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A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity (Anglais) Broché – 21 juin 2013


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" ... do not be put off by the title! This is a great book on relativity which nicely bridges the gap between those books catering for readers who know little or nothing about relativity and those texts intended for physics mathematical specialists." - Amazon.co.uk

"Well done - a magnificent achievement" - Amazon.co.uk

"Highly recommended for anyone willing to invest some time and effort." - Amazon.com

Synopsis
Based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence - Einstein's theories of special and general relativity together form a cornerstone of modern physics. Special relativity has some strangely counter-intuitive consequences, including time dilation, length contraction, the relativity of simultaneity and mass-energy equivalence, whilst general relativity is at the heart of our understanding of black holes and the evolution of the universe.

Using straightforward, accessible language, with numerous fully solved problems and clear derivations and explanations, this book is aimed at the enthusiastic general reader who wants to move beyond maths-lite popularisations and tackle the essential mathematics of this fascinating theory. (To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics.) For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution; the four classical tests of general relativity; simple black holes; the mysteries of dark energy and the cosmological constant; and the Friedmann equations and Friedmann-Robertson-Walker cosmological models.

Understand even the basics of Einstein's amazing theory and the world will never seem the same again.

Contents
Preface
Introduction
1 Foundation mathematics
2 Newtonian mechanics
3 Special relativity
4 Introducing the manifold
5 Scalars, vectors, one-forms and tensors
6 More on curvature
7 General relativity
8 The Newtonian limit
9 The Schwarzschild metric
10 Schwarzschild black holes
11 Cosmology
Bibliography
Appendix - Planetary motion data
Acknowledgements



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Amazon.com: 25 commentaires
66 internautes sur 70 ont trouvé ce commentaire utile 
Fantastic!!! 3 août 2013
Par Alan T. Lefor - Publié sur Amazon.com
Format: Broché Achat vérifié
This is absolutely the best "first book" there is for anyone intending to learn General Relativity. As anyone interested in the subject knows all too well, people interested in the field are often stumped by the necessary differential geometry. This is especially true for those pursuing self-study. There are very few books that make tensors comprehensible to the uninitiated, especially those without a course to guide study and a professor you can ask questions to. This book does guide you gently into tensors and explains in very easy-to-understand terms what they are and how to use them. I have not found a better description anywhere. From this book, one can then graduate to a book like "A first course in Gen Rel" by Schutz, or "Gravity" by Hartle, or "Einstein Relativity in a Nutshell" by Zee. Following that, progression to the Bible (MTW) will be fairly smooth.
44 internautes sur 49 ont trouvé ce commentaire utile 
A very mathematical book 4 octobre 2013
Par Kindle Customer - Publié sur Amazon.com
Format: Broché Achat vérifié
I have two comments about this book. First, that it provides an excellent overview of general relativity for the reader who has a good grasp of university level mathematics - at least a first year course in calculus and geometry. Second, that the introduction to the book states that it is intended for the general reader with only a limited knowledge of mathematics - and this it is certainly not. Try clicking on the book and then go to "surprise me" a couple of times so that you see a few random selections of the equations you will be faced with. I found the book heavy going because my honors degree in mathematics is over 40 years old, apart from that I certainly intend reading it again when I have the time to devote to it and believe that it is a very good book on the relativity and provides a refreshingly new view of the subject.
I gave the book four stars, not five, only because the book requires more mathematics than the initial description would lead you to believe. If the book was advertised as requiring a fairly good mathematical background I would have definitely given it five stars.
14 internautes sur 15 ont trouvé ce commentaire utile 
Amazing! 26 mars 2014
Par Alex Czajka - Publié sur Amazon.com
Format: Broché
I just want to put this out there: this is a great book. I am 14 years old and am aspiring to be a mathematician/physicist, so a friend of mine lent me this book and I've got to say I'm impressed. The author did very well at teaching relativity and more. My education of mathematics(not including mathematics I studied recreationally) doesn't exceed that of Algebra 2 and its preceding subjects as taught in California public schools, yet this book explained, in just enough detail, everything that I didn't know! It does get tricky at some points, but if you are truly motivated to learn about relativity it is a great read!
8 internautes sur 8 ont trouvé ce commentaire utile 
Just right for the layman beginner 24 janvier 2014
Par dhruva patil - Publié sur Amazon.com
Format: Broché Achat vérifié
For those people out there looking for a book to start of with before diving into the complex Math of General Relativity and are searching for a mathematical introduction from the very basic, this book is perfect. It starts out from with basic Math (functions, graphs) and accelerates towards Newtonian mechanics and special relativity within 80 or so pages. This book is, for the most part, mathematically understandable. He goes through each and every step while deriving any equation and shows us why the math is the way it is. He doesn't go in-depth about the scientific reasons and the predictions that an equation provides. But he does do more than just state the equation, which, for a mathematical book, is a lot. He gives a pretty good introduction to special relativity and General relativity.
If you are a beginner, then you will find the chapters on Schwarzschild metric, black holes and cosmology mathematically challenging. But that shouldn't matter as this is just a very basic introduction to general relativity and few of its applications. One cannot hope to become a master of general relativity by reading just one book.
Conclusion:
I ordered this book from India and it cost me around 20$ just for shipping. So when I say this was worth every dollar, I mean, worth ever dollar of the ~35$ I paid. Go for it. It is a perfect first book for Relativity. But beware, as you cannot just skim through the equations and the chapters on tensors and hope to understand anything that follows.
13 internautes sur 15 ont trouvé ce commentaire utile 
Promising, but not quite 13 janvier 2014
Par AmazonMan - Publié sur Amazon.com
Format: Broché Achat vérifié
I have read many books on the special theory of relativity but was put off by the standard texts on the general theory, so this looked promising. I did carefully go through about 2/3 of the book but then gave up as I felt things were coming at me too hot and heavy and without enough explanation. I give four stars for the effort and the possibility that it is me, not the author, at fault here.

But one thing was "incomprehensible" - the book starts out with the assumption that you know basically no mathematics and literally goes through geometry, the derivative, integral etc. I think it highly unlikely that someone without any math background would be able to keep up with what comes later on. Maybe it would have been a better idea if the author had eliminated all that upfront material and spent more time on the mathematics of GR.
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