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Howard Jerome Keisler (born 3 December 1936) is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis. His Ph.D. advisor was Alfred Tarski at Berkeley; his dissertation is Ultraproducts and Elementary Classes (1961).
Keisler, H. Jerome (1976), Elementary Calculus: An Approach Using Infinitesimals, Prindle Weber & Schmidt, ISBN 978-0871509116 Keisler, H. Jerome (1976), Foundations of Infinitesimal Calculus , Prindle Weber & Schmidt, ISBN 978-0871502155 , retrieved 10 January 2007 A companion to the textbook Elementary Calculus: An Approach Using Infinitesimals .
H. Jerome Keisler, David Tall, and other educators maintain that the use of infinitesimals is more intuitive and more easily grasped by students than the "epsilon–delta" approach to analytic concepts. [10] This approach can sometimes provide easier proofs of results than the corresponding epsilon–delta formulation of the proof.
Keisler's Elementary Calculus: An Infinitesimal Approach defines continuity on page 125 in terms of infinitesimals, to the exclusion of epsilon, delta methods. The derivative is defined on page 45 using infinitesimals rather than an epsilon-delta approach.
"Radically elementary probability theory" of Edward Nelson combines the discrete and the continuous theory through the infinitesimal approach. [citation needed] [1] The model-theoretical approach of nonstandard analysis together with Loeb measure theory allows one to define Brownian motion as a hyperfinite random walk, obviating the need for cumbersome measure-theoretic developments.
The review criticized Keisler's text for not providing evidence to support these statements, and for adopting an axiomatic approach when it was not clear to the students there was any system that satisfied the axioms . The review ended as follows: The technical complications introduced by Keisler's approach are of minor importance.
Nicholas Rostow, who served as special assistant to the president for national security affairs and legal adviser to the NSC under Reagan and George H.W. Bush also signed the letter.
Vopěnka's principle was first introduced by Petr Vopěnka and independently considered by H. Jerome Keisler, and was written up by Solovay, Reinhardt & Kanamori (1978).