The Calculus Gallery

William Dunham

288 pages, parution le 02/03/2005

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Résumé

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. William Dunham lucidly presents the definitions, theorems, and proofs. "Students of literature read Shakespeare; students of music listen to Bach," he writes. But this tradition of studying the major works of the "masters" is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.

Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original "category theorem" (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable.

Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

L'auteur - William Dunham

William Dunham is the Truman Koehler Professor of Mathematics at Muhlenberg College in Allentown, Pennsylvania. He has won two awards for excellence in expository writing from The Mathematical Association of America: the 1993 George Polya Award, and in 1997, the Trevor Evans Award. His books journey Through Genius: The Great Theorems of Mathematics, and The Mathematical Universe have both been selections of the Book-of-the-Month Club and the History Book Club. He has also been the recipient of several grants from the National Endowment for the Humanities to fund seminars on the great theorems of mathematics in listorical context.

Sommaire

Newton
Leibniz
The Bernouillis
Euler
First Interlude
Cauchy
Riemann
Liouville
Weierstrass
Second Interlude
Cantor
Volterra
Baire
Lebesgue

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	William Dunham
Parution	02/03/2005
Nb. de pages	288
Format	16 x 24
Couverture	Relié
Poids	490g
Intérieur	Noir et Blanc
EAN13	9780691095653
ISBN13	978-0-691-09565-3