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Higher Trigonometry, Hyperreal Numbers, and Euler's Analysis of Infinities

by Mark McKinzie and Curtis Tuckey

Award: Carl B. Allendoerfer

Year of Award: 2002

Publication Information: Mathematics Magazine, Vol. 74(2001), pp. 339-368

Summary: Euler's Introductio in Analysin Infinitorum viewed through the lens of nonstandard analysis.

Link to Article

About the Authors: (from Mathematics Magazine, Vol. 74 (2001)) Mark McKinzie teaches in the Mathematics Department at St. John Fisher College. He has a Ph.D. in mathematics from the University of Wisconsin; his dissertation, on the early history of power series, was completed under the supervision of M. Bleicher. Work on this paper started while he was an intern in the Information Sciences Division of Bell Laboratories, and sparked his interest in the history of mathematics in general, and of series in particular.

Curtis Tuckey is director of the Oracle Voice Laboratory. Before joining Oracle Corporation he held various research and development positions at Motorola, Lucent Technologies, AT&T, and General Motors. He has occaisionally taught at Loyola, DePaul, and Northwestern. This paper was written while he was a research member of the Information Sciences Division of Bell Laboratories. He has a Ph.D. in mathematics from the University of Wisconsin, where he wrote a dissertation in non-standard analysis under H.J. Keisler. He lives in Chicago.

Subject classification(s): Logic and Foundations | Model Theory | Algebra and Number Theory | Algebra | Sequences and Series
Publication Date: 
Wednesday, February 7, 2007