Customer Reviews

The Calculus Gallery: Masterpieces from Newton to Lebesgue

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4 star:		(1)
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First of all, this is not a graduate textbook or reference book. I would not compare it with Counterexamples in Analysis even though both books have something in common. This is rather a "popular math" book with lots of proofs. And for a popular book with this much details, I am impressed . Those proofs are not just some nice-to-have's sweeped aside in the appendix. They are actually the main events and are showcased after each exihibit of the chapter. The table of content does not do justice to the richness and excitement of the examples in the book. Interesting topics include a function that is everywhere continuous but nowhere differentiable, a function that is nowhere continuous yet integrable, and other noteworthy discoveries throughout the history of calculus (or, rather, analysis). The book's title says "gallery". But, in my opinion, it aims more towards becoming a "museum". This book should be a good read for most people interested in the subject.

If you like math, I guarantee you'll like this book! The author starts out with some very nice infinite sums from 17th and 18th century mathematics (Newton, Leibniz, the Bernoullis, and Euler's Gamma function). He continues into the 19th century with Riemann and Lebesque integrals, Weierstrass' pathological functions, Cantor's set theory, and winds up with Baire's category theorem.

Reading this book is like taking a guided tour through Real Analysis (= calculus of one real variable) with the math prof you always wished you had. Its only prerequisite is a working knowledge of calculus; the main points are explained very clearly, so the reader can skip through the book or fill in the details, and will learn a lot, either way. The book is very well written, and a great pleasure to read; I highly recommend it, for students, fans, and teachers!

There are many good things about this book - the theorems are beuatiful and they are part of 'real' mathematics. The writing is reasonably good. The only qualm I have is that the audience is quite specialized, more so than for most 'popular math' books. I think that anyone who has not had at least 3 semesters of calculus will find this mostly meaningless. However, for those who are familiar with calculus, this is an excellent book.

I got far more out of the Dunham chapters on Baire and Lebesgue than I got 50 years ago in a course on measure theory and integration. I actually understood, for the first time, why what was going on was going on. Plus, what was going on is told with crystal clarity.

I'd recommend this book highly to anyone who likes a bit of history with his math but doesn't want the history to overshadow it.

I haven't had a math class in 30 years. I wish I had this book when I was in college. The author mentions studying the art masters if you're an art student, so why not study the math masters if you're a math student? Sometimes the reading gets tedious during one sitting, but after a break it's fascinating once again. Be sure that a few calculus memories are floating in the back of your head before you start, and you'll be well-rewarded.

And by "solid background", I mean a good understanding of honors-level algebra (high school senior variety) AND a reasonably thorough understanding of basic calculus notions such as limits, integration, and differentiation. Even if your background is not quite this strong, I feel you will understand parts of the Newton Leibnitz Euler chapters, but you may start to struggle a touch after that. And, as was pointed out in an earlier review, this book is NOT for the General Reader. Very far from it, in spite of professor Dunham's substantial skill as a science/math writer. (A pleasure to read the gentleman!)

In fine: I studied applied math at UCLA some 55 years ago, and I have not done any serious math since about 1970, so I may be overstating the requirements necessary to enjoy this work, given my own very dim memory of some key elements of mathematics and of the mathematical proof. But for those who feel qualified, this is yet another wonderful piece of work by a truly gifted author.

Naf February 2007; Los Altos CA

I wish this book had been around when I was taking calculus a few decades ago. It is extremenly well written and explains all the reasons why mathematicians had to introduce all the concepts and definitions you encounter in a calculus course. Reading this book on the side will tell you exactly why you're doing what you're doing, and where you are going. All students of calculus will benefit from this book.

If you enjoyed "Journey through Genius" by the same author, you will also enjoy the present volume. It requires more math knowledge (at least a working knowledge of calculus), but the level is aimed at a bright high school AP student, or a college undergraduate I would recommend it for even serious mathematicians who would like to know more about how the present state of knowledge of analysis came about. I would especially recommend it for teachers and students of calculus. Too often, ideas which took literally centuries to mature are presented in finished form, as if some mathematician sat down one day and wrote out finished, rigorous theorems. Seeing how even venerable mathematicians like Newton and Cauchy got results without the rigour which we see as necessary today is an eye-opener, and should be an encouragement to experiment and "learn by doing", and not to be afraid to go boldly forth, even if you haven't dotted all the "i" and crossed all the "t".

If you are up on your math it almost reads like a novel. I can't say anything about it that hasn't already been said, but just affirm all the positive comments. If you like math you will love this book.

wonderful book, adds mathematical context to the ideas developed. good to read along a textbook on analysis.