Abstracts of Invited Talks
Abstract: We will examine some female contemporaries of Leonhard Euler (1707 - 1783) — some famous, some not so famous. We will also look at mathematics that was written both by and for women in the time of Euler.
Biography: Betty Mayfield is the current 1st Vice President of the MAA. She earned a B.A. in mathematics from the University of North Carolina at Greensboro and an M.S. and Ph.D. from the University of Rhode Island. Between undergraduate and graduate school, she taught high school mathematics.
Since 1979, Mayfield has served on the faculty of Hood College in Frederick, Maryland, where she has chaired the mathematics department since 1999. She has enjoyed doing research, often with students or colleagues in other disciplines, in underwater acoustics, mathematics pedagogy, and the history of mathematics.
She became involved in the MAA first in the Maryland-DC-Virginia Section, and enjoys attending meetings in other Sections and learning about them. She is also proud to be a consultant for Project NExT.
Abstract: Briefly, Voltaire wrote a story based upon a 1735—6 French scientific expedition to test Newton's claim that the earth was flattened at the poles. The main character is an exiled alien 23 miles tall who encounters a shipload of mathematicians returning from taking measurements at the arctic circle; at the end of their discussion he gives them a book containing the answers to all questions; but upon examination the book is blank. My talk is a case study of how mathematical/scientific knowledge becomes common knowledge. The talk includes some of the mathematics of this polar expedition; why, some 50 years after Newton's Principia, the French mathematical community were still hesitant in accepting Newton's conclusions; why the giant is so tall; and why the book is blank. Most of my talk will be accessible to any undergraduate math major.
Biography: Andrew J. Simoson is originally from Minnesota, earned a B.S. in mathematics in Oklahoma, and then a Ph.D. in mathematics in Wyoming, met his wife in New York, and raised two sons in Tennessee. He has twice been a Fulbright professor, one year (1990) at the University of Botswana in Gaborone, located at the edge of the Kalihari Desert, and another year (1997) at the University of Dar es Salaam in Tanzania near the equator on the Indian Ocean.
For thirty years, he has been the chairman of the mathematics and physics department at King College, located in the foothills of the Appalachian Mountains. By providence and good luck, he has won the Chauvenet Prize in 2007 and the George Polya Award in 2008. He has authored two books, both in the MAA's Dolciani series, Hesiod's Anvil: Falling and Spinning through Heaven and Earth (2007), and Voltaire's Riddle: Micromegas and the Measure of All Things (2010). Besides trying to be a mathematician, he and his wife teach ballroom dance as a college activity class each spring term, and go scuba diving for at least a week each summer, usually in the Caribbean.
Abstract: As we study mathematics we are inundated with examples. Every definition in every textbook is followed by examples to show what the definition means. However, there are a lot more interesting objects out there than are typically shown to students. In this talk, we will look at some of the many interesting and exceptional examples out there. Along the way we will talk a little bit of math history, contstruct a bunch of examples (mostly subjects one sees in calculus or intermediate algebra), and give a lot of encouragement for students to find some topic to work on their own.
Abstract: High-speed digital communications must anticipate the possibility of channel errors in transmission. Nontrivial mathematical approaches to this date back to 1948, and constitute the subject of Algebraic Coding Theory. The principle of using the coefficients of polynomial remainders as a checksum to detect errors goes back to at least 1961; this idea blended well with the technology of shift registers, and is used in everything from the GPS system to the internet. Advances in modern technology such as Field Programmable Gate Arrays (FPGA), allows for very efficient vector addition of long binary inputs, and open new possibilities.
This talk will explain CRC checksums from first principles, show how abstract algebra plays a pivotal role, and finally, present a new mathematical algorithm (developed at NSA) to process them. Although the approach will be explained with some simple linear algebra, it implicitly takes advantage of an underlying quotient-ring context that is usually ignored. Potential advantages for FPGA use will be discussed.
Suggested background: Linear Algebra