A Tour of the Calculus Paperback – 1 Feb 1997
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|Paperback, 1 Feb 1997||
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From the Inside Flap
Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe.
"An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review
About the Author
David Berlinski holds a Ph.D. from Princeton University and is the bestselling author of such books as A Tour of the Calculus, The Advent of the Algorithm, and Newton s Gift. A senior fellow at the Discovery Institute in Seattle and a former fellow at the Institute for Applied Systems Analysis and the Institut des Hautes Etudes Scientifiques, Berlinski writes frequently for Commentary, among other journals. He lives in Paris.
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Top Customer Reviews
At least the technical stuff is basically good. I liked his description of what continuous-ness is all about, and the (presumably fictionalised) accounts of teaching the material to small classes are quite entertaining.
Most Helpful Customer Reviews on Amazon.com (beta)
Most disappointing was the constant distraction of mathematical errors, small and large, throughout the book. For example, there are typos, errors in notation, and misleading or confusing notation. For these problems, I understood the author's intention at these points (being a calculus teacher myself), but to a reader less familiar with calculus, these problems will hinder understanding. When a reader can't understand the mathematical details, much of the meaning is lost.
A few errors were utterly irreparable, such as the proof of the Intermediate Value Theorem. In that case, a correct proof would diverge greatly from that of the author. This specific error is unfortunate because it is for this theorem that the author develops the real numbers (which takes chapters), and upon this theorem that all later theorems are based.
Finally, I found the author's style annoying, especially the fictional accounts of specific actions taken by historical mathematicians (crossing a river, contemplating calculus while sitting in an overstuffed chair, etc.). The author must enjoy hearing himself wax poetic on any subject which enters his head, but I don't.
The book's back cover likens this book to Douglas Hofstadter's classic _Godel, Escher, Bach_, but the comparison is laughable. Hofstadter's book has a direct and clear style of writing, whereas _A Tour of the Calculus_ is unfocused and its numerous errors makes it is mathematically a sham.
Don't get me wrong though: the book isn't absolutely terrible. Some commenters have derided the author for using words that are too big, widely unknown, etc. But that's one of the things I enjoyed about the book: a few years back when I read it I underlined every word I didn't know or was fuzzy about and used this book as a way to build my vocabulary. I wouldn't describe myself as a cheery optimist, but I definitely turned the heightened language of the book to my advantage...instead of just whining about it on Amazon.
As for learning calculus: if you are a new student to calculus, this book won't really help. I bought this book years ago as a supplement to my calculus course and quickly found I was just wasting my time reading it. If you are a non-mathematician and just want a little glimpse into calculus, then this might be a good book. I would laugh at anyone who said they learned calculus from the book though.
In other news (finally, my qualifications...bla, bla, bla): since I've bought the book, I've taken all the calc and differential equations courses, abstract and linear algebra courses, analysis courses, graduated with a degree in physics and have completed one year of graduate school physics. With this in mind: Upon re-reading sections of the book recently, I would say that this is a pretty fun SUMMER READ for super nerds who already know it all, but just want to leisurely read about some elementary calculus by an author who writes in a conversational tone.
This book got glowing reviews so I bought it without leafing through it. My mistake. Compared to Berlinsky's book, the average college calculus textbook is a model of clarity.
Berlinsky is infatuated with words. He's never heard of a simple declarative sentence. One metaphor per sentence isn't enough. Indeed, if there is a literary conceit he doesn't indulge in to excess, I can't think of it.
His editor should have required him to read Strunk and White's Elements of Style daily for a year.
In short, as far as I am concerned, the other negative reviews I have read here are not only right on the money but not harsh enough.
I give him 2 stars instead of one because the material underlying the terrible writing is interesting and worth knowing. Hopefully someone will write a readable book on this material!