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Was Newton's Calculus A Dead End? The Continental Influence Of Maclaurin's Treatise Of Fluxions, Judith V. Grabiner
Was Newton's Calculus A Dead End? The Continental Influence Of Maclaurin's Treatise Of Fluxions, Judith V. Grabiner
Pitzer Faculty Publications and Research
We will show that Maclaurin's Treatise of Fluxions did develop important ideas and techniques and that it did influence the mainstream of mathematics. The Newtonian tradition in calculus did not come to an end in Maclaurin's Britain. Instead, Maclaurin's Treatise served to transmit Newtonian ideas in calculus, improved and expanded, to the Continent. We will look at what these ideas were, what Maclaurin did with them, and what happened to this work afterwards. Then, we will ask what by then should be an interesting question: why has Maclaurin's role been so consistently underrated? Thse questions will involve general matters of …
What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen
What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen
All HMC Faculty Publications and Research
My first attempt at using computers as an aid to teaching calculus began in 1966 and culminated with the publication in 1971 of Single Variahle Calculus, written jointly with Milton Lees. Everyone used a mainframe and punched cards and few knew how to program. Computer use was limited to supplementary exercises that could be done today with a hand-held programmable calculator. A constructive sequential approach to limits and elementary numerical analysis were emphasized. The absence of programming displeased computer scientists, but it was too avant garde for all but a tiny minority of teachers of calculus. Attempts by others …
Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner
Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner
Pitzer Faculty Publications and Research
This paper recounts the history of how calculus came to get a rigorous basis in terms of the algebra of inequalities. The result is a brief history of the 150 years from Newton and Leibniz to Cauchy that produced the foundations of analysis.
Závisí Matematická Pravda Od Času?, Judith V. Grabiner
Závisí Matematická Pravda Od Času?, Judith V. Grabiner
Pitzer Faculty Publications and Research
This is a Slovak translation of Judith Grabiner's "Is Mathematical Truth Time-Dependent?," published in Volume 81 of American Mathematical Monthly (April 1974).
Is Mathematical Truth Time-Dependent?, Judith V. Grabiner
Is Mathematical Truth Time-Dependent?, Judith V. Grabiner
Pitzer Faculty Publications and Research
Another such mathematical revolution occurred between the eighteenth and nineteenth centuries, and was focused primarily on the calculus. This change was a rejection of the mathematics of powerful techniques and novel results in favor of the mathematics of clear definitions and rigorous proofs. Because this change, however important it may have been for mathematicians themselves, is not often discussed by historians and philosophers, its revolutionary character is not widely understood. In this paper, I shall first try to show that this major change did occur. Then, I shall investigate what brought it about. Once we have done this, we can …
Calculus And The Computer: A Conservative Approach, Melvin Henriksen
Calculus And The Computer: A Conservative Approach, Melvin Henriksen
All HMC Faculty Publications and Research
This paper describes a program for making the use of numerical methods an integral part of the freshman college course in single variable calculus.