Customer Reviews

Applied Differential Geometry

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The previous review is amazingly perceptive into Bill Burke's personality and thinking. He was not the most discplined writer or lecturer, (I had no less than 4 courses from him) but his insight and intuition could be amazing. I would recommend this book as a companion to something more traditional. If you are interested in General Relativity, which is what the book was suppose to be a precursor for, get Schutz or Misner, Thorne and Wheeler, or Wald.

Also, if you do want this book, get the errata from Burke's webpage,...is quite helpful.

I would also hearitly recommend Burke's best book: Geometry, Spacetime and Cosmology which is out of print. It is much physical and the examples are clearer. He taught english majors and theater students general relativity with that book.

A unique book. Changes the way one thinks about geometry. The concepts and tools become second nature. I strongly recommend it for engineers who need differential geometry in their research (they do, whether they know it or not).

To give an example from page 134: "Vector fields that do not commute are called anholonomic. If two transformations commute, then the system would never leave a 2-surface. This obvious results is called the Frobenius Theorem."

Now after reading about the Frobenius Theorem elsewhere, few people would call in "obvious." Nonetheless, when you read Burke, you will agree. (Granted, it will not happen at first reading unless you are already familiar with the material. So you will read the book several times, which only adds to the pleasure.) Afterwards, you will be happy to consult the proof elsewhere.

Caveat: this book is not the place to go for a formal presentation. It may cause conniptions in the more ideological bourbakistes. Nothing should prevent one from also reading some of the excellent texts that present the material in a precise way, for instance those by Manfredo Perdigão do Carmo, Spivak, or Lang. Nonetheless, Burke is the one to go for the intuition.

I'm not a physicist or mathematician but I play one on TV. So I am more qualified to review a book on differntial geometry than either of the above professionals. This book is a very good introduction to all the hairy squibbles that theoretical physicists are writing down these days. In particular if you are perplexed by the grand unification gang then this book will help you understand the jargon. However, having only had physics when advanced vector calculus was enough to get by, it is a bit hard going due to the frequent errors and glosses the author makes. Burke gives a very hip and entertaining introduction to some of the most beautiful ideas in physics. It is enjoyable to read if you like sinking your teeth into something more rewarding than Ann Rice. I gave it a six rating because the errors and glosses are so annoying. I suspect Burke's puckishness is responsible; the book has no actual problem sets but he does work out problems that don't always work out. So the reader really has to work at understanding by correcting the possibly(?) intentional errors. Very sly of him. I am on my second reading and suspect that several readings down the line I will probably get the message. The book deserves loving attention.