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Title: The History of the Calculus and Its Conceptual Development by Carl B. Boyer ISBN: 0486605094 Publisher: Dover Pubns Pub. Date: September, 1980 Format: Paperback Volumes: 1 List Price(USD): $11.95 |
Average Customer Rating: 4
Rating: 4
Summary: The history of an amazing and extremely useful idea
Comment: Since Boyer writes from the perspective of a math professor in the thirties and forties, some of his style is dated. Nevertheless, his content is not and remains just as accurate as it was when first written. There are few mathematical tools that are more useful than the calculus and yet it is based on several abstractions that are never achieved. However, we act as if it they are, manipulating limits as if they were whole numbers and manipulating infinities as if they are real objects.
The original ideas that began the development of the calculus are very old, the first known exposition of the problems of limits is the well known paradox proposed by Zeno, which dates back to ancient Greece. Zeno's arguments involving the Tortoise and Achilles still serve as intellectual fodder for many a philosophical debate. Therefore, the second chapter deals with the mathematics of antiquity that began the long intellectual journey towards the dual creation of calculus by Newton and Liebniz.
While there were some advancements in the medieval years, they were relatively unsubstantial and therefore Boyer spends only a brief time with them. Unfortunately, he concentrates on the activity in Europe, ignoring some of the work in other parts of the world. The fourth chapter deals with the century before Newton, where the last of the foundation ideas were set down and Newton's giants did their work and puffed out their shoulders.
The fifth chapter is devoted largely to the parallel work of Newton and Liebniz, where they independently invented what we now call differential and integral calculus. While the utility of the new mathematics could not be denied, there were many people who found great fault in it. It is easy for us to think of these critics as short sighted, but in fact many of their arguments were valid. Despite all the genius of Newton and Liebniz, there were still many gaps in the calculus that had to be corrected, which is the subject of the remaining chapters.
Written at a level so that mathematicians and laypeople alike can understand the ideas and how they expanded over the centuries, this is a book that is still of use in histories of mathematics and the centuries long development of ideas.
Rating: 4
Summary: Vivid history of the calculus, fascinating!
Comment: This book clearly shows how the underlying concept of the caculus had been developed from geometric intuiton to formal logical elaboration. It feels good to know that even Newton himself was having trouble defining the infinitesimals. Now I can understand why modern calculus books are filled with so many strict definitions of continuity and limits. Mathematicians had to establish rigorous formulation of the calculus to free themselves from the vague definition of physical realities which modern physicist cannot understand even now.
Rating: 4
Summary: Here is the waited History
Comment: The way I look at this book is that it is giving me the historical development of Calculus in a compact book. It starts with ancient grreks goes to middel ages, developes with Lebnitz and Newton and finale with modern theory. I am not interested in the Philosophy of History or not in position to allocate prizes to Scientist of the past. From that point of view I believe this book gives you the chronology with a lot of information about some obscure mathematicians who contributed to the field. I wish there was a littel more mathematics in it such as fluxions etc more descriptive examples but do you know any other book.
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Title: A History of Mathematics by Carl B. Boyer, Isaac Asimov ISBN: 0471543977 Publisher: John Wiley & Sons Pub. Date: 06 March, 1991 List Price(USD): $39.95 |
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Title: Foundations and Fundamental Concepts of Mathematics by Howard Eves ISBN: 048669609X Publisher: Dover Pubns Pub. Date: May, 1997 List Price(USD): $14.95 |
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Title: Concepts of Modern Mathematics by Ian Stewart ISBN: 0486284247 Publisher: Dover Pubns Pub. Date: February, 1995 List Price(USD): $10.95 |
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Title: A History of Vector Analysis : The Evolution of the Idea of a Vectorial System by Michael J. Crowe ISBN: 0486679101 Publisher: Dover Pubns Pub. Date: February, 1994 List Price(USD): $12.95 |
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Title: A Concise History of Mathematics by Dirk J. Struik ISBN: 0486602559 Publisher: Dover Pubns Pub. Date: September, 1987 List Price(USD): $8.95 |
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