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A Tour of the Calculus Hardcover – Jan 1996

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Product details

  • Hardcover: 331 pages
  • Publisher: Pantheon Books (Jan. 1996)
  • Language: English
  • ISBN-10: 0679426450
  • ISBN-13: 978-0679426455
  • Product Dimensions: 3.8 x 16.5 x 24.8 cm
  • Average Customer Review: 2.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 120,721 in Books (See Top 100 in Books)

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2.5 out of 5 stars
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Most Helpful Customer Reviews

8 of 9 people found the following review helpful By A Customer on 16 April 2001
Format: Paperback
Berlinski has clearly decided that he wants to avoid the stereotypical mathematical tradition that has texts be as terse as possible. He has erred too far in the other direction. Good science writing doesn't need to imagine Leibniz groping serving maids. It doesn't need to invent overly elaborate language and metaphors.
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.
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1 of 1 people found the following review helpful By Terry Franks on 6 Oct. 2014
Format: Paperback Verified Purchase
The point of this book, like another by Berlinski (One, Two, Three) is overwhelmed by his unnecessary, floridly descriptive narratives and pointless references to his supernatural beliefs. It's a ramble. If you want to learn about maths, read De Sautoy et al.
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4 of 7 people found the following review helpful By David Bonar on 23 July 2007
Format: Paperback
The two stars are for the technical content, which is basically sound. But I can't give any stars for Berlinski's writing style. It's as though he's trying (far too hard) to write a classic novel with some maths in it. The idea of conveying some fairly complex maths by using flowery, descriptive, even evocative language is in principle an interesting one, but the prose is so purple as to make it hard to make out what point he's trying to make, and in many places obscures the meaning completely. If you want to read purple prose, try Tolstoy. If you want to understand calculus, try the Open University. Either way, don't bother with this book.
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2 of 4 people found the following review helpful By A Customer on 7 Aug. 1999
Format: Hardcover
This book goes well into the mental rigour of the calculus and hence shows the thorough underlieing logic and mental disciplin of its developement and useage. However, the author can occasionally be overelaborate in his language and story-telling. This sometimes makes the book seem like a novel. However there are some good appendixes containing mathematical proofs which contain more mathematics than linguistic flair. An interesting read for the pre A level student or the first year a level student really.
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Most Helpful Customer Reviews on (beta) 157 reviews
127 of 153 people found the following review helpful
Mathematically poor and stylistically overdone 5 Sept. 1999
By Michael Maltenfort ( - Published on
Format: Paperback
I hoped for an insightful view into calculus. Indeed, there are many deep and interesting aspects of calculus which are generally obscured in a typical calculus textbook (or in a calculus class). This is not such a book.
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.
33 of 38 people found the following review helpful
I love this book! 6 Oct. 2005
By Mockingbird - Published on
Format: Paperback
I seem to be rather in the minority when I say that I actually liked Berlinski's verbose style; frankly, I don't really see what was so difficult to understand about it. On the other hand, I approached this book from the position of wanting something fun to read, and that's what I got, with the welcome addition of what I thought was lovely writing - if I had been searching for something that would give me an in-depth look at calculus, I would have looked elsewhere. Basically, I thought the book was really well-written and exciting (I had just begun calculus when I read it, so I found it really interesting to look at all the stuff we hadn't yet done.), and I highly reccomend it for a piece of fun reading and a decent overview.
40 of 47 people found the following review helpful
Meh. 30 May 2009
By Kevin Urban - Published on
Format: Paperback
By reading some of these reviews, one thing is obvious: anyone who first lists their qualifications as a mathematician or calculus teacher is basically going to nay-say the heck out of the book. And in a way, I'd say this is semi-appropriate: the book is definitely not a math book; I think the grievances arise basically because it's sold as one. Sure, the word "tour" is in the title, but that does little to suggest that this book would be more appropriately marketed as....well....a memoir? Maybe?

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.
22 of 26 people found the following review helpful
Worse than useless 11 Feb. 2008
By nd - Published on
Format: Paperback
I found it fascinating that there are (at the time of writing) about as many 5's as 1's among the reviews of this book. As you can probably tell by the title, I am not a fan.

I confess that I did not read the whole book: I could not. As I went on, I found myself getting angry at this book, for reasons that I hope will be a little clearer by the end of the review. At that point I gave up on reading the whole book and dipped in here and there.

Here's what I think:

I found the prose purple, precious and pretentious (just like this sentence!-), but that is hardly the book's worst fault. Neither is the interjection of the author's opinions on things unrelated and irrelevant (the comment on the Duke University English Department springs to mind: a one-sentence insult is as inventive as the almost proverbial "your mama" - I find the Sokal Affair a much more effective and amusing skewering).

The worst fault of the book, imo, is that there was no light shed on the subject (nacreous or otherwise), no effulgence... (BTW, if you like these words, you *might* like the book but no guarantees). On the contrary, confusion and inaccuracy abound: the Dedekind cuts chapter is full of them for example - I had to go back to a real exposition (Ferrar's appendix in his 1938 book on "Convergence" fwiw) to regain my sanity. Somebody else pointed out the sine/cosine graph flub. The graph in the chapter on Rolle's theorem shows a function that does not satisfy the conditions of the theorem as stated two pages earlier. I found most of the explanations similarly confused and confusing: I cannot imagine how anybody can learn much from this book, be it beginner, expert or anywhere in between.

Somebody else mentioned that he enjoyed the "historical anecdotes". I 'm not sure that there are any that are not figments of Mr. Berlinski's imagination. Every time that he started a description that I assumed was factual, it ended by being clearly an invention of the author - and there was no way to tell where facts ended and invention began.

The author mentions the comment of his high school English teacher who said (I paraphrase from memory here, so the figure may be wrong, but the meaning should be clear): "Mr. Berlinski, once more you took ten pages to say nothing." The comment to some degree applies to the book. I can only assume that the poor editors who tried to cut it down to something reasonable gave up exhausted at the futility of the task.

So for me, the book fails as exposition or history of the subject. It also fails as entertainment. Is there anything left?

For an example of a book that I think is genuinely informative, honest, useful *and* entertaining, I suggest John Derbyshire's "Prime Obsession." Although you can get a whiff of Derbyshire's (rather quirky) political conservatism in the book, nevertheless the book is always about its subject (the Riemann hypothesis) and never becomes an object for the author's own aggrandizement. Mr. Berlinski's book in contrast is very much about Mr. Berlinski.
15 of 17 people found the following review helpful
Hugely Disappointing 17 Oct. 2001
By dd9000 - Published on
Format: Paperback
I am not a mathematician. I took calculus in college but never really understood it. I have, however, always wanted to understand it.
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.
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