USA MathStat Graduate Student Seminar

Spring 2008

The USA MathStat Graduate Student Seminar this semester will meet on Fridays from 9:05 to 9:55 am in ILB 465. Everyone is welcome to attend.

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. 229-231.

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 even-regular, path-perfect 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. 638-640.

In this note, the author gives an application of this theorem to street-sweeping 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, 116--119.

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. 189-197.

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 Nim-Type Game
David Gale
The American Mathematical Monthly Vol. 81, No.8. Oct.,1974, pp.876-879

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. 227-230.

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. 402-421

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 2-3 of the proofs will be discussed at the seminar.

Apr 18 Terry Fulford

Apr 25 Sarah Gelsinger

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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. 229-231. 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 even-regular, path-perfect 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. 638-640. In this note, the author gives an application of this theorem to street-sweeping 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, 116--119.
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. 189-197. 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 Nim-Type Game David Gale The American Mathematical Monthly Vol. 81, No.8. Oct.,1974, pp.876-879 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. 227-230. 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. 402-421 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 2-3 of the proofs will be discussed at the seminar.
Apr 18	Terry Fulford
Apr 25	Sarah Gelsinger