A Tour of the Calculus (Paperback)

by David Berlinski (Author) "SOME THINGS WERE GREEK TO THE GREEKS..." (more)
Key Phrases: integral wishes, unbearable smoothness, function vel, Tour of the Calculus, Hafez the Intelligent, Leper's Depot (more...)

Editorial Reviews

From Library Journal
Berlinski (Black Mischief: The Mechanics of Modern Science, LJ 2/15/86) presents an unconventional work on the foundations of calculus. It is in part an informal history of the subject, the author inrerweaves the historical fragments with expository sections that explain the concepts from a modern viewpoint. He gives special attention (very appropriately) to the concept of limits and to several of the fundamental theorems that underpin calculus. He also shows how differential calculus deals with rates of change and how integral calculus works to determine areas under curves. Writing in a breezingly informal style, the author includes a plethora of humorous asides as well as a number of clearly fictitious anecdotes. At times his prose gets a bit too ripe, but the overall effect is to make the book quite readable. The work should be especially useful for providing perspective to college and advanced high school students currently learning calculus. Recommended for all public and college libraries.?Jack W. Weigel, Univ. of Michigan Lib., Ann Arbor
Copyright 1995 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

From Booklist
Even those who flailed through calculus class sense the power and perfection of that branch of mathematics, and Berlinski rekindles the interest of lapsed students in this pleasing excursion through graphs and equations. Berlinski's goal is to explain the mystery of motion and the area and volume of irregular shapes, issues that gave rise to Leibnitz and Newton's invention of calculus. He makes his points one concept at a time, but not so dryly as asking and answering, "What is a function?" No, with dashes of biography or images of his walking around old Prague (to illustrate continuity), Berlinski tangibly grounds the abstract notions, so that attentive readers can ease into and grasp the several full-blown proofs he sets forth, as of the mean-value theorem. Though the math-shy won't necessarily jump to the blackboard to begin differentiating and integrating polynomial equations, Berlinski's animated presentation should tempt them to sit forward and appreciate the elegance of calculus--and perhaps banish recollections of its exam-time terrors. Gilbert Taylor --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Paperback: 352 pages
• Publisher: Vintage (January 28, 1997)
• Language: English
• ISBN-10: 0679747885
• ISBN-13: 978-0679747888
• Product Dimensions: 8 x 5.2 x 0.8 inches
• Shipping Weight: 8.5 ounces (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars See all reviews (127 customer reviews)
• Amazon.com Sales Rank: #221,837 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

39 of 45 people found the following review helpful:

1.0 out of 5 stars Mathematically poor and stylistically overdone, September 5, 1999

By	Michael Maltenfort ([e-mail]) (Chicago, Illinois) - See all my reviews

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.

7 of 7 people found the following review helpful:

1.0 out of 5 stars Worse than useless, February 11, 2008

By	nd (Arlington, MA) - See all my reviews

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.

6 of 6 people found the following review helpful:

4.0 out of 5 stars Makes abstract concrete. Pretentious style gets in the way., May 1, 1997

By A Customer

LIKES: 1. Providing historical perspective/background of the key developments in the Calculus. Prior to reading this book, I only knew Cauchy's name from the various theorems that bear his name. How many people knew that he was the one who developed the concept and method of using limits? 2. Tied the abstract (x,y) to the concrete through examples where x=time and y=position. Allowed me to understand the Fundamental Theorem of Calculus not in terms of x's, y's, derivatives, and antiderivatives, but rather in terms of distance = rate * time. DISLIKES: 1. The style is pretentious, as if the writer was on a great high that only he could appreciate. 2. A few typo's like '6(t)' instead of 'G(t)'. I would recommend this for anyone who has studied the Calculus and would like 'the rest of the story'. It might also serve well as an introductory survey of the topic before delving into formal study.