The Calculus Gallery: Masterpieces from Newton to Lebesgue

כריכה קדמית
Princeton University Press, 2005 - 236 עמודים
9 ביקורות

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.

  

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Review: The Calculus Gallery: Masterpieces from Newton to Lebesgue

ביקורת משתמש  - Karel Baloun - Goodreads

Difficult, yet rewarding קרא סקירה מלאה

Review: The Calculus Gallery: Masterpieces from Newton to Lebesgue

ביקורת משתמש  - Jc Price - Goodreads

An essential read for any undergrad taking real analysis. קרא סקירה מלאה

ספרים קשורים

תוכן

INTRODUCTION
1
Newton
5
Leibniz
20
The Bernoullis
35
Euler
52
First Interlude
69
Cauchy
76
Riemann
96
Second Interlude
149
Cantor
158
Volterra
170
Baire
183
Lebesgue
200
Afterword
220
Notes
223
Index
233

Liouville
116
Weierstrass
128

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אודות המחבר (2005)

About the author WILLIAM DUNHAM is a Phi Beta Kappa graduate of the University of Pittsburgh. After receiving his PhD from the Ohio State University in 1974, he joined the mathematics faculty at Hanover College in Indiana. He has directed a summer seminar funded by the National Endowment for the Humanities on the topic of "The Great Theorems of Mathematics in Historical Context.

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