“Calculus: Have we Been Teaching it Wrong?”

Nicol Hall, Room 222, Beirut campus

The seminar will be given by Professor Michael Range, State University of New York at Albany.

Abstract of talk:
A method introduced in the 17th century by R. Descartes and F. van Schooten for finding tangents to classical curves is combined with the point-slope form of a line in order to develop the differential calculus of all functions considered in the 17th and 18th centuries based on simple purely algebraic techniques. This elementary approach avoids infinitesimals, differentials, and similar vague concepts, and most importantly it does not require any limits in the study of algebraic functions. It naturally leads to continuity and to the modern definition of differentiability — in an elegant formulation introduced by C. Carathéodory — which needs to be considered when studying the elementary transcendental functions. This approach suggests new ways to teach calculus in the 21st century.

Biography of Dr. Michael Range:
Dr. Michael Range is currently a professor of mathematics at the State University of New York in Albany. He has a Ph.D. in Mathematics from the University of California. His research interests include multidimensional complex analysis, integral representations, boundary regularity of the Cauchy-Riemann equations, spaces of holomorphic functions in several variables, and function algebras. His other interests are on the Calculus curriculum and the use of MAPLE in instruction.
He has held various research positions in prestigious places such as the Mathematical Research Institute in Berkeley (1996) and the Mittag-Leffler Institute in Stockholm (1988). He has also received numerous awards including The Lester R. Ford Award of the Mathematical Association of America, in recognition of the publication of a noteworthy expository article in the American Mathematical Monthly (2004,) and Distinguished Lecturer, Frontiers in Mathematics Lecture Series, Texas A&M University (2001).

He has two books: Calculus in One and in Several Variables (under review), and Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, New York 1986; 2nd corrected printing 1998.

He has also various publications from which the following are selected:

  1. On Antiderivatives of the Zero Function. Mathematics Magazine 80 (2007), 387 - 390
  2. Kneser’s paper on the boundary values of analytic functions of two variables. In: Hellmuth Kneser, Gesammelte Abhandlungen, 872 - 876, ed. G. Betsch and K. H. Hofman, deGruyter, Berlin 2005.
  3. On the Decomposition of Holomorphic Functions by Integrals and the Local CR Extension Theorem. Adv. Studies in Pure Math. 42 (2004), Math. Soc. Japan, 269 - 273.
  4. Complex Analysis: A Brief Tour into Higher Dimensions, Amer. Math. Monthly 110 (2003), 89 - 108. (Selected for the 2004 Lester R. Ford Award of the Mathematical Association of America.)
  5. Extension Phenomena in Multidimensional Complex Analysis: Correction of the Historical Record. The Mathematical Intelligencer 24, no 2 (2002), 4 - 12.
  6. On d-bar Problems on (Pseudo) - Convex Domains. Topics in Complex Analysis, Banach Center Publ. 31, 311 - 320, Polish Acad. of Sci., Warszawa 1995.
  7. Integral Kernels and Hölder Estimates for d-bar on pseudoconvex domains of finite type in C^2. Math. Ann. 288 (1990), 63 - 74.
  8. Cauchy-Fantappie Formulas in Multidimensional Complex Analysis. Proc. Int. Conf. “Geometry and Complex Analysis”, Bologna 1989, Lect. Notes in Pure and Appl. Math 132, 307 - 32, Marcel Dekker, New York 1991.
  9. Integral Representations and Estimates in the Theory of the d-bar Neumann Problem. (with I. Lieb) Ann. of Math. 123 (1986), 265 - 301.

Event organizer: LAU’s School of Arts and Sciences – Department of Computer Science and Mathematics