Rating: 
Summary: If you like Math...
Review: A good read for anyone interested in mathematics. Berlinski makes calculus interesting, juxtaposing the Mean Value Theorem and comical anectdotes during his childhood. Definitely not your average book about calculus.
Rating: 
Summary: A mixed accomplishment...
Review: Being somewhat a mathematical and literary dillitante myself, I looked forward to reading this book. Perhaps my expectation were a bit too high.Berlinski is writing in an arena where there arre a lot of heavy hitters: James Newman's "The World of Mathematics", Gamow's "One, Two, Three, Infinity" and other books, "The Histoty of Pi", and so forth. A number of excellent writers have taken up the challange of presenting important mathematical concepts to a general audience. Berlinski's intent is to impart to the reader a feeling of what the calculus as well as its historical evolution and import. He sets for himself the difficult task of teaching you the calculus while simultaneously entertaining and diverting you. This is not an easy task, and Berlinski is only partially successful at doing so. The intial half of the book tends to give the mathematics short shrift while the author waxes effusively over an assortment of historical tidbits. Some are fascinating, some merely diverting, but Berlinski's can be a little off-putting. He's one of those authors who is enamored of italics; every other sentence seems to have a word or phrase italicized in an attempt to emphasize certain notions that he thinks are important. But this is an amateur's technique, as well as a rather annoying affectation. If a thought cannot be conveyed by words alone, attempting to add suggested vocal inflections doesn't help convey the information any better. The latter half of the book has some good (though brief) explainations of a number of important topics, but they're too terse to really instructional and too dense to be something the casual reader can look at say oh, I see, and go on. I suspect the best audience for this book would be a student just beginning the study of calculus, or perhaps a gifted high school student looking for something to inspire him or her to go off in search of more didactic works.
Rating:
Summary: A Tour of the Calculus
Review: David Berlinski has written two popular books on mathematics, the first entitled, "A tour of the Calculus," and second, "The Advent of the Algorithm." The theme of this duo of books is that mathematicians have produced two great ideas of "the great scientific culture of the West." Neither book requires the reader to have more than a high school level of mathematical knowledge. He does present proofs in appendices that a lay-person might find difficult or beyond their ability to follow; however, these are not required in order to understand the major ideas of the books. The author's thesis, as stated at the beginning and end of both books, is that the analytical thought of Calculus has gone through it's cycle of growth and is now, for the most part, come to a stand-still, while the sort of mathematical logic embodied in the computer's use of the algorithm, has emerged as the succeeding great idea "of the great scientific culture of the West." Yet, the content of both books is not so much an argument in support of this thesis but a guided tour of the essential ideas of both mathematical methods. Mr Berlinski is an emancipated professor of college mathematics and clearly knows his subject. He also is a sophisticated writer, presenting the reader with plenty of rhetorical devices in an attempt to make the terse matter of mathematical concepts easier to digest. These devices include imaginary reconstructions of plausible scenes and dialog he might have had with the great pioneering mathematicians, past professors and students. He also frequently meanders into metaphysical interpretations of the mathematical ideas, particularly between sections of the book bearing proofs. His choice of vocabulary can be challenging; I recommend having a pocket dictionary on hand. In his first book, A Tour of the Calculus, Mr. Berlinski traces the evolution of the first great idea of "the great scientific culture of the West": the Calculus. The time was ripe in the 16th century for both Issac Newton and Gottlieb Leibnitz to simultaneously discover the art of reckoning instantaneous rates of change. While Newton is able to use these calculations to write the great Principia, Leibnitz devises an ingenious set of symbols for representing the strange articles of the Calculus. Neither mathematician would have been able to advance upon the work of the ancient Greeks had it not been for the recently deceased Rene Decartes' fortuitous dream whereby geometrical shapes are represented as coordinates along the X-Y axis of a 2-dimensional grid. However, the phenomenon of acceleration is not a mere polygon, but a continuous function of time. To map this on the Cartesian coordinate system, mathematicians conceived continuous functions. For every possible moment in position of a moving object, another moment from the continuous flow of time is required-with no interludes. This was a logical problem that had not been solved since the ancient Greek, Zeno, proposed his famous mathematical riddles about the impossibility of passing over a continuous distance. Yet by the nineteenth century, logicians Richard Dedekind, Karl Weierstrass, and George Cantor, constructed the ideas of Real Numbers and a logically cogent definition of a limit that finally seemed to answer Zeno's riddles to the satisfaction of most modern philosophers of mathematics.
Michael Rolle's theorem of local maximum and minimum points in a curve cleared the way for the important mean-value theorem. This theorem guarantees the existence of a differential value equal to, and somewhere within the two data points that determine the average rate of change in something always changing (such as a car accelerating). This is a hard idea to comprehend and even harder to appreciate; however Mr. Berlinski devotes much of the book to this quintessential theorem. The reader soon sees how it is put to use, proving the other great theorem, the fundamental theorem of calculus, that links together the operations of integration (i.e. finding the area beneath a curve) and differentiation (i.e. finding the instant rate of change of a function). Mr. Berlinski marvels that these two seemingly different quantities are mathematically related.
Rating:
Summary: the basics
Review: first of all, let me say that David Berlinski is a great writer. That being said, his book lacks a few things. If before you read this book you say "calculus? what?" this books is perfect, it will introduce you to the concept with startling ease. after you have read this book if you wish to learn more about calculus you may want to consider a more rigorous book. this book provides many examples but few or no test-practice problems. this is not a book to learn calculus from, it is merely an introduction.
Rating: 
Summary: If you loved Strunk & White...you'll hate Berlinski.
Review: I approached this book with some trepidation...after all, it was "recommended" to me be a friend who claimed that it was "the worst book ever written." How could I pass up such a magnificent opportunity? Berlinski's prose has obviously been a sticking point for a lot of reviewers, so I'll address it first. It's terrible, no question--pretentious, and with a very low signal to noise ratio. It's just a never-ending series of digressions, few of which add any meaningful insight. In one episode, we're regaled with a tale of Cauchy stopping to use a public restroom. One has to surmise that the editor himself was unable to make it past the first chapter, or such drivel couldn't possibly have ever made it to press. On the mathematical front, the story is less dire (though still not good). If you were to wade through the verbiage, you could conceivably gain some intuition on limits or the mean value theorem. But I didn't find much to chew on in his treatment of the integration or differentiation, unfortunate for a book about "the" calculus. Berlinski also has an unfortunate, if somewhat excusable, tendency to confuse math and physics. At one point, he claims that "speed is a fundamental concept of the calculus". Kinematics is certainly the most obvious source of example problems for elementary calculus, but the two really are distinct. In the end, I don't agree that "A Tour of the Calculus" is "the worst book ever", but I'm hard pressed to recall a non-technical book I've liked less. Berlinski's goal is noble, but the execution leaves a lot to be desired.
Rating:
Summary: If you loved Strunk & White...you'll hate Berlinski.
Review: I approached this book with some trepidation...after all, it was "recommended" to me be a friend who claimed that it was "the worst book ever written." How could I pass up such a magnificent opportunity? Berlinski's prose has obviously been a sticking point for a lot of reviewers, so I'll address it first. It's terrible, no question--pretentious, and with a very low signal to noise ratio. It's just a never-ending series of digressions, few of which add any meaningful insight. In one episode, we're regaled with a tale of Cauchy stopping to use a public restroom. One has to surmise that the editor himself was unable to make it past the first chapter, or such drivel couldn't possibly have ever made it to press. On the mathematical front, the story is less dire (though still not good). If you were to wade through the verbiage, you could conceivably gain some intuition on limits or the mean value theorem. But I didn't find much to chew on in his treatment of the integration or differentiation, unfortunate for a book about "the" calculus. Berlinski also has an unfortunate, if somewhat excusable, tendency to confuse math and physics. At one point, he claims that "speed is a fundamental concept of the calculus". Kinematics is certainly the most obvious source of example problems for elementary calculus, but the two really are distinct. In the end, I don't agree that "A Tour of the Calculus" is "the worst book ever", but I'm hard pressed to recall a non-technical book I've liked less. Berlinski's goal is noble, but the execution leaves a lot to be desired.
Rating:
Summary: A Nice Try
Review: I'd like to give this book a better score. I appreciate the author's attempt to make the calculus accessible to the casual reader but, unfortunately, he only partically succeeded. While he does use non-mathematic language to explain difficult concepts, he gets way too carried away with endless digressions.
Rating: 
Summary: I liked the book!
Review: I'm giving this book a 9 because it dares to be different. It has a very personal style, and is written in prose ("tending" to verbosity). I'm sure that this puts off typical "mathies" , people who want mathematical insight and "damn the torpedoes" (ie, words) and I don't think that this book will teach calculus to the newcomer, though it may be useful as a supplement. I liked it as a review of things I learned quite awhile ago. Sometimes, especially for the first third of the book, I would get impatient with the author's wordiness, waiting for him to "drop the other shoe". I found, though, that my patience and willingness to hold the thought while he rambled on resulted in the realization that he was making a valid point, but taking a parallel avenue of using words, which made the route longer (I have the feeling that this technique exercised both sides of my brain). I also thought that his placement of mathematical appendices was well spaced and properly positioned throughout the text. By the time I finished the book, I felt that I had acheived an integration of my knowledge of the calculus, and had a renewed appreciation for it. However, I can understand why some people didn't like this book. At least this author has the "fierceness" to be different, and it is one of the most "different" book on the calculus that you'll find!
Rating:
Summary: Inspiring
Review: If you have little math knowledge and read this book, it may inspire you like it did me. If you like deeper meaning behind things, you may like this book. If you are good at doing math problems and that is how you see mathematics, then you probably not like this book
Rating:
Summary: a reason to like the book
Review: It's been a long time since I HAD to take a calculus course.I've been told that calculus for business majors isn't even required anymore. I remember strugling with the simplest treatment of the calculus;something called "A breif course in calculus. It was primarily designed for non science students. I spent hours trying to understand the most basic concepts. And although I never used calculus,and barely if at all,understood it, I found over the years that it was a great mental excercise everytime my mind got lazy.For those impatient critics of the book, they must realize by now, that I have meandered and digressed much like Berlinski has been accused.My point is that many of us enjoy reading for it's own sake; we're not all science and math majors. Also,after reading the book, I think I have a better understanding of calculus. I didn't expect to learn calculus by reading the book. I do understand,however, that now I have more time to enjoy the journey while students and thier teachers do not.
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