Invited Talks

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2009/10 MAA Polya Lecturer

Judy Walker is Professor and Graduate Chair at the University of Nebraska-Lincoln. Her main research interests are in algebraic coding theory, and her current work focuses primarily on codes on graphs. She has also studied connections between coding theory and both algebraic geometry and number theory. She is co-founder of the Nebraska Conference for Undergraduate Women in Mathematics and an editor for the Journal of Pure and Applied Algebra, Advances in Mathematics of Communications and the Rose-Hulman Undergraduate Math Journal.

2009 Burton W. Jones Distinguished Teaching Award Recipient

Richard Grassl received his BA in mathematics from Santa Clara University and his graduate degrees from The University of Oregon and The University of New Mexico. After teaching at the U.of San Diego, UNM and as the Truman Koehler Prof. of Mathematics at Muhlenberg College in Pennsylvania he was appointed Chair of Mathematics at The University of Northern Colorado. After 14 years as chair, and several semesters as assistant dean of the newly formed College of Natural and Health Sciences he has returned to full time teaching and research at UNC.
His 42 years in higher education has resulted in numerous publications in both mathematics (conbinatorics) and mathematics education, participation in a major NSF teacher enhancement grant, undergraduate research projects, and mentorship of talented secondary students through his involvement in statewide mathematics contests, first at UNM and now at UNC. Through the development of problem solving seminars he helped coach the UNM Putnam team to a ranking of #20. He started and has directed for the past 18 years the UNC Statewide Mathematics Contest for students in grades 7-12. Participation has grown from 150 initially to over 2200 recently.
Following the reception of teaching awards at UNM, Dr. Grassl earned college awards in three areas at UNC: Teaching , Research and Leadership.

MAA National Featured Speaker

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and President of the Mathematical Association of America. He served in the Peace Corps, teaching math and science at the Clare Hall School in Antigua, West Indies before studying with Emil Grosswald at Temple University and then teaching at Penn State for 17 years. He chaired the Department of Mathematics and Computer Science at Macalester from 1995 until 2001. He has held visiting positions at the Institute for Advanced Study, the University of Wisconsin-Madison, the University of Minnesota, Université Louis Pasteur (Strasbourg, France), and the State College Area High School.

David has received the MAA Distinguished Teaching Award (Allegheny Mountain Section), the MAA Beckenbach Book Award for Proofs and Confirmations, and has been a Pólya Lecturer for the MAA. He is a recipient of Macalester's Jefferson Award. He has published over fifty research articles in number theory, combinatorics, and special functions. His other books include Factorization and Primality Testing, Second Year Calculus from Celestial Mechanics to Special Relativity, A Radical Approach to Real Analysis (now in 2nd edition), A Radical Approach to Lebesgue's Theory of Integration, and, with Stan Wagon, A Course in Computational Number Theory.

David has chaired the MAA special interest group, Teaching Advanced High School Mathematics as well as the AP Calculus Development Committee and has served as Director of the FIPSE-sponsored program Quantitative Methods for Public Policy.


Codes on graphs: Shannon's challenge and beyond
Judy Walker, University of Nebraska, Lincoln
2009/10 MAA Polya Lecturer

Whenever information is transmitted across a channel, errors are bound to occur. It is the goal of coding theory to find efficient ways of adding redundancy to the information so that errors can be detected and even corrected. Coding theory began in 1948 with Shannon's groundbreaking result that efficient, reliable transmission of information is possible. This result was existential rather than constructive, however, and the challenge over the past half century has been to actually find the codes that Shannon proved must exist. In the past 10-15 years, it has been shown that certain graph-based codes come close to achieving Shannon capacity. Even with these recent advances, however, it is not clear whether Shannon's challenge has truly been answered. We will discuss the current situation as well as what the next big problems are for the field of coding theory.

The ah Ha moment
Richard Grassl, University of Northern Colorado
2009 Burton W. Jones Distinguished Teaching Award Recipient

Well designed problem solving episodes often elicit such moments from a broad range of audiences ranging from secondary students , to mathematics majors, and to inservice teachers; for example, the nice 10th grade problem: How many positive integers are there whose digits are in strictly increasing order ( like 2478)? has an unexpected ah ha moment. Sometimes the presence of multiple disparate solutions ultimately yields the defining ah ha moment as often occurs with the following type of question: Verify that

( m+n
)-( m
)-( n
) =mn.
Several such episodes will be highlighted as they have manifested themselves in my involvement over the years with problem solving courses for elementary and for secondary teachers ( both preservice and inservice), with undergraduate research projects, and with the UNC Statewide Mathematics Contest. A brief presentation of the history, philosophy and results of the past 18 years of this contest will further illuminate how the trio Teaching – Research – Mentoring are intimately related.

Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture
David Bressoud, Macalaster College

What is the role of proof in mathematics? Most of the time, the search for proof is less about establishing truth than it is about exploring unknown territory. In finding a route from what is known to the result one believes is out there, the mathematician often encounters unexpected insights into seemingly unrelated problems. I will illustrate this point with an example of recent research into a generalization of the permutation matrix known as the "alternating sign matrix." This is a story that began with Charles Dodgson (aka Lewis Carroll), matured at the Institute for Defense Analysis, drew in researchers from combinatorics, analysis, and algebra, and ultimately was solved with insights from statistical mechanics. This talk is intended for a general audience and should be accessible to anyone interested in a window into the true nature of research in mathematics.

Calculus as a High School Course
David Bressoud, Macalaster College

Over the past quarter century, 2- and 4-year college enrollment in first semester calculus has remained constant while high school enrollment in calculus has grown tenfold, from 50,000 to 500,000, and continues to grow at 6% per year. We have reached the cross-over point where each year more students study first semester calculus in US high schools than in all 2- and 4-year colleges and universities in the United States. There is considerable overlap between these populations. Most high school students do not earn college credit for the calculus they study. This talk will present some of the data that we have about this phenomenon and its effects and will raise issues of how colleges and universities should respond.