A Tour of the Calculus [Hardcover]

David Berlinski (Author)

Book Description

ISBN-10: 0679426450 | ISBN-13: 978-0679426455 | Publication Date: January 13, 1996 | Edition: 1st

In its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps its greatest meditation on the theme of continuity. Charts and graphs throughout.

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.

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

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Product Details

• Hardcover: 350 pages
• Publisher: Pantheon Books; 1st edition (January 13, 1996)
• Language: English
• ISBN-10: 0679426450
• ISBN-13: 978-0679426455
• Product Dimensions: 9.3 x 6.4 x 1.2 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 3.0 out of 5 stars  See all reviews (140 customer reviews)
• Amazon Best Sellers Rank: #1,880,291 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

18 of 19 people found the following review helpful:

3.0 out of 5 stars Meh., May 30, 2009

By 

Kevin Urban "inverseuniverse" - See all my reviews
(REAL NAME)   

This review is from: A Tour of the Calculus (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.

82 of 100 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

This review is from: A Tour of the Calculus (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.

15 of 17 people found the following review helpful:

5.0 out of 5 stars I love this book!, October 5, 2005

By 

Mockingbird "A nerd" (Mars) - See all my reviews

This review is from: A Tour of the Calculus (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.