Abstract
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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