Department of Mathematics, WUSTL -
Math Club,  2008-09

Washington University in St. Louis, Cupples I Hall, One Brookings Drive, St. Louis MO. 63130

 

 

Meetings will be in Room 199 in Cupples I.

Talks will run from 5:30 to 6:15, and will be followed by free pizza.

Date: April 20th                                                   Room: 199

Speaker: Richard Rochberg                                 Title: Benford’s Law

 

Abstract: If you go through the first few pages of a newspaper and list all the numbers you find there, what percent of them do you suspect will start with the digit 1? What is the general pattern? What is the history of this observation? What is the theory behind it? Why is the Internal Revenue Service interested?

 

Date: April 6th                                                     Room: 199

Speaker: Andy Soffer                                          Title: Proofs with Pirates

 

Abstract: No, I will not be making any pirate jokes. I will be going through several graph theoretic theorems, and proving them with the help of pirates. We will prove Euler's theorem, Sperner's Lemma (for fairly dividing cake among three pirates), and maybe a few others. Please leave your eyepatches at the door.

 

Date: March 23rd                                                 Room: 199

Speaker: Jimin Ding                                            Title: Is there a discrimination in graduate school admission? -- Simpson's Paradox
 
Abstract: An observational study on sex bias in graduate school admission was done at UC Berkeley in 1973 (Bickel et al. 1975 Science). Among 
8442 male and 4321 female applicants, 44% of men and 35% of women were admitted. Based on a formal statistical test (Pearson Chi-square test),
 the difference in admission rates appears to provide a strong evidence to show that women were unfairly treated in the admission procedure. 
However, when each major looked its own admission data separately, no general bias against women was found. On the whole, in fact there is 
an evidence of bias in favor of women! The puzzle is an example of Simpson's paradox, which will be discussed in this talk. More interesting
 historical examples will be also given and I will interpret the paradox from the probabilistic and geometric point of views.

 

 

Date: February 16th                                             Room: 199

Speaker: Ron Freiwald                                       Title: Calculus without limits
 
 
Abstract:  In the very early days of calculus, for want of something
better, arguments were given that used "infinitesimals" -- numbers assumed
to be positive but "infinitely small." Calculus made rigorous (=
"beginning analysis") didn't arrive until the latter part of the 19th
century, when a careful definition of limits and the real number system
provided the tools to banish infinitesimals. In fact, the definition
finally given for the real number system implies that infinitesimals
cannot exist.
          However, about 1960, a Dutch mathematician named Abraham
Robinson created a new, enlarged number system called the
"hyperreals" -- one that contains the real numbers but where
infinitesimals also exist.  Working inside this new system, we
can do all the standard material of calculus with no limits at
all.
          The construction of the hyperreals is too complicated for us to
discuss, but we will describe this new number system and show
how simple some arguments and definitions become when
infinitesimals are available.
 

 

 

Date: January 26                                                  Room: 199

MOVIE                                                                Title: 21
 
Plot: Students work out how to win lots at Blackjack in Las Vegas.
www.sonypictures.com/homevideo/21/

 

Date: December 1st                                                            Room: 199

Speaker: Al Baernstein                                        Title: You might go home again: Recurrence and transience
                                                                                            of symmetric random walks in the first three dimension
 
Abstract: Suppose you start at the origin of the real line, toss a fair coin, then move  one step to the right or left 
according as the coin falls heads or tails.  Repeat the process, starting from your new position, then repeat again 
and  again, ad infinitum. This process has evident analogues in all dimensions. What is the probability that you 
will ever return to your starting  point? In particular, will you return with probability 1, or is there a  positive 
probability you will never return? We'll see that the answer depends  upon the dimension of the world you live in.
 

 

Date: November 17th                                                          Room: 199

Speaker: Andy Soffer                                          Title: Infinitely many proofs that there are infinitely many primes
 

Date: October 20th                                              Room: 199

Speaker: Joe Bohanon                                         Title: Adventures in Group Theory
 
 

Abstract: Groups are one of the most fundamental tools in mathematics, showing up in nearly every field.  Abstractly, a group is a set with a binary relation that satisfies certain axioms which we will define. We will look at groups that show up naturally, specifically the group that lies underneath a Rubik's cube.  It turns out that solving the Rubik's cube is more-or-less equivalent to a special case of the "word problem".  No prior knowledge of group theory is necessary for this talk

Date: September 29th                                           Room: 199

Speaker: John McCarthy                                      Title: The mathematics of voting, or how to ensure your candidate is democratically elected
 
Abstract: In many elections, the choice of voting system determines the outcome.

 

Date: September 15th

 

Movie: “The Proof”  This is a one hour movie about Andrew Wiles’s proof of Fermat’s last theorem. (Unlike last year, Shubho has checked that we actually have the right movie this time). Afterwards we’ll have pizza (lots) and say words (a few) about the math club.

 

Home: Department of Mathematics at WUSTL . Comments: web@math.wustl.edu, Marie Taris.