Department of Mathematics

West Chester University

Mathematics Information
Office: Room 101
25 University Avenue
West Chester, PA 19383
Phone (610) 436-2440
Fax (610) 738-0578
Email: Department Chair

# Spring 2011 Colloquium/Seminar Schedule

Each Thursday there will be a mathematics seminar (usually in UNA 127 from 3:15-4:15), while colloquium talks will normally be on a Wednesday (usually in UNA 158 from 3:15-4:15).

These seminars/colloquium talks may be by visiting speakers, WCU faculty, or WCU students, and are open to all interested students and faculty.

Send an e-mail to jmclaughl@wcupa.edu, if you would like to be on the e-mail list to receive advance notice of upcoming talks.

Thursday, January 25th, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - I

Thursday, February 3rd , 2011
3:15 - 4:15 pm in UNA 161
Dr. Kofi Adragni (University of Iowa) Sparse Principal Fitted Components in High Dimensional Regressions

## Abstract

Principal fi tted components (PFC) models are parametric inverse regression models for sufficient dimension reduction (Cook, 2007). Given a set of p predictors $x \in R^p$ and an outcome Y , PFC yields a reduced set of predictors $R(X) \in R^d; d < p$ such that R(X) retains all the regression information of X on Y . When a number of predictors is inactive in explaining Y , a sparse reduction is sought. We develop a method to obtain the sparse sufficient dimension reduction. It performs variable selection as well as forward linear regression methods like the lasso (Tibshirani, 1996), but moreover, it encompasses cases where the distribution of Y |X is non-normal or the predictors and the response are not linearly related.

Thursday, February 10th , 2011
3:15 - 4:15 pm in UNA 161
Dr. Trent Gaugler (Penn State University) Fully Nonparametric Mixed Effects Models: Testing for the Fixed Main Effect

## Abstract

We present a new nonparametric model for the two-way crossed mixed effects design which allows the random main and interaction effects to be correlated. In this model, we consider testing the hypothesis of no main fixed effects. The asymptotic theory of the test statistic is derived under the Neyman-Scott framework, in the sense that the number of levels of both the fixed and random effects are large but the group sizes can remain fixed. In the non-additive case, the limiting distribution is an infinite weighted sum of independent chi^2 random variables. An approximation to this limiting distribution is proposed. In addition we propose a novel bootstrap test procedure. In the case of an additive model, the limiting distribution of the test statistic is normal. Extensive simulations indicate that the proposed test procedures outperform the classical F and Hotelling's procedures. An analysis of a dataset from the Mussel Watch Project is presented.

Friday, February 11th , 2011
3:15 - 4:15 pm in UNA 125
Dr. Daniel Ilaria Using Questioning (and Technology) to Support Student Engagement and Learning

## Abstract

Currently, mathematics educators argue that teachers should create classrooms where students are engaged in conversation about mathematical ideas. However, to achieve these goals, it is important that teachers understand how to engage students in discussion. I address this issue by attempting to answer two research questions: What kinds of questions do these two mathematics teachers in student-centered settings ask; and to what extent and in what ways did these teachers' questions engage students in mathematical conversation? This main focus of this talk will be to share results of a study that identified teacher questions and student responses, and examined how teachers used questioning to engage students in conversation. I will also briefly share my experiences with technology and the ways technology influences teaching. The combination of my research background and technology experience supports ongoing research that can inform the educational community, particularly future teachers, about student learning.

Monday, February 14th , 2011
3:15 - 4:15 pm in UNA 125
Dr. Rebecca Schmitz (University of Minnesota) Student Learning and Retention of Key Concepts in Sequences and Series

## Abstract

We explore student understanding of key concepts in sequences and series including the understanding of infinite repeating decimals and their connections to infinite series. In addition to talented high school students in honors University calculus, we look at several standard and honors freshman and sophomore calculus and post-calculus courses and examine students' pre- and post-instructional knowledge. The data obtained indicates significantly differing levels of understanding before and after instruction as well as differing levels of gain. These results have implications for the structure and teaching of bridge courses to higher-level mathematics. Finally, there is additional evidence that conceptual approaches to teaching and learning result in better retention of these ideas.

Thursday, February 17th , 2011
3:15 - 4:15 pm in UNA 155
Faye Goldman Using Origami to Teach Mathematics

## Abstract

Origami is the process of folding paper. I will present a seminar defining Origami, presenting a brief history of Origami, and showing how origami touches many fields of study. Mathematical concepts are used to understand the underpinnings of origami science. Teachers can use Origami to teach mathematical concepts at all levels. Origami often looks like play to students, and they love creating three-dimensional objects from flat pieces of paper. At the early levels, simple arithmetic concepts and shape recognition can be taught. Geometry and trigonometry are obvious subject matter for middle to high school level students. Origami has great benefits in college level courses dealing with graph theory and abstract algebra. I will conclude by sharing a simple hands-on lesson.

Wednesday, February 23rd , 2011
3:15 - 4:15 pm in UNA 162
Eric Werley (Lehigh University) Some General Identities on Fibonacci Numbers

Thursday, March 3rd, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - II

Wednesday, March 16, 2011
3:15 to 4:15PM UNA 162
Spring 2011 Computer Science & Mathematics Colloquium RYAN HAYWARD (University of Alberta)

"The Story of Hex"

I will give a brief history of Hex, the classic 2-player connection game, and a report on some recent developments, including a Hex handicap strategy (on the nxn board, the 1st player wins if allowed (n+1)/6 stones on the 1st move), tips on playing Reverse/Misère Hex, and the current state of automated Hex players and solvers.

(This is joint work with Broderick Arneson and Philip Henderson.)

Ryan B. Hayward was raised in Vancouver, Winnipeg and Lethbridge. He attended UBC, transferred to Queen's, and --- after a study/travel/ski hiatus based in Grenoble --- completed a BSc (Queen's math '81) and an MSc (Queen's math '82, supervisors Selim Akland Peter Taylor). He next moved to Montreal --- and Paris for a few months in '84 --- where he completed a PhD on perfect graphs (McGill cs '87, supervisor Vašek Chvátal). In addition to his supervisors, his many teachers include Mr. Oleksy, Mr. Hori, Mr. Kosaka, Walter Gage, Jim Verner, Dan Norman, Jon Davis and David Gregory. Fellow doctoral students include Chính Hoàng, Bruce Reed, and Stephan Olariu. He was an assistant professor (cs) at Rutgers for three years before taking an Alexander von Humboldt fellowship at Bonn. He returned to Canada in '90, and held academic positions at Queen's (cs) and Lethbridge (math/cs) before joining the UofA in '99, where he is currently a professor in the department of computing science. He studies algorithms related to graphs or games. He is particularly interested in the two-player board game Hex, which he learned from Claude Berge. A member of the UofA's GAMES research group, he leads a team --- including Broderick Arneson and Philip Henderson --- that developed a Hex solver and players. The solver has solved half of the 9x9 openings and is stronger than human. The players Wolve ('08) and MoHex ('09, '10) won gold in Hex at the Computer Games Olympiad. He commutes by bike, and once rode solo from Vancouver to Lethbridge.

For further information e-mail mfisher@wcupa.edu

Thursday, March 17th, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - III

Wednesday, March 23, 2011
3:15 to 4:15PM UNA 162
Spring 2011 Mathematics Colloquium MICHAEL ORRISON (Harvey Mudd College)

## "Generalizing the Condorcet Criterion"

The Condorcet Criterion is relatively straightforward: In an election, if there is a candidate that would beat every other candidate in a head-to-head race, then that candidate should be declared the winner. In this talk, I'll describe a natural family of generalizations of the Condorcet Criterion that led us to some unexpected questions and answers concerning forbidden "words of generalized Condorcet winners."

This is joint work with Aaron Meyers, Jen Townsend, Sarah Wolff, and Angela Wu.

Michael Orrison is an associate professor of mathematics at Harvey Mudd College, where he has been since 2001. He received is A.B. from Wabash College, and his Ph.D. from Dartmouth College. His research interests include voting theory and harmonic analysis on finite groups. In particular, he enjoys finding, exploring, and describing applications of the representation theory of finite groups with the help of his talented and energetic research students.
For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu

Thursday, March 24th, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - IV

Wednesday, March 30, 2011
3:15 to 4:15PM UNA 162
Spring 2011 Mathematics Colloquium Hal Switkay (Instructor, West Chester University)

"Multi-Candidate Selection Methods"

Choosing between two alternatives is a simple exercise for groups of voters of any size. Once there are more than two alternatives to choose among, the result of the election may be almost arbitrary, and may reflect the choice of voting procedure more than the consensus of the voters' preferences. This talk will present several examples, both fictitious and historical, to show the weakness of well-known voting methods. We will also examine positive results in decision theory and present one possible algorithm for making a selection among multiple alternatives. This talk should be easily accessible to undergraduates and non-math majors.

Hal M. Switkay earned his Ph.D. in mathematics at Lehigh University in the study of set theory. After graduation, his interests shifted towards symmetry, lattices, groups, and higher-dimensional geometry. He has taught mathematics, from remedial to advanced, has done public speaking, is a musician and composer, and has earned certification as a teacher of Tai Chi Easy™ and as a practitioner of reiki and Thai massage. He is currently enrolled in West Chester University’s graduate certificate program in applied statistics. His business card lists the following interests: mathematics; music; philosophy; health and wellness; and syncretic panendeism.

Thursday, March 31st, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - V

Thursday, April 7th, 2011
3:15 - 4:15 pm in UNA 120
Professor Lin Tan (West Chester University) "Why we are interested in representations of groups."

Thursday, April 14th, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - VI

Thursday, April 21st, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - VII

Thursday, April 28th, 2011
3:15 - 4:15 pm in UNA 120
Professor Peter Zimmer (West Chester University) Dirichlet Characters and Group Representations - VII