Professor Dave Richeson is one of the most exuberant math people I've gotten to know but I didn't know how exuberant he was until I interviewed him. He's also involved in a bunch of neat projects. It was one of these projects, documented in Dave Richeson's blog article, How I teach topology: an inquiry-based learning approach, that caught my attention since I have a real passion for collaborative learning.
About Dave Richeson
Dave Richeson is an Associate Professor of Mathematics at Dickinson College. He graduated from Hamilton College in 1993 with a degree in mathematics and received a Ph.D. in mathematics from Northwestern University in 1998. He came to Dickinson College after a postdoctoral position at Michigan State University. He is passionate about many areas of mathematics, but his research focuses on dynamical systems, topology, the history of mathematics, and mathematics pedagogy. He is the author of Euler's Gem: The Polyhedron Formula and the Birth of Topology, which was published by Princeton University Press. Euler's Gem received the 2010 Euler Book Prize from the Mathematical Association of America and it was selected by Choice Magazine as an "Outstanding Academic Title" for 2009. He is currently writing a book on the four problems of antiquity. He is editor-elect for Math Horizons, a publication of the Mathematical Association of America. He enjoys sharing his enthusiasm of mathematics with others on his blog (Division by Zero, http://divisbyzero.com) and on Twitter (@divbyzero).
About "Euler's Gem"
From the Princeton University Press web-site:
Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.
From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.
Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.