# Invited Speakers

## John Adam, Ph.D.

Department of Mathematics & Statistics, Old Dominion University. Norfolk, VA

**Talk Title** (Thursday 6/23, 8:00 - 9:00 p.m.)**:** *Mathematical Patterns in Nature*

**Abstract:** What aspects of nature do you notice when you are outside during the day? Whether we live in the country, suburbia or the city, it is probable that we will notice a variety of trees, different types of clouds, birds and flowers, or waves on bodies of water (or at least puddles!). This presentation will include many color photographs of naturally-occurring patterns. Such patterns can be fascinating, intriguing, and frequently very beautiful, and are exhibited. For example, in rainbows, ice crystal halos, sundogs, waves, sunflowers and daisies, pinecones, spider webs, clouds, trees, river meanders, mountain shadows, glitter paths and sunbeams, to name but a few! Only the most elementary of mathematical features will be identified in this general talk, but the patterns are accessible to anyone with a love of nature, and a willingness to look up, down or around! [It is recommended that this not be done, however, while driving or operating heavy machinery :) ]. So: when you are outside, look for patterns, look for the way that the light displays what you see, and bask in the mathematical beauty of nature, at no matter what scale.

**Brief Biography: **John Adam is the Designated University Professor of Mathematics (for excellence in teaching) at Old Dominion University. He has held teaching and research positions at University of Sussex, England; University of St. Andrews, Scotland; concurrent positions at New University of Ulster and Dublin Institute of Advanced Studies, Ireland; he was a Fulbright Scholar and Visiting Professor in the Department of Mechanical Engineering at University of Rochester; and, since 1984, has been at Old Dominion University, Virginia. His areas of interest and research have included a wide range of fields, including wave theory, astrophysics, mathematical physics, mathematical biology, applications of mathematics to medicine, and meteorological optics.

He has, at least, 95 publications in a wide variety of journals and has published four books, one of which, *Mathematics in Nature: Modeling Patterns in the Natural World*, was winner of The Association of American Publishers Mathematics and Statistics Professional/Scholarly Award and one of *Choice*'s Outstanding Academic Titles for 2004. Another book, *Guesstimation: Solving the World's Problems on the Back of a Napkin*, which he co-authored with Lawrence Weinstein, presents "an eclectic array of estimation problems that range from devilishly simple to quite sophisticated and from serious real-world concerns to downright silly ones." In his latest book, *A Mathematical Nature Walk, *John "presents ninety-six questions about many common natural phenomena--and a few uncommon ones--and then shows how to answer them using mostly basic mathematics."

John Adam was the winner of the 2007 Outstanding Faculty Award for the State of Virginia. According to the web site for the State Council of Higher Education for Virginia (SCHEV), the Outstanding Faculty Awards are the Commonwealth's highest honor for faculty at Virginia's public and private colleges and universities. These awards recognize superior accomplishments in teaching, research, and public service.

To find out more about John Adam, go to http://www.odu.edu/~jadam/index.html

## David Bressoud, Ph.D.

Department of Mathematics,Statistics and Computer Science, Macalester College, Saint Paul, Mn

**Talk 1 Title **(Friday 6/24, 9:15 - 10:15 a.m.)**:** *Issues of the Transition to College Mathematics*

**Abstract:** 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 60,000 to 600,000, and continues to grow at 6% per year. We have passed 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. In theory, this should be an engine for directing more students toward careers in science, engineering, and mathematics. In fact, it is having the opposite effect. This talk will present what is known about the effects of this growth and what needs to happen in response within our high schools and universities.

**Talk 2 Title **(Friday 6/24, 8:00 - 9:00 p.m.)** :** *The Truth of Proofs *

**Abstract:**Mathematicians often delude themselves into thinking that we create proofs in order to establish truth. In fact, that which is "proven" is often not true, and mathematical results are often known with certainty to be true long before a proof is found. I will use some illustrations from the history of mathematics to make this point and to show that proof is more about making connections than establishing truth.

**Brief Biography: **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*.

To find out more about David, go to http://www.macalester.edu/~bressoud/

## Karen Seyffarth, Ph.D.

Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada

**Talk Title** (Thursday 6/23, 8:00 - 9:00 p.m.)**:** *Colorful Graph Theory*

**Abstract: **Graph coloring has a long history, and provides a rich source of interesting problems, often with practical applications. In it's simplest form, graph coloring is concerned with assigning colors to the vertices of a graph *G* so that adjacent vertices receive different colors, and such that the total number of colors used is minimum. This minimum is the *chromatic number* of *G*, denoted *Χ*(*G*). Arguably, the most famous graph coloring problem is the *Four Color Problem* which asks whether or not every planar graph is 4-vertex-colourable (c1852), i.e., whether or not *Χ*(*G*)≤4 for any planar graph *G*. Often, the Four Color Problem is stated in an equivalent form: can the countries of any map be colored with four colors in such a way that any two countries that share a border receive different colors?

One of my current interests is a variation on the chromatic number called the *distinguishing chromatic number*, first introduced in a 2006 article by Karen Collins and Ann Trenk. A coloring of the vertices of a graph *G* is *distinguishing* provided no automorphism of *G*, other than the identity, preserves the colors of the vertices. Thus a distinguishing coloring of the vertices of a graph is a way of destroying the symmetries of the graph. The *distinguishing chromatic number* of *G*, denoted *Χ*_{D}(*G*), is the minimum number of colors required to color the vertices of *G* so that the resulting coloring is distinguishing. I will be presenting some results concerning the distinguishing chromatic number, and providing many examples to illustrate these results. In addition, I will discuss the related concept of the *distinguishing number* of a graph, which involves labelling the vertices of a graph so as to destroy nontrivial automorphisms, but not requiring the labels on adjacent vertices to be distinct. Determining the distinguishing number of a graph turns out to be a generalization of the problem *The Blind Man's Keys* posed by Frank Rubin in a 1979 issue of the *Journal of Recreational Mathematics*.

**Brief Biography: **Karen Seyffarth is an Associate Professor in the Department of Mathematics and Statistics at the University of Calgary, in Alberta, Canada. She received her Ph.D. from the Department of Combinatorics and Optimization at the University of Waterloo in 1990, and arrived at the University of Calgary in 1992, after completing a post-doctoral fellowship at Simon Fraser University.

Karen's research is in the area of combinatorial mathematics, with a focus on graph theory. Her research programme encompasses a variety of problems that involve graphs with well defined structure, such as planar graphs, graphs with fixed diameter or maximum degree, graph products, and line graphs. She has published articles about path and cycle covers of graphs, dominating sets in graphs, and constructions of graphs with fixed diameter and maximum degree. Recently, her interest has been directed towards graph coloring. This is a rich and diverse area in graph theory, ideal for experienced researchers and students alike.

Karen's passion for graph theory stems from the fact that many problems can be simply and elegantly stated, yet the solutions to some of these problems involve complex and sophisticated techniques. The beauty lies in the fact that even though the solutions may not be readily accessible, the problems themselves are often easily accessible. One of the prime examples of this is the famous Four Color Problem, which is thought to date back to the 1850s, and whose correct solution, the Four Color Theorem, did not emerge until 1976. Many graph-coloring-type problems provide wonderful opportunities to experiment and explore mathematics without becoming overly burdened with terminology and notation.

Karen gave her first conference presentation at the *Thirteenth Conference on Numerical Mathematics and Computing* at the University of Manitoba while still an undergraduate student, and has delivered many research talks since then. She has held research grants from the *Natural Sciences and Engineering Research Council of Canada*, and is currently supervising three graduate students. Karen has also been the Managing Editor for the e-Journal *Contributions to Discrete Mathematics* since 2007.

Outside of mathematics, Karen is an enthusiastic hiker and an avid runner. She ran her first marathon in 2001, and has since completed 10 more, including the Boston Marathon in 2006. Her PB in the marathon is 3 hours, 36 minutes, 48 seconds.

To find out more about Karen, go to http://math.ucalgary.ca/profiles/karen-seyffarth