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Differential Geometry for Physicists and Mathematicians: Moving Frames and Differential Forms (Englisch) Gebundene Ausgabe – 7. April 2014


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3 von 3 Kunden fanden die folgende Rezension hilfreich
Interesting Book! 21. April 2014
Von Jessie Hearle - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
I'm not done reading and studying this book but I have perused it and read the introductory chapter. I like the author's conversational approach and he has some ideas that he presents that I've not seen in print before, my background being a BS Degree in Applied Mathematics and Physics, with some additional study in Civil and Electrical Engineering. I have studied math through the level of advanced calculus and some advanced 400/500 level courses in differential equations, partial differential equations, special functions of mathematical physics, complex analysis, and vector analysis. I share the author's view that much energy is wasted and the real reason for the math is obscured in making formal proofs and not getting down to the business of applications early on. In short, anyone new to the study of any branch of mathematics would prefer being shown what it can be used for first, then gradually introduced to the proofs later in their studies.

The book contains no problem sets, only a number of illustrative examples scattered throughout the text. It might be better titled "Lectures on Differential Geometry for Physicists and Mathematicians." The author even cites Feynman's "Lectures on Physics" and references a passage from one of Feynman's lectures in the first chapter. In many ways, it is very similar in its approach to Feynman's Lectures, though the material it covers is certainly of much different character and at a somewhat more advanced level, while it remains accessible to perhaps an advanced undergraduate student with the mathematical maturity that would be expected of perhaps an honors student in intermediate calculus or differential equations. By this I mean to say it isn't the easiest read but with a bit of patience, it can be understood.

I have a few criticisms intended for the author. There are some glaring flaws in spelling and English grammar stemming from his mother language obviously being Spanish rather than English. However, the manner of writing, the numerous misspellings, and grammatical errors should in no way be viewed as detrimental to the reading of the book. I quickly made up my mind that the author views getting the material into print far more important than satisfying academia's stuffy approach to making proper sentences. This is mathematics, not a course in English literature after all! Perhaps my biggest criticism is in his overeducated way of throwing complicated words into his sentences where a simpler word would have been a better choice. But having been guilty of a lot of that myself until late in my university education, I know how difficult it can be to trim the fat out of the language as well as sentence structure. Some might consider it arrogance but I'd say that view would be wrong. He is, after all, trying to help in the best way he knows to get some very valuable views into the hands of those who are best equipped to use it.

In short, I find the author very real and down to earth, though rightfully proud of his work. And why shouldn't he be? It is, after all, rather unique!

My suggestions for improvement in a future edition would be the following:

1.) Have someone proof read the manuscript and correct the English, eliminating overly pompous writing in favor of a direct, modern, and very clear style while keeping the tone informal. Simpler is always better when it comes to writing.

2.) Add some graded problem sets at the end of each chapter that contain numerous application examples and brief, detailed solutions to every problem in an appendix at the back of the book. Have the solutions thoroughly checked by a couple of colleagues. Don't try to add proofs. Proofs will only make the book less accessible to the intended audience of physicists and applied mathematicians. If there is a desire to add proof problems, collect all of them in an appendix at the back of the book and include detailed steps to each proof in the solutions appendix..
3 von 4 Kunden fanden die folgende Rezension hilfreich
Not for the non mathematician 14. Mai 2014
Von olligist - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
I have a graduate degree in Physics and am familiar with the cartan calculus and bought the book hoping to get a clear explanation of the tetrad and Newman Penrose formalism. This book may be okay for someone who is an expert but is not one to try to learn something from. The notation also is archaic.
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