University of Wisconsin - Madison
Undergraduate Math Club

Abstract: : The theory of integer partitions is a subject of much interest, and filled with the true romance of mathematics. A partition of a positive integer n is a way of writing n as a sum of positive integers. One might ask: how many ways can this be done? We will discuss various results about partitions ranging from classical identities to very recent theorems.

Speaker: Marie Jameson
When: Monday, November 23, 4:35 p.m.
Where: Room 901 Van Vleck.

Abstract: In how many essentially different ways can the six faces of a cube be colored with n colors? Because of the symmetry of the cube, the answer is much smaller than the obvious n^6. It is this symmetry that makes the problem difficult, but the mathematical language used to discuss symmetry provides a solution. This language is called "group theory", but no previous knowledge of groups is necessary in order to understand this talk. Everything necessary, to solve this problem and others like it will be explained.

Speaker: Martin Isaacs
When: Monday, November 16, 4:35 p.m.
Where: Room 901 Van Vleck.

Abstract: Why is a doughnut different from a ball, but the same geometric space as a coffee-cup? Well, count the number of handles! I'll present a linear algebra construction called homology which formalizes this answer, and gives us a tool to distinguish between curved geometric spaces. A number of applications, both within geometry and outside, will be given; finally, if time permits, I'll try to introduce derived categories, a mathematical device which has been getting a lot of press lately because of conjectures in physics and representation theory.

Speaker: Sukhendu Mehrotra
When: Monday, October 26, 4:35 p.m.
Where: Room 901 Van Vleck.

Abstract: At a game show the contestant can win any one of 20 possible prizes. The prizes are shown one by one (in a random order) and the contestant must accept or reject the prize on the spot (she cannot go back and change her mind). There is a clearly defined ordering between the prizes and the contestants aim is to choose the best prize out of the 20. Unfortunately, the list of prizes is not known beforehand, so she can only compare any given prize with the ones she has already been shown. If the contestant takes home the prize that was shown first then she has a 5% chance of winning. Can she do any better? What should be her strategy to have the highest probability of winning? How will the probability of winning behave as the number of prizes goes to infinity? Free Pizza will be served.

Speaker: Benedek Valko
When: Monday, October 5, 4:30 p.m.
Where: Room 901 Van Vleck.

Abstract: We will kickoff this year with officer elections and ideas for the talks this year. Anyone interested in running for a position or simply interested in the math club is welcome to attend. Free Pizza will be served.

When: Monday, September 21, 4:30 p.m.
Where: Room 901 Van Vleck.

Abstract: In the meeting, we will count some more and prove some well known math results such as the formula for the geometric series, the infitude of primes, and Fermat's little theorem. Come and see why Proofs by Counting are appealing.

Speaker: Ali Godjali
When: Monday, May 4, 4:30 p.m.
Where: Room B139 Van Vleck.

Abstract: Who is Srinivasa Ramanujan? With virtually no formal training in mathematics, it's a wonder that renound English number theorist G.H. Hardy "discovered" the man behind hundreds of pages of scribbled formulas, some so deep that they remained a mystery for decades. Learn more about the legacy of mathematics surrounding this young visionary, and his influence on fundamental areas of present day mathematical research in number theory, combinatorics, and modular forms.

Speaker: Amanda Folsom
When: Monday, April 27, 4:30 p.m.
Where: Room B139 Van Vleck.

Abstract: I'll will give a very basic overview of two problems: 1. How can we pack oranges into a box as tightly as possible? 2. How can we reliably send a signal in a noisy environment and be sure that the target receives the message exactly as we sent it? The point of the talk is the surprising fact that 1 and 2 are essentially the same problem.

Speaker: Jordan Ellenberg
When: Monday, April 13, 4:30 p.m.
Where: Room B139 Van Vleck.

If you haven't come to a Math Club event yet, this is your chance! Come chat with other math junkies, meet the Math Club officers, and find out what we're all about! Food will be provided by Jamerica, but we also encourage everyone to bring a dish to pass (even if it's just chips, soda, or cookies!) Don't have a dish to bring? We still want you there!

What: MathClub Movie Night
When: Thursday, April 2, 7:00 p.m.
Where: Ninth Floor Lounge, Van Vleck.

This talk will provide a gentle introduction to the topic of Markov chain Monte Carlo (MCMC) and apply this computational tool to the problem of estimating gorilla divergence times from individual DNA sequences. MCMC is a computer-based simulation tool for taking dependent samples from general probability distributions. I will aim to provide the audience with an intuitive understanding of how MCMC works, a description of the most common form of an MCMC proposal algorithm, and a brief explanation of the theoretical justification for the methods.

Speaker: Bart Larget
When: Monday, March 30, 4:30 p.m.
Where: Room 901 Van Vleck.

As the name implies, group rings are a meeting place for group theory and ring theory. They serve as a tool in group theory and in ring theory, and they are interesting, easily defined, objects in their own right. In this talk, I will quickly explain how group rings are defined and briefly mention some applications. For the most part, I will discuss how group rings of infinite groups are studied, including some of the successes and also some open, quite difficult, problems.

Speaker:Donald Passman
When: Monday, March 2, 4:30 p.m.
Where: Room 901 Van Vleck.

All of us have grown up doing puzzles. But, did you know that your body works by matching the geometries of molecules? For example, this is how you become immune to a disease. Your immune system works to create a shape that is a match to the invader. I will talk about how mathematics can be used to understand molecular geometry, and how understanding this geometry can be used to design new cancer drugs and other useful molecules. Along the way, you will learn what a gene really is and why mutations in our genes can cause diseases. I will try to describe everything in basic, intuitive terms and hope that anyone with an interest in math and science will enjoy the lecture.

Speaker:Julie Mitchell
When: Monday, February 16, 4:30 p.m.
Where: Room 901 Van Vleck.

Elections were held on Monday the 24th for the offices of President, Vice President, Activities Chairs, Treasurer, and Webmaster. The results are as follows:

08 Math Club Officers

President - Tess Anderson

VicePresident - Ruth Stoehr

Activities Chairs - MengMeng Chen and Zhizhong Pang

Treasurer - Daniel Lecoanet

PR Chair - Sally Wolfe

Web Master - Sean Finley

In a room with sufficiently many (18) people there are four people who either all know each other or are all do not know each other. This is an instance of Ramsey's Theorem. There's also an infinite version of Ramsey's Theorem, which says that if you could put infinitely many folks in a room, then an infinite subset of them would either all know each other or all not know each other. It turns out we can prove both versions of Ramsey's Theorem using nonstandard natural numbers. Nonstandard numbers are infinite numbers that act just like finite numbers because they don't know they're infinite. However, we know they're infinite, and we'll use that to our advantage. Pizza.
Speaker: David Milovich
When: Monday, November 10, 4:30 p.m.
Where: Room 901 Van Vleck.

A Famous Theorem of Kenneth Arrow (a Nobel Laureate in Economics) says that it is impossible to have a fair election among three or more candidates. More precisely, there is no election procedure which satisfies certain principles of fairness that we will make precise in the talk. The proof consists in showing that, given an election procedure, the aforementioned fairness principles imply that a certain family of subsets of the electorate is an ultrafilter (this is not a type of coffee filter). Click here for a partially written exposition of the talk. We will eat pizza as we consider the ramifications for the upcoming election!
Speaker:Prof. Joel Robbin
When: Monday, October 27, 4:30 p.m.
Where: Room 901 Van Vleck.

What is the probability that a truly random positive integer is prime? How about square? Squarefree? You may be familiar with the divergence of the harmonic series, but what can we conclude about the reciprocal sum of various subsets of integers? These questions and more will be answered, intuition will be both confirmed and betrayed, and still more mysteries will be left open as we explore the intricacies of the most elementary infinite set in all of mathematics. This material is completely accessible to anyone with a working knowledge of elementary sequences and series, and you must like free pizza.
Speaker:Alex Rice
When: Monday, October 13, 4:30 p.m.
Where: Room 901 Van Vleck.

Have you ever noticed that long extension cords are twisted many times? There is a mathematical problem that is closely related to this phenomenon and whose solution is illustrated in this sequence. In the talk the details will be provided, along with FREE PIZZA!! Click here for a longer description of the talk.
Speaker:Prof. Alexandar Jurisic
When: Monday, Sept. 29, 4:30 p.m.
Where: Room 901 Van Vleck.

Think you know how? Come and find out, and enjoy some free pizza! Here is the poster.
Speaker:Prof. Fedor Nazarov
When: Monday, Sept. 15, 4:30 p.m.
Where: Room 901 Van Vleck.