# Madison Math Circle

## Contents

# What is it?

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/

After each talk we'll have snacks 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 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

# 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 click the "Register" link for the date that your group will be attending.**

**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

# Questions?

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, Betsy Stovall, and Philip Matchett Wood): math-circle@math.wisc.edu.

## Talks this semester, Spring 2013

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

Date and RSVP links | Speaker | Topic (click for more info) |
---|---|---|

February 4, 2013 | Jonathan Kane | Infinitely Often |

February 11, 2013 | Jean-Luc Thiffeault | TBA |

February 18, 2013 | Alison Gordon | TBA |

February 25, 2013 | Mimansa Vahia | TBA |

March 4, 2013 | TBA | TBA |

March 11, 2013 | Greg Shinault | TBA |

March 18, 2013 | TBA | TBA |

March 25, 2013 | Spring Break | No Meeting |

April 1, 2013 | Uri Andrews | TBA |

April 8, 2013 | TBA | TBA |

April 15, 2013 | TBA | TBA |

April 22, 2013 | TBA | TBA |

April 29, 2013 | TBA | TBA |

### Infinitely Often

February 4th, 2013, **6pm**, Van Vleck Hall room B223, UW-Madison campus

** Infinitely Often**

So you think you can add two numbers, three number, even a lot of numbers together? Well, can you add an infinite number of numbers together? See how thinking about infinite processes can be used to add infinite sums, evaluate repeating decimals, understand infinite continued fractions, and calculate areas and volumes. Also see what strange things can go wrong when dealing with infinity.

### TBA

**To Be Announced:**
Keep an eye out---we'll have more information soon!

## Talks last semester, Fall 2012

Date and RSVP links | Speaker | Topic (click for more info) | Event and poster links |
---|---|---|---|

October 1, 2012: Register | Richard Askey | Counting: to and then beyond the binomial theorem | Combined High School Math Night & Math Circle (Poster) |

October 8, 2012: Register | Philip Matchett Wood | Proofs with Parity | Math Circle |

October 15, 2012: Register | Philip Matchett Wood | Fun Flipping Coins | Math Circle (Poster) |

October 22, 2012: Register | Saverio Spagnolie | Random walks: how gamblers lose and microbes diffuse | Combined High School Math Night & Math Circle (Poster) |

October 29, 2012: Register | Beth Skubak | non-Euclidean geometry | Math Circle (Poster) |

November 5, 2012: Register | Mihai Stoiciu | Rubik's Cubes | Combined High School Math Night & Math Circle (Poster) |

November 12, 2012: Register | Alison Gordon | Curious Catalan Numbers | Math Circle (Poster) |

November 19, 2012: Register | Gregory Shinault | Tiling Problems | Math Circle |

November 26, 2012: Register | Claire Blackman | Binary Numbers | Math Circle |

### Counting: to and then beyond the binomial theorem

October 8th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Richard Askey.** How many ways can zeros and ones be put into n places?
It is easy to see this is 2^n. It is also easy to show that there
are n! ways of ordering n different objects. There are problems
which go beyond these two. How many ways can k zeros and n-k ones be
put into n places? How many inversions are there in the n! ways of
ordering the numbers 1,2,...,n. [123 has no inversions, 132 has one,
312 has two, 321 has three]. These will lead us to what has been
called "The world of q".

### Proofs with Parity

October 8th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Philip Matchett Wood.** Parity---matching objects up in pairs---is a surprisingly useful tool for answering math questions. Bring a pencil and notebook, and we will explore many different situations where parity plays a role.

### Fun Flipping Coins

October 15th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Philip Matchett Wood.** Flip a coin many times, and what happens? A whole mess of cool probability, that what! Bring a notebook, pencil, and some sharp common sense.

### Random walks: how gamblers lose and microbes diffuse

October 22nd, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Saverio Spagnolie.** We will explore one of the most famous mathematical models of random activity, the random walk. After an introduction to some basic ideas from probability, we will see that the same mathematical tools can be used to study completely different types of problems. In particular, we will find that there are no gambling strategies that can be used to beat the casino, and that tiny microorganisms can't stop moving even if they want to!

### Non-Euclidean geometry

October 29th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Beth Skubak.**
Most of the geometry we see in school is based on the ideas of the Greek mathematician Euclid, who lived around 300 BC. While his ideas are pretty useful, we want to consider geometry in some "non-Euclidean" scenarios, like when instead of being flat, our surfaces are curved.

### Rubik's Cubes

November 5th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Mihai Stoiciu.** Rubik's Cubes. Some people describe mathematics as the science of patterns. We will explore patterns, permutations, orientations, and counting with the famous Rubik's Cube.

### Curious Catalan Numbers

November 12th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Alison Gordon.** The Catalan numbers are a sequence that shows up as solutions to all sorts of problems in mathematics. Join us as we count handshakes, match parentheses, and build mountains in order to understand these interesting numbers!

### Tiling Problems

November 19th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Greg Shinault.** Remember tangrams? You know, given some tiles build a specific shape using them. That is an example of a tiling problem, and to some mathematicians they are serious business. We are going to play with a variety of these puzzles, and talk about some of the things that have been figured out about them.

### Binary Numbers

November 26th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Claire Blackman.** We're all used to doing arithmetic with the 10 digits 0 to 9. But there's no reason why we shouldn't use just two digits, 0 and 1, instead. We'll be exploring the world of binary arithmetic, which is based on powers of two.