Monthly Past, Monthly Present, and Monthly Future (with Apologies to Charles Dickens)
by Scott T. Chapman, Professor and Scholar in Residence at Sam Houston State University, Huntsville, Texas; Editor, The American Mathematical Monthly
For over 115 years, the American Mathematical Monthly has served as Mathematics’ most widely read journal for general audience papers. The Monthly holds a unique niche amongst journals in the Sciences, as its articles are intended to inform, stimulate, challenge, enlighten, and even entertain; Monthly articles are meant to be read, enjoyed, and discussed, rather than just archived. The long history of the Monthly does not just include papers which had signicant impact on both the research and teaching communities, but its articles can be used as a mirror which reflects the trends and attitudes of not only Mathematicians, but academics in general. In this talk, I will briefly cover the history and accomplishments of the Monthly. I shall then look at three papers, one from the past pages of the Monthly, another that has recently been published, and a third which will appear over this coming summer. I will close with a brief discussion of some of the topics fueling the ever changing world of academic publishing.
Cloaking: Where Science Fiction Meets Science
by Graeme W. Milton, Distinguished Professor of Mathematics, The University of Utah, Salt Lake City, Utah
Cloaking involves making an object partly or completely invisible to incoming waves such as sound waves, sea waves or seismic waves, but usually electromagnetic waves such as visible light, microwaves, infrared light, or radio waves. Camouflage and stealth technology achieve partial invisibility, but can one achieve true invisibility from such waves? This lecture will survey some of the wide variety of ideas on cloaking: these include transformation based cloaking, non Euclidean cloaking, cloaking due to anomalous resonance, cloaking by complementary media, active interior cloaking and active exterior cloaking. Beautiful mathematics is involved.
Which Graphs are Coloring Graphs?
by Heather M. Russell, Assistant Professor of Mathematics,Washington College, Chestertown, Maryland
For a simple graph G and a positive integer k, the k-coloring graph of G, denoted Ck (G), is the graph whose vertex set is the set of all proper (vertex) k-colorings of G with two k-colorings adjacent if and only if they differ at exactly one vertex of G. In this talk, we consider the question: which graphs are coloring graphs? We give examples of families of graphs whose members are always, sometimes, and never coloring graphs and discuss techniques useful for investigating this inverse problem. No prior knowledge of graphs is necessary. We will begin with the definition of a graph and give lots of examples along the way! (This is joint work with Julie Beier (Earlham College), Janet Fierson (LaSalle University), Ruth Haas (Smith College), and Kara Shavo (Presbyterian College).)
Embodying Mathematics: Implications for the Teaching and Learning of Mathematics
by Hortensia Soto-Johnson, Professor of Mathematics, University of Northern Colorado, Greeley, Colorado
Embodied cognition adopts the philosophy that the body influences our cognition. In this talk, I will share studies where embodied cognition served as the foundation for mathematics classroom activities and the impact that they had on student learning. Many educators and mathematicians generally associate manipulatives with embodied cognition, but I will share how body movements and gesture can influence the learning of mathematical concepts including proof construction.