This book explores the background of a major intellectual revolution: the rigorous reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his contemporaries in the first part of the 19th century. Their generation changed the calculus from a method of solving problems to a collection of theorems, based on precise definitions, about limits, continuity, series, derivatives, and integrals. The book shows how Cauchy reshaped inherited 18th-century concepts to create an approach to rigor that we still accept today. In so doing, The Origins of Cauchy's Rigorous Calculus provides fresh insights and a new perspective on the foundations of analysis. After defining rigor and describing the characteristics of 19th-century thinking about analysis, the book examines 18th-century views of the calculus and the manifest lack of interest in the foundations of analysis. The greater part of the book concerns itself with tracing how specific achievements of 18th-century mathematics were transformed by Cauchy into the basis of his rigorous calculus (especially the development of the algebra of inequalities: ideas on limits, continuity, and convergence; and certain 18th-century treatments of the derivative and integral), with the work of Joseph-Louis Lagrange shown to be crucial in the transition to new ways of thinking.

The Origins of Cauchy's Rigorous Calculus

Science & Math

Grabiner, Judith V.

Mathematics

Mit Pr

This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition.

The Origins of Cauchy's Rigorous Calculus (Dover Books on Mathematics)

Dover Publications

Judith Grabiner has written extensively on the history of mathematics, principally for mathematicians rather than historians. This collection of her work highlights the benefits of studying the development of mathematical ideas and the relationship between culture and mathematics. She also considers the struggles and successes of famous mathematicians with the aim of inspiring students and teachers alike. A large part of this book is the author's The Calculus as Algebra: J.-L. Lagrange, 1736-1813 which focuses on Lagrange's pioneering attempt to reduce the calculus to algebra. The nine other articles are on a broad range of other topics such as some widely held myths about the history of mathematics and the work of heavyweight mathematicians such as Descartes, Newton, Maclaurin and Lagrange. Six of these articles have won awards from the MAA for expository excellence. This collection is an inspiring resource for history of mathematics courses.

A Historian Looks Back: The Calculus as Algebra and Selected Writings (Spectrum)

American Mathematical Society

See the best price to sell, buy, or rent books by Grabiner, Judith V.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Grabiner, Judith V.

See the best price to sell, buy, or rent books by Grabiner, Judith V.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The Origins of Cauchy's Rigorous Calculus

The Origins of Cauchy's Rigorous Calculus (Dover Books on Mathematics)

A Historian Looks Back: The Calculus as Algebra and Selected Writings (Spectrum)