A Tour of the Calculus (Hardcover)

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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 (126 customer reviews)
• Amazon.com Sales Rank: #1,006,845 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

43 of 49 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.

25 of 32 people found the following review helpful:

4.0 out of 5 stars Really Good for those Who Like Math, March 3, 2001

By	Timothy Haugh (New York, NY United States) - See all my reviews (TOP 500 REVIEWER)    (REAL NAME)

This review is from: A Tour of the Calculus (Paperback)

Why anyone who didn't like math would read a book about calculus, I don't know, but let me preface this review by saying that if you don't like math, then you probably won't like this book. On the other hand, if you like math, then there is a lot to like in this book. And if you are currently in a calculus class--even if it's a required class--this book can help you make some sense out of what you're learning and put it in an historical context. This book is certainly a better development of the most basic concepts than you'll find in many of those 1000+ page Calculus textbooks. (Of course, it's just a conceptual development. You'll find little in the way of technique and problem-solving.)

I think the main reason I enjoyed reading this book is because I enjoy math and it's clear that Berlinski does too. It's always fun to read a book by someone who clearly enjoys what he is writing about. And he's structured the book well, giving the conceptual developments of the subject as they were ispired by the attempts to solve particular historical problems. He's also given us a taste of the personalities (Newton, Leibnitz, Cauchy, Riemann, etc.) who moved the subject forward, a look at what appears to be insights from his own experience as a teacher of calculus and mathematician, and relagated the formal math to appendices. This is a nicely done book.

My only complaint is that in his historical and classroom interludes, he gets almost a little flippant. Maybe a little too "fictional." It's certainly fun and engaging to read these sections but I began to wonder what was real and what wasn't. When he's talking about his students and colleagues who may or may not be real people this is fine but when he's reimagining important historical figures I began to wonder about accuracy. As a lover of mathematical history, I found this disturbing.

This is a small complaint, however. This is very worthwhile reading for someone who wants to understand why calculus was developed in the first place.

11 of 13 people found the following review helpful:

1.0 out of 5 stars Read several Reviews BEFORE Buying this Book!, April 1, 2002

By A Customer

This review is from: A Tour of the Calculus (Paperback)

I had just finished reading a couple of excellent books on mathematics and science (Fermat's Engima and e=mc2) and wanted to continue with a review of calculus that would be both instructive and interesting to read. I picked up this book without reading the reviews first, and boy was that ever a mistake! I made it through the first three chapters (barely) and couldn't take it anymore. This is definately a book for English majors (the prose goes on and on) and not for people truly interested in mathematics (cause there's very little).
An example from the first chapter, while describing Leibnitz: "He has a high forehead, arched cheekbones, wide-set staring eyes, and a large handsome nose; his is the face of a man, I think, who would enjoy mulled wine, poached eggs on buttered toast, a warm fire as the wind rattles the windows of a country castle, a young serving girl bending low over the plates and after dinner saying softly but without real surprise: Why, Herr Leibnitz, really now, bitte!" Who edited this book? They should be fired! I'm no english major, but that is certainly a run on and on and on sentence. But this is just one example, every paragraph is just like this, needlessly wordy, with very little actual calculus. Its like Mr. Berlinski is writing for the Danielle Steel crowd instead of an amateur science/math oriented audience that is more likely to buy this book. I give this book 0 stars! If you're looking for very well-written mathematics books that you don't have to be a mathematician to read - Fermat's Enigma by Simon Singh.