The Calculus Gallery: Masterpieces from Newton to Lebesgue

  • Title: The Calculus Gallery: Masterpieces from Newton to Lebesgue
  • Author: William Dunham
  • ISBN: 9780691095653
  • Page: 285
  • Format: Hardcover
  • The Calculus Gallery Masterpieces from Newton to Lebesgue 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
    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 atMore 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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      Posted by:William Dunham
      Published :2019-04-06T13:14:58+00:00

    About William Dunham


    1. An American writer who was originally trained in topology but became interested in the history of mathematics and specializes in Leonhard Euler He has received several awards for writing and teaching on this subject.


    482 Comments


    1. This book is a wonderful hybrid of mathematics and "art", hence the title, "The Calculus Gallery". It is nice to be able to walk though the halls of higher mathematics and appreciate some of it's major "works" just as one would paintings on the wall of a great art gallery. It brings mathematics itself into the "great conversation" of art, literature, and music as Raphael depicts in his famous fresco, "The School of Athens". Here we see geometers working in a great hall along with scribes and mus [...]

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    2. Newton was more interested in integration than differentiation and did most of his work using infinite series. (Infinite series had been discovered independently in India at least 150 years before, but I have yet to read that the Indians knew anything about calculus. China and the Islamic world were no longer major players in mathematics after the Mongol invasions.) Leibniz created most of the modern notation, including dy/dx for differentiation, the long s for integration and the Leibniz rule d [...]

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    3. Calculus, by and large, has been considered one of the most difficult subjects undergraduate students have ever dealt with for decades. Just because most calculus textbooks are full of mathematical concepts, theorems and tools without any in-depth explanation of their foundations and the way they have elvoved onto something we know up to date. As if everything was just coming out of the mathematical "black hole". William Dunham, the author, really did a great job to cover all of the most remarka [...]

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    4. When I studied calculus I always longed for a bit of historical context of its development because I like to place the things I learn into an historical perspective. Finally, my curiosity got pleased as William Dunham's book does exactly that: He presents a timeline in which the most important theorems and definitions of calculus got developed, giving you a sense of how these great mathematicians build steadily on the ideas presented by their precursors."The Calculus Gallery" is not a calculus t [...]

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    5. Math for people who like stories!When I took an Analysis course I hated it, but was surprised by the very different picture of Calculus that it provided.This book presents Analysis as a riveting series of developments from the 17th to 20th century. Each chapter focuses on a specific mathematician and a few of their most surprising results. The proofs are concise and act in service of the big picture, which is a roller coaster of funky observations, counterexamples, and generalizations.It's a gre [...]

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    6. An essential read for any undergrad taking real analysis.

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    7. I've moved this review, in edited form, to my website blumsmithmath

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    8. Dunham's "Journey Through Genius" is more general, accessible and broadly appealing, so start with that. If you loved it, read this next.

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    9. Absolutely brilliant and thoroughly engaging tour of a wonderful subject!

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    10. Difficult, yet rewarding

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    11. An okay book, not as good as expected

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