksheet distributed during the circle can be found File:Pick.pdf.)

October 5 2015

Jessica Lin

Title: The Math of Sudoku

Have you ever sat next to someone in the airport or airplane who plays sudoku? Have you ever tried to play yourself? When you play, do you have some strategies that help you to complete the puzzle? It turns out that there is some deep mathematics behind this simple game. Come to math circle this week to learn about it, and maybe you can help the person next to you solve his/her sudoku!

October 12 2015

Ryan Julian

Title: The Geometry of Hockeysticks and Eight Dimensional Oranges

Like most people, I've often considered opening an eight dimensional grocery store. Of course, the main difficulty with this plan is that I'd need some way of neatly stacking all of the eight dimensional fruit that I'd be selling. In this talk, we'll explore a variety of elementary counting problems, discover that nearly all elementary counting problems are really the same problem, and we'll apply these new insights to determine how to stack 8 dimensional fruits into neat 8 dimensional pyramids.

October 26 2015

Megan Maguire

Title: Aperiodic tilings: Beyond your parents' bathroom floor

A tiling is a way of covering the plane with geometric shapes such that there are no overlaps or gaps. If you have any tile in your home (maybe in your kitchen or bathroom) that is most likely an example of a tiling. Come learn about the cool math behind tilings and about the coolest tiling of all, the Penrose tiling.

November 2 2015

Marko Budisic

Title: Mathematics of GPS Satellites

GPS is a system of satellites circling the Earth at a height 12,500 miles. That means you could easily fit both Mars and Venus in the distance between your phone and each car-sized satellite hovering in space. Once considered science fiction, GPS is now a part of our everyday life: we can use it through our phones, through our car navigation, and even some watches. Simple math equations lie at the heart of this system, and we will write them down, understand what they mean, and figure out how to solve them.

November 9 2015

Tess Anderson

Title: Gold Coins and Goast

What do pulling gold coins out of a a hat have to do with the famous Monty Hall "Goat Problem" in which you are a game show contestant trying to pick out the one prize hidden behind one of three doors? Come and find out while savoring some chocolate gold coins. We will also discuss a jailer problem in which an infinite number of jailers try to free an infinite number of prisoners. If time permits, other fun problems will be discussed.

November 16 2015

DJ Bruce

Title: To Infinity and Beyond?

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

November 23 2015

Prof. Tullia Dymarz

Title: To Infinity and Beyond?

TBA

February 1 2016

Will Mitchell

Title: Are these networks the same?

The question of deciding whether two things are the same comes up in many different places in math. In this session we'll consider the problem of deciding if two networks or "graphs" are the same. This leads to some entertaining and challenging puzzles. We will also learn a bit about how people try to solve similar problems using computers. This problem has applications in the design of electronic circuits and in searching for organic chemical compounds within large databases. The handout, presentation, and solutions, can be found here, here, and here respectively.

February 8 2016

Lalit Jain

Title: Large amounts of small money

This week we will talk about coins, change and some of the surprising mathematics and computer science behind a very simple problem: How many ways are there to make change for a dollar?

February 15 2016

Daniel Erman

What is the biggest number?

The title is something of a joke, though a more serious question would be: what are the biggest numbers that have actually been used in mathematics or science? We will use this question as a launching off point for exploring the use of exceptionally large numbers in math and science. Along the way, we will touch on ideas related to the prime numbers, chemistry, astrophysics, and graph theory.

February 22 2016

Soumya Sankar

What would you do if you had only nickels and dimes?

This is an instance of the classical Frobenius Coin problem: If you are given two denominations of coins and asked to combine them to get different values, after what point, if at all, can you get all subsequent values of money? Starting from this simple problem, one can ask a variety of questions. I will talk about how one can play around with some of these.

February 29 2016

Soumya Sankar

How big is your infinity?

If a "box" A fits inside a "box" C, with room to spare, is A "smaller" than C? Oddly, if A and C are infinite, the answer may be negative. In this talk, we generalize the concept of "counting" to sets with infinitely many elements. We then find examples of infinite sets which are "equal in size" even though one contains "several copies" of the other. We also show that not all infinite sets have the same size.

High School Meetings

September 28 2015

Prof. Daniel Erman

Title: How to Catch a (Data) Thief

I will discuss some surprising statistical facts that have been used to catch companies that lie about data.

October 19 2015

Carolyn Abbott

Title: Donuts and coffee cups: the topology of surfaces

A classic problem in topology is to decide whether one surfaces can be deformed into another, without creating any holes or connecting any new points (stretching and bending is allowed!). If you can do so, such surfaces are considered 'the same.' We will formalize this notion and classify all closed surfaces, along the way answering such questions as whether a coffee cup is the same as a donut.