ITLApplied  Computational Mathematics Division
ACMD Seminar Series
Attractive Image NIST

In conjunction with DLMF Seminar Series

Complex Mappings From an Evolutionary Viewpoint

Steve Casey
Department of Mathematics and Statistics, American University

Tuesday, April 2, 2002 15:00-16:00,
Room 145, NIST North (820)
Tuesday, April 2, 2002 13:00-14:00,
Room 4550

Abstract: The graph of a complex-valued function of a complex variable lives in four real dimensions. Given that we only live in three spatial dimensions, visualization is tricky. The talk shows us how we can use our fourth dimension - time - as a tool to help us understand complex functions. We watch a given function evolve in time, starting from the unaltered complex plane and ending with the range of the function. Mathematically, this deformation of the function is a homotopy, from the identity to the target function. The computer provides us with an ideal tool to see this evolution. We compute a frame-by-frame movie of the evolution off-line, and show it at relatively high speed, giving the appearance of a continuous deformation. This new approach of teaching complex functions appears to lead not only to a much quicker, but also to a much deeper, understanding of complex functions. The talk will present excerpts of the computer projects used by students in the complex variables class at American University, and a discussion on how this new learning tool interfaces with a traditional complex class. We close by exploring some of the more visually stunning aspects of complex variables, from views of infinity on the Riemann sphere, to Escher's tilings of the Poincare disk.
Contact: B. V. Saunders

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

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Last updated: 2011-01-12.