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Title: The Calculus Gallery: Masterpieces from Newton to Lebesgue
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Manufacturer: Princeton University Press
List Price: $19.95
Our Price: $15.16
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| Customer Reviews: |
| The Calculus Gallery: Masterpieces from Newton to Lebesgue by Princeton University Press Another masterpeice by William Dunham | | 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". | | The Calculus Gallery: Masterpieces from Newton to Lebesgue by Princeton University Press stresses the important aspects. | | wonderful book, adds mathematical context to the ideas developed. good to read along a textbook on analysis. | | The Calculus Gallery: Masterpieces from Newton to Lebesgue by Princeton University Press Great Read | | 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. | | The Calculus Gallery: Masterpieces from Newton to Lebesgue by Princeton University Press Very Good IF you have a solid background | And by "solid background", I mean a good understanding of honors-level algebra (high school senior variety) AND a reasonably thorough understanding of basic calculus notions such as limits, integration, and differentiation. Even if your background is not quite this strong, I feel you will understand parts of the Newton Leibnitz Euler chapters, but you may start to struggle a touch after that. And, as was pointed out in an earlier review, this book is NOT for the General Reader. Very far from it, in spite of professor Dunham's substantial skill as a science/math writer. (A pleasure to read the gentleman!)
In fine: I studied applied math at UCLA some 55 years ago, and I have not done any serious math since about 1970, so I may be overstating the requirements necessary to enjoy this work, given my own very dim memory of some key elements of mathematics and of the mathematical proof. But for those who feel qualified, this is yet another wonderful piece of work by a truly gifted author.
Naf February 2007; Los Altos CA | | The Calculus Gallery: Masterpieces from Newton to Lebesgue by Princeton University Press Great side reader for a calculus course | | I wish this book had been around when I was taking calculus a few decades ago. It is extremenly well written and explains all the reasons why mathematicians had to introduce all the concepts and definitions you encounter in a calculus course. Reading this book on the side will tell you exactly why you're doing what you're doing, and where you are going. All students of calculus will benefit from this book. | | The Calculus Gallery: Masterpieces from Newton to Lebesgue by Princeton University Press Product Description | 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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