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The Program: The story of trigonometry is nothing like the lifeless collection of algorithms seen in high school. It came into being at the birth of science itself --- at the merging of geometrical models of the motions of celestial bodies with the desire to predict where the planets will go. The math itself was much deeper as well, flowing almost seamlessly into numerical analysis (as much as can be done without calculus), and mostly taking place on the surface of a sphere. In the mornings we shall explore the development of trigonometry through the astronomy of Greece, India and Islam, its surprising diversion into geography through the needs of Muslim religious ritual, and the beautiful modern spherical theory pioneered by John Napier alongside his invention of logarithms. In the afternoons we shall explore the forgotten art of spherical trigonometry as conceived by several cultures from ancient to modern times. This will include:
The Lecturer: Glen Van Brummelen is a historian of mathematics, especially trigonometry and astronomy in ancient Greece and medieval Islam. He is past president and current vice president of the Canadian Society for History and Philosophy of Mathematics, and was a senior fellow at the Dibner Institute for History of Science at MIT. In addition to authoring 30 scholarly and 10 encyclopedia articles, he is co-editor of Mathematics and the Historian's Craft (Springer) and recently published the first history of trigonometry in over a century with Princeton University Press called The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Van Brummelen has taught most of the traditional courses in mathematics as well as classes in mathematics and music, mathematics and democracy, mathematics and computer graphics, how to be an ancient astronomer, and spherical trigonometry (an award-winning class, using a 19th-century textbook). A passionate teacher-scholar, Dr. Van Brummelen has dedicated most of his career to teaching in a liberal arts setting, and has successfully guided several students through the process (and publication) of their undergraduate research.
ACTUALLY DOING IT!:A Hands-On Approach to Computational Combinatorial Geometry
Jesús De Loera, University of California, Davis
July 19-24, 2009
St. John's University, Collegeville, Minnesota
Experimental Mathematics in Action: Insight Through Computation
Jonathan Borwein, Dalhousie University
Carleton College, Northfield, MN
July 16-20, 2007
Bioinformatics: Where Mathematics Meets Molecules
Laurie Heyer, Davidson College
University of Minnesota-Duluth, Duluth, MN
July 18-22, 2005
A Tour of Combinatorial Games
Elwyn Berlekamp
Gustavus Adolphus College, St. Peter, MN
August 4-8, 2003
The History of Mathematics
V. Frederick Rickey, United States Military Academy
Bemidji State University, Bemidji, MN
July 24-27, 2001
Counting and Calculus
Richard Askey, University of Wisconsin - Madison
University of Minnesota - Duluth, Duluth, MN
August 9 - 13, 1999
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