Howard Jerome Keisler
December 3, 1936|
|Institutions||University of Wisconsin-Madison|
|Doctoral advisor||Alfred Tarski|
|Doctoral students||Frederick Rowbottom|
|Known for||Non-standard analysis|
Following Abraham Robinson's work resolving what had long been thought to be inherent logical contradictions in the literal interpretation of Leibniz's notation that Leibniz himself had proposed, that is, interpreting "dx" as literally representing an infinitesimally small quantity, Keisler published Elementary Calculus: An Infinitesimal Approach, a first-year calculus textbook conceptually centered on the use of infinitesimals, rather than the epsilon, delta approach, for developing the calculus.
He held the named chair of Vilas Professor of Mathematics at Wisconsin.
Among Keisler's graduate students, several have made notable mathematical contributions, including Frederick Rowbottom who discovered Rowbottom cardinals. Several others have gone on to careers in computer science research and product development, including: Michael Benedikt, a professor of computer science at the University of Oxford, Kevin J. Compton, a professor of computer science at the University of Michigan, Curtis Tuckey, a developer of software-based collaboration environments; Joseph Sgro, a neurologist and developer of vision processor hardware and software, and Edward L. Wimmers, a database researcher at IBM Almaden Research Center.
- Chang, C. C.; Keisler, H. J. Model theory. Third edition. Studies in Logic and the Foundations of Mathematics, 73. North-Holland Publishing Co., Amsterdam, 1990. xvi+650 pp. ISBN 0-444-88054-2
- Elementary Calculus: An Infinitesimal Approach. Prindle, Weber & Schmidt, 1976/1986. Available online at .
- Criticism of non-standard analysis
- Non-standard calculus
- Elementary Calculus: An Infinitesimal Approach
- Influence of non-standard analysis
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