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The calculus gallery : masterpieces from Newton to Lebesgue / William Dunham.

By: Dunham, William, 1947-.
Material type: materialTypeLabelBookPublisher: Princeton, N.J. ; Woodstock : Princeton University Press, 2008Description: 236 p. : ill., ports. ; 24 cm. + hbk.ISBN: 9780691136264 ; 0691136262 .Subject(s): Calculus -- HistoryDDC classification: 515
Contents:
Introduction -- Newton -- Leibniz -- The Bernoullis -- Euler -- First interlude -- Cauchy -- Riemann -- Liouville -- Weierstrass -- Second interlude -- Cantor -- Volterra -- Baire -- Lebesgue.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 515 (Browse shelf(Opens below)) 1 Available 00188189
Total holds: 0

Enhanced descriptions from Syndetics:

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--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. 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.

Originally published: 2005.

Includes bibliographical references (pages 223-231) and index.

Introduction -- Newton -- Leibniz -- The Bernoullis -- Euler -- First interlude -- Cauchy -- Riemann -- Liouville -- Weierstrass -- Second interlude -- Cantor -- Volterra -- Baire -- Lebesgue.

Table of contents provided by Syndetics

  • Illustrations (p. ix)
  • Acknowledgments (p. xiii)
  • Introduction (p. 1)
  • Chapter 1 Newton (p. 5)
  • Chapter 2 Leibniz (p. 20)
  • Chapter 3 The Bernoullis (p. 35)
  • Chapter 4 Euler (p. 52)
  • Chapter 5 First Interlude (p. 69)
  • Chapter 6 Cauchy (p. 76)
  • Chapter 7 Riemann (p. 96)
  • Chapter 8 Liouville (p. 116)
  • Chapter 9 Weierstrass (p. 128)
  • Chapter 10 Second Interlude (p. 149)
  • Chapter 11 Cantor (p. 158)
  • Chapter 12 Volterra (p. 170)
  • Chapter 13 Baire (p. 183)
  • Chapter 14 Lebesgue (p. 200)
  • Afterword (p. 220)
  • Notes (p. 223)
  • Index (p. 233)

Reviews provided by Syndetics

CHOICE Review

A deficiency of many treatments of the history of mathematics is a tendency to be overly biographical, offering much about the lives of great mathematicians but often little about their mathematics. This delightful offering by Dunham (Muhlenberg College) provides an excellent historical perspective on the development of the calculus, from its introduction in the late 1600s by Newton and Leibniz, through the rigor added by the likes of Cauchy and Riemann in the 1800s, to the birth of modern analysis in the work of Lesbesgue in the early 1900s. What distinguishes this selection is it truly provides a history of mathematics, not just a history of mathematicians. Dunham selects 12 mathematicians who were instrumental in the development of the calculus and entertains the reader with at least one masterpiece from each. These masterpieces are theorems, definitions, or ideas attributed to the mathematicians and are presented in their original forms, albeit with modern notation. The mathematics presented requires a certain amount of training in the subject but is interspersed with marvelously witty exposition. If a better historical treatment of the development of the calculus is available, this reviewer has yet to see it. ^BSumming Up: Essential. Upper-division undergraduates through faculty. D. S. Larson Gonzaga University

Author notes provided by Syndetics

William Dunham , Koehler Professor of Mathematics at Muhlenberg College, is the author of Journey Through Genius: The Great Theorems of Mathematics ; The Mathematical Universe ; and Euler: The Master of Us All . He has received the Mathematical Association of America's George Pólya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing.