A Tour of the Calculus

If you need a practical introduction to basic calculus technique, you would be better served by Silvanus Thompson's Calculus Made Easy. If you want to gain some understanding of why calculus is, like the cathedrals or the music of J.S. Bach, one of the greatest achievements of the human mind, try this. Depending on your temperment, you will either want to pitch it out a window or keep on your nightstand. If you dislike art, music, or poetry you would do well to leave it alone.

Baffled by rude intemperate reviews after having paid a small fortune to my public library for having kept the Berlinski book out too long, I am driven to support a book which does not need my praise but whose potential readers do need my corrective review. As an undergraduate at Harvard, I had the good fortune to be taught "the calculus" by Professors Sternberg and Loomis, a wonderful experience. I am now preparing myself to teach AP Calculus and need books to help students "connect" to the subject in an eclectic manner, students whose background is also eclectic. I love W.W. Sawyer and Morris Kline and Georg Polya and Courant and Robbins and the wonderful anthology by James Newman. But I was moved to both laughter and tears and a few eurekas by Berlinski's tour de force de calculus. And I am going to order the book to enjoy those feelings again and again so I can share them with my students. My touchstone for clarity and good humor is Richard Feynman. I am reading his introductory lectures on physics next. Berlinski is closer to Feynman in temperament and intellect than he is to his intemperate reviewers. He is modest and self-deprecatingly humorous. One could ask for the same in some of your reviewers.

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!

What a tour this book delivers! We visit all the great mathematicians who contributed to the development of the calculus, looking in on their lives in an intimately revealing way. Their ideas are presented clearly--and also in an entertaining (and sometimes wickedly funny) way. The book is written in graceful, "literary" prose, a fact that some reviewers apparently found annoying, but I found an added treat. Finally, Berlinski presents informal proofs of key theorems, but sets them apart from the main text so readers have a choice between merely gaining an appreciation of concepts or working through the math. I read this book during my daily commutes. An attractive young woman--a coed, I'm guessing-- spotted it in my hand and ventured a comment: "That's a great book." If I had been 20 years younger this might have been the start of something big, but in the circumstances all I managed was to grin in agreement. Highly recommended