2011 meeting of the Michigan MAA & MichMATYC

May 6-7, 2011
Western Michigan University (Kalamazoo, MI)

Program information - Locally invited speakers

 

Teena Gerhardt, Michigan State University

"Brussels Sprouts and Bridges: Exploring the Euler Characteristic"
Algebraic topology is a branch of mathematics that uses algebraic objects, such as numbers, to study geometric objects called spaces. The Euler characteristic is one such number that we can associate to a space. For example, a doughnut has Euler characteristic 0, while a basketball has Euler characteristic 2. In this talk we will use a game, a classical problem about bridges, and lots of pictures to explore the Euler characteristic and the field of algebraic topology.

Teena Gerhardt earned her B.S. in mathematics from Stanford University in 2002 and her Ph.D. from MIT in 2007. She is currently an Assistant Professor of Mathematics at Michigan State University and was previously a Zorn Postdoctoral Fellow at Indiana University. Her research is in the field of algebraic topology. Her work uses techniques in equivariant stable homotopy theory to study algebraic K-theory. Gerhardt is also very involved in undergraduate education. At Michigan State she has a joint position, teaching in both the Mathematics department and Lyman Briggs College, a residential undergraduate college within the university.



Michael Merscher, Lawrence Tech University

"Products of Sines"
Degrees as an angle measure is an arbitrary choice, possibly based on ancient Persian observations of the advance of the stars about the celestial pole by about 1/360 of a circle per day. The sine values at degree measures are generally irrational numbers and there is scant reason to believe that the product of these sine values would lead to anything of value. But with a little trigonometry and algebra, we can find a result of such a product to be rather amazing. The final result will evaluate the product of the sine values for angles from 1° to 179°. These topics grew out of a friendly competition in graduate school to see what obscure trig identities could be arrived at through elementary means.

Professor Michael Merscher received his graduate degree from the University of Michigan, and has taught at Lawrence Tech University since then. He is a past chair of the Exam Committee for the Michigan Mathematics Prize Competition. He has been for many years the author of the LTU Annual High School Mathematics Competition. He was named LTU's Faculty Person of the Year in 2003, and was awarded the Mathematical Association of America Distinguished Teaching Award in 2010.



   

David Murphy, Hillsdale College

"Euler's Sum of Like Powers Conjecture: history and related problems"
When can a k-th power be written as the sum of other k-th powers? Euler conjectured that it is impossible to express a k-th power as a sum of fewer than k others, but suggested that it should be possible when you allow k or more summands. If the first part of his conjecture is true, Fermat's Last Theorem would be a special case. In this talk, I will present both parts of this conjecture, give some answers, and ask more questions.

After receiving his Ph.D. from the University of Illinois at Urbana-Champaign in 2004, David Murphy accepted a teaching post-doctoral position at Kalamazoo College for three years. In 2007 he moved to Hillsdale College, another small liberal arts college in southern Michigan, where he is now an assistant professor. His research interests include algebraic groups, invariant theory, and algebraic geometry, as well as elementary number theory. In addition, he is currently the president of Michigan NExT, the Michigan MAA section's Project NExT program.



Jack Rotman, Lansing Community College

"General Education Mathematics: Really Mathematics? Filter or Enabler?" 
Many Michigan universities have a mathematics requirement for a degree, as do several community colleges. An overall analysis of these requirements shows more divergence than convergence, leading to the question:  Are the general education mathematics courses really mathematics? In some cases, the requirements are a subset of the pre-calculus/STEM courses … leading to the question: Are we more interested in filtering students or in enabling students? Behind these questions is a fundamental issue for all of us:  What is "mathematics" in this context … what are the powerful ideas of this mathematics that all students should understand? This talk will begin with some data on our requirements, and proceed to questions that arise. I will articulate a vision for general education mathematics that suggests how we can serve our students better, and we will connect our work to existing professional resources.

Jack has been at Lansing Community College since 1973, with a focus on "developmental" mathematics, and has an MA from Michigan State University. He has been active in the state professional organizations, with multiple presentations at both Michigan-MAA and MichMATYC. Nationally, Jack has contributed to the AMATYC standards (both "Crossroads" and "Beyond Crossroads"), and has chaired the AMATYC Developmental Mathematics Committee twice for a total term of 9 years. Currently, he is leading a project to re-invent developmental mathematics - the AMATYC "New Life for Developmental Mathematics" project, and is involved as a content liaison for the "Pathways Grants" of the Carnegie Foundations for the Advancement of Teaching. Jack seeks to combine an understanding of mathematicians, of college mathematics, and of cognitive psychology to bring a new perspective on mathematics in the first two years.



Ping Zhang, Western Michigan University

"GRAPH THEORY -- 275 Years and Counting"
This year graph theory celebrates its 275th birthday. Although almost
all of the progress in this area of mathematics has taken place
during the 20th and 21st centuries, we take a look at some of the
historical events of this subject that occurred during the 18th and
19th centuries.

Ping Zhang is a Professor of Mathematics at Western Michigan University. She received her Ph.D. in mathematics from Michigan State University in 1995. After one year as a Visiting Assistant Professor at the University of Texas at El Paso, she went to Western Michigan University in 1996 and has been at WMU since then. Her main research interests are in the areas of algebraic combinatorics and graph theory. Ping Zhang has co-authored four books: Mathematical Proofs: A Transition to Advanced Mathematics (second edition), Introduction to Graph Theory, Chromatic Graph Theory, Graphs & Digraphs (fifth edition). She has authored or co-authored over 180 research articles in algebraic combinatorics and graph theory and has given over 60 invited and contributed talks at universities and at regional, national and international conferences. Ping Zhang has directed the dissertations of four doctoral students and is currently supervising the dissertations of two doctoral students.