The Mathematical Association of America Maryland-District of Columbia-Virginia Section

The Spring 2016 Meeting of the MD-DC-VA section of the MAA was held at the Germantown campus of Montgomery College, on April 15-16, 2016.

On Friday, Laurie Lenz of Marymount University ran a workshop entitled Introduction to Process Oriented Guided Inquiry Learning (POGIL) in Mathematics Classrooms, and John Adam of Old Dominion University giae the banquet address, Rays, Waves and Rainbows: A brief tour through some mathematical history.

The Saturday morning address, A Potpourri of Mathematics in Popular Games, was given by David Taylor of Roanoke College, and the Saturday Afternoon Address, The ART of Tomography, was given by Timothy Feeman of Villanova University.

Laurie Lenz

Friday workshop: Introduction to Process Oriented Guided Inquiry Learning (POGIL) in Mathematics Classrooms

Abstract: A pressing question for the improvement of education is, “If not lecture, then what?” There has recently been much research into inquiry-based learning (IBL) as a way to engage and stimulate student interest in many disciplines, including mathematics. This workshop will introduce faculty to an IBL method of instruction called POGIL (Process Oriented Guided Inquiry Learning). The workshop will provide participants with a basic introduction to facilitation techniques and insight into the structure of a POGIL activity. Participants will use hands-on methods to learn the crucial elements in a successful guided inquiry classroom.

Biographical Sketch: Laurie Lenz is a Professor in the Department of Mathematics at Marymount University in Arlington, VA, just outside Washington D.C. She received an NSF grant to support scholarships for undergraduate STEM majors and another to develop inquiry-based learning materials for gateway courses in mathematics which has resulted in the publication of a book of calculus activities. She has co-directed several multi-day workshops and mini-courses on active learning in the mathematics classroom and she currently serves as chair of the math department. Her research interests are in mathematics education.

John Adam

Banquet Address:Rays, Waves and Rainbows: A brief tour through some mathematical history.

Abstract: Rainbows are exquisitely beautiful both optically and mathematically. This very informal (and rainbow-illustrated!) talk will be an attempt to summarize some of the history of 'rainbow theory' from the time of Descartes and Newton onwards. This will involve us in some elementary geometry, trigonometry and calculus to the more sophisticated treatment of the ‘rainbow integral’ (related to Airy functions) introduced by Sir George Biddle Airy, in his celebrated 1838 paper “On the Intensity of Light in the Neighbourhood of a Caustic”. But the theory of the rainbow was not placed on a completely satisfactory mathematical basis until the mid-1970’s, when, via the theory of complex variables, deep connections were made with this beautiful optical phenomenon and molecular, atomic and nuclear scattering theory. Most recently, the theory of diffraction catastrophes has played a role in the understanding of multiple bows of various orders. There are many connections here with ‘deep’ mathematics (at least they are deep as far as the speaker is concerned!)

Biographical Sketch: Dr. John Adam has been Professor of Mathematics at Old Dominion University since 1984. His Ph.D. from the University of London was in theoretical astrophysics (an exceedingly long time ago). He has broad interests in mathematical modeling and applied mathematics, ranging from mathematical biology to meteorological optics. He is a frequent contributor to Earth Science Picture of the Day). In 2007 he was winner of an Outstanding Faculty Award for the State of Virginia. In 2012 he was a recipient of a Carl B. Allendoerfer Award from the Mathematical Association of America (MAA). The Award is made to authors of expository articles published in the MAA journal Mathematics Magazine. He has written several books (all published by Princeton University Press): Mathematics in Nature: Modeling Patterns in the Natural World, X and the City: Modeling Aspects of Urban Life and A Mathematical Nature Walk. He is also co-author (with physicist Lawrence Weinstein) of Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. His latest book, Rays, Waves and Scattering: Topics in Classical Mathematical Physics should be published in Fall 2016.

David Taylor

Saturday Morning Address:A Potpourri of Mathematics in Popular Games

Abstract: Mathematics plays an ever-increasing role in today's world, whether it be in modeling complex processes in the body, predicting winners for March Madness, or showing that a particular chemistry study has validity. Mathematics can also be used to study many games where random chance, perhaps through the rolls of dice or the drawing of cards, plays a role, providing a way to make decisions that advance your quest to win. While a quick read of any introduction to probability book can provide the basis of rolling a few dice or grabbing a few cards, topics such as multinomial coefficients, stochastic matrices, and integer partition analysis are neat, easily understood, topics that can advance our study and understanding of games; in this talk, we apply these topics to games such as Yahtzee, Monopoly, and Blackjack. The speaker reserves the right to add more games and mathematical topics as his whimsical mind allows.

Biographical Sketch: Dr. David Taylor is an Associate Professor of Mathematics at Roanoke College where he has been teaching since the fall of 2007. He holds his Ph.D. and M.S. in mathematics from the University of Virginia and his Bachelor's degree in both mathematics and computer science from Lebanon Valley College. In the spring of 2012, he was awarded the Dean's Exemplary Teaching Award as a result of his ability to "make mathematics fun again," according to his students, balancing the desire to have energetic and enthusiastic classes with maintaining high standards of learning and teaching. He currently serves as chairperson for the Department of Mathematics, Computer Science, and Physics and most recently published a textbook, The Mathematics of Games: An Introduction to Probability (Taylor & Francis/CRC Press, 2015), that is based on a class he developed for Roanoke's "Intensive Learning" May Term that focuses on combining hands-on probability with the development of mathematical ideas and formulas stemming from natural questions people ask about games. In his personal life, he happens to own over 70 board, card, and dice games, and loves playing these games with his friends (and studying the mathematics that often drives him to success and his friends less so). He loves to travel and spend time outside, recently discovering new hiking destinations and enjoying the winter on the slopes, using his new snowboard.

Timothy Feeman

Saturday Afternoon Address:The ART of Tomography

Abstract: We will look at how an algorithm from linear algebra, called Kaczmarz's Method, can be used to create a CAT scan image from X-ray data.

Biographical Sketch: I received my doctorate in Mathematics at The University of Michigan, in 1984, under the supervision of the late Allen L. Shields. I have been on the Mathematics and Statistics faculty at Villanova University since 1986. My research interests have ranged from operator theory and functional analysis to cartography, medical imaging, and, lately, statistical problems related to ranked set sampling. My favorite courses to teach are advanced calculus and linear algebra. My best score on the Putnam Math Competition was 20, despite which I have been the faculty advisor for Villanova's Putnam team for quite a few years now. My Erdos number is 2. For fun and fitness, I am an avid cyclist and a devotee of the London Times Cryptic Crossword.