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The Calculus Gallery
Masterpieces from Newton to Lebesgue
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William Dunham
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With contributions by:
William Dunham
Language:
English
Published/Copyright:
2019
About this book
More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to 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. Now with a new preface by the author, this book documents 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, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.
Author / Editor information
William Dunham is a Research Associate in Mathematics at Bryn Mawr College. He is the author of Journey Through Genius: The Great Theorems of Mathematics, The Mathematical Universe, and Euler: The Master of Us All, and is a co-editor (along with Jerry Alexanderson and Don Albers) of The G.H. Hardy Reader. He received the Mathematical Association of America's George Polya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing.
Reviews
"This is a book that should be part of the personal library of any mathematician."---Mark Hunacek, Mathematical Gazette
“The Calculus Gallery is a wonderful book. The style is inviting; the explanations are clear and accessible…. Mathematicians, scientists, and historians alike can learn much that is interesting, much that is mathematically significant, and a good deal that is both.”—Judith V. Grabiner, Science
“If a better historical treatment of the development of the calculus is available, this reviewer has yet to see it…. Essential.”—Choice
“[A] brilliant book…. I predict that Dunham’s book will itself come to be considered a masterpiece in its field.”—Victor J. Katz, American Scientist
“A joy to read…. [The Calculus Gallery] is a lovely and engaging gallery of the ‘masters’ that belongs in the library of everyone who seriously teaches or studies the subject.”—Diane M. Spresser, Mathematics Teacher
Topics
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Frontmatter
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Contents
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Illustrations
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Acknowledgments
xiii -
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Preface to the Princeton Science Library Edition
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INTRODUCTION
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CHAPTER 1. Newton
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CHAPTER 2. Leibniz
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CHAPTER 3. The Bernoullis
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CHAPTER 4. Euler
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CHAPTER 5. First Interlude
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CHAPTER 6. Cauchy
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CHAPTER 7. Riemann
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CHAPTER 8. Liouville
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CHAPTER 9. Weierstrass
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CHAPTER 10. Second Interlude
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CHAPTER 11. Cantor
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CHAPTER 12. Volterra
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CHAPTER 13. Baire
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CHAPTER 14. Lebesgue
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Afterword
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Notes
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Index
233
Publishing information
Pages and Images/Illustrations in book
eBook published on:
November 13, 2018
eBook ISBN:
9780691184548
Pages and Images/Illustrations in book
Main content:
256
eBook ISBN:
9780691184548
Keywords for this book
Mathematician; Theorem; Mathematics; Series (mathematics); Bernhard Riemann; Continuous function; Pointwise; Summation; Riemann integral; Real number; Infinitesimal; Natural number; Division by zero; Differentiable function; Counterexample; Augustin-Louis Cauchy; Interval (mathematics); Coefficient; Karl Weierstrass; Polynomial; Set theory; Nowhere continuous function; Quantity; Algebraic number; Equation; Transcendental number; Infinity; Dense set; Uniform convergence; Geometry; Continuous function (set theory); Infimum and supremum; Georg Cantor; Harmonic series (mathematics); Henri Lebesgue; Mathematical analysis; Derivative; Differential calculus; Tangent; Q.E.D.; Integer; Theory; Scientific notation; Existential quantification; Measurable function; Princeton University Press; Vito Volterra; Geometric progression; Real analysis; Geometric series; Fourier series; Intermediate value theorem; Westmont College; Bounded function; Mean value theorem; Rational number; Binomial theorem; Subset; Contradiction; Absolute value; Antiderivative; Sign (mathematics); Unit interval; Baire category theorem; Fundamental theorem; Lebesgue integration; Upper and lower bounds; Notation; Diagram (category theory); Countable set
Audience(s) for this book
College/higher education;Professional and scholarly;
