USA MathStat Graduate Student Seminar Spring 2008


Date 
Speaker 
Topic 
Jan 25  James Douglass 
On the Problem of Partitioning {1,2,...,n} into Subsets having Equal Sums H. Joseph Straight, Paul Schillo Proceedings of the American Mathematical Society, Vol. 74, No. 2. (May,1979), pp. 229231. In this talk I will follow the proof constructed by Straight and Schillo attempting to solve the problem of partitioning {1,2,...,n} into subsets of equal sum. The proof provides us with a sufficient condition for such subsets to exist. We will then use this result to answer a question regarding the existence of evenregular, pathperfect graphs. 
Feb 1  Nhiem Nguyen 
A New Applicable Proof of the Euler Circuit Theorem Alan Tucker The American Mathematical Monthly, Vol. 83, No. 8 (Oct., 1976), pp. 638640. In this note, the author gives an application of this theorem to streetsweeping and, in the process, finds a new proof of the theorem. 
Feb 8  Terry Fulford 
Connected Sprouts Lam, T. K. Amer. Math. Monthly 104 (1997), no. 2, 116119. 
Feb 15  Sarah Gelsinger 
Conway’s ZIP Proof George K. Francis & Jeffrey R. Weeks, December 28, 2000 http://new.math.uiuc.edu/zipproof/ I will discuss a classification of surfaces based on Conway's zip proof. 
Feb 22  James Douglass 
Pascal Matrices Alan Edelman and Gilbert Strang The American Mathematical Monthly, Vol. 111, No. 3 (Mar., 2004), pp. 189197. I will provide several proofs concerning a special result of Pascal matrices and their relation to the unique properties of Pascal's triangle. 
Feb 29  Nhiem Nguyen 
A Curious NimType Game David Gale The American Mathematical Monthly Vol. 81, No.8. Oct.,1974, pp.876879 In this note, the author defines a type of game. He then identifies two cases in which general winning strategies are known. Then, he proves the following theorem: For all m and n the game is a win for P1. Finally, this question, "Is the winning first move unique for all m and n?" is discussed. 
Mar 7  Terry Fulford 

Mar 14  Spring Break 

Mar 21  Sarah Gelsinger 
On the Topology of the Singularities of a Sphere Eversion This is my thesis. I will attempt to explain it to you. 
Mar 28  James Douglass 
A Simple Fact about Eigenvectors That You Probably Don't Know Warren P. Johnson Mathematics Magazine, Vol. 74, No. 3. (Jun., 2001), pp. 227230. In this talk I will discuss an interesting yet simple fact concerning eigenvectors that many have never considered. 
Apr 4  no seminar  
Apr 11  Nhiem Nguyen 
Six Ways to Sum a Series Dan Kalman The College Mathematics Journal, Vol. 24, No. 5 (Nov., 1993), pp. 402421 In this paper the author discusses a single infinite sum, namely, the sum of the squares of the reciprocals of the positive integers. The purpose in this paper is to review several different proofs to this sum a series. However, only 23 of the proofs will be discussed at the seminar. 
Apr 18  Terry Fulford 

Apr 25  Sarah Gelsinger 