Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.
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18 of 18 people found the following review helpful:
4.0 out of 5 stars
Good, but not great,
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This review is from: Understanding Infinity: The Mathematics of Infinite Processes (Dover Books on Mathematics) (Paperback)
Most of the books I have given a 4-star rating to would be in the category of "If they'd only done this thing differently, I'd have given it 5." This book is different. I'm taking literally the definition "5 = I love it!" and on that basis this book cannot get 5 stars, though I can't say exactly _what_ I don't quite like.The book does a good job of taking the reader through the steps needed to explain "why the calculus works" -- and it really doesn't require calculus to understand most of this book, though you need calculus to understand the _motivation_ for a lot of what the book does. You need only have a decent grounding in high school geometry and algebra to understand the book. Still, it isn't an _easy_ read. I've found myself putting the book down and coming back to it later several times. Yet I can't say that the book is hard to read because it's badly written; I think it's written decently well. I think it's just that the topics it covers are harder going than a lot of the math I read. So, while I don't _love_ this book, I'd recommend it to someone who wants to know something about the motivation for all those weird epsilons and deltas and the non-intuitive definitions of topics like continuity. It does that job, and does it as well as any book I know of.
5 of 5 people found the following review helpful:
4.0 out of 5 stars
Careful look at the basis of calculus,
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This review is from: Understanding Infinity: The Mathematics of Infinite Processes (Dover Books on Mathematics) (Paperback)
An unusual and interesting look at the basis for calculus and analysis. The only book I know of that provides a strong motivation for the Dedekind/ Weirstrass foundation of calculus. Recommended for anone doing analysis.Quite accessible for anyone who has done first year or even high school calculus
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