The Calculus Gallery: Masterpieces from Newton to Lebesgue | Date: 04 May 2011, 08:58
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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. 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.
Reviews
Summary: William Dunham in his elemens!!!
Rating: 5
If you have read William's Dunham's " Journey through Genius ", "Euler,The Master of Us All", there is no need to add anymore praise to this book,just buy it and enjoy it!!!
Summary: Calculus is Good but Hard!
Rating: 5
Well worth the effort! The beginning is easy (but very informative) if you've had college level differential and integral calculus. Then there's Cantor and Lebesgue!! Tough going, but very satisfying!
Pete
Summary: Another masterpeice by William Dunham
Rating: 5
If you enjoyed "Journey through Genius" by the same author, you will also enjoy the present volume. It requires more math knowledge (at least a working knowledge of calculus), but the level is aimed at a bright high school AP student, or a college undergraduate I would recommend it for even serious mathematicians who would like to know more about how the present state of knowledge of analysis came about. I would especially recommend it for teachers and students of calculus. Too often, ideas which took literally centuries to mature are presented in finished form, as if some mathematician sat down one day and wrote out finished, rigorous theorems. Seeing how even venerable mathematicians like Newton and Cauchy got results without the rigour which we see as necessary today is an eye-opener, and should be an encouragement to experiment and "learn by doing", and not to be afraid to go boldly forth, even if you haven't dotted all the "i" and crossed all the "t".
Summary: stresses the important aspects.
Rating: 5
wonderful book, adds mathematical context to the ideas developed. good to read along a textbook on analysis.
Summary: Great Read
Rating: 5
If you are up on your math it almost reads like a novel. I can't say anything about it that hasn't already been said, but just affirm all the positive comments. If you like math you will love this book.
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