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How I’m Spending The Summer

June 16, 2015

For most of this summer, I’ve been studying general relativity.  I have a pile of physics textbooks here on my desk and I’ve been reading and working through them.  When I research something, I tend to go online and find book reviews and order the textbooks which get the highest reviews.  Strangely, that process didn’t work so well for me with general relativity.

If you read the reviews, they’ll all tell you go with Bernard Schutz’s A First Course in General Relativity.  So I did, and I worked through a bunch of it, but I really don’t care for it.  I did not find it very clear.  I ended up reading several other textbooks, but the one which really worked for me is this one.

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It’s extremely clear and easy to understand.  It’s filled with all kinds of helpful pictures, has lots of worked examples, and concepts are explained very clearly.  I can’t recommend it more.

I found this textbook by chance when I was looking for solutions to another textbook I had already purchased.  There are university course websites where professors use a particular textbook and have assigned homework problems to their students and then post their solutions.  That’s really helpful to a person who self-studies like me.  A professor had posted solutions to about half of the problems in this book and I was really excited about that.  Plus the course had all kinds of special notes the professor wrote up, explaining things even more. That’s just perfect for me.  Past exams with solutions.  Past homework with solutions.  I can work through an entire course on my own that way.

Another great book to learn the main concepts and ideas from is Exploring Black Holes: Introduction to General Relativity, by Edwin Taylor and John Wheeler.  This book avoids tensors entirely, explaining all the concepts using basic high school level calculus.  You’d think that would limit the authors to explanations that are too basic to be worthwhile, but you’d be wrong.  I’ve learned a great deal from it.

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Using words and thought experiments, Wheeler manages to explain the central ideas without resorting to all this complicated tensor mathematics.  It’s fantastic.  It’s helped me have a much deeper intuitive understanding of what goes on within black holes, curved space-time, and all that sort of thing.

As for all the general relativity textbooks, most all of them offer brief introductions to tensor mathematics, but it’s not thorough.  They all begin with a short crash course on contravariant and covariant vectors, tensors, manifolds, metrics, and all that.  But if you want to learn the mathematics of tensor calculus really well and “get” it, I’d highly recommend Pavel Grinfeld’s textbook Introduction To Tensor Analysis and the Calculus of Moving Surfaces.

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I would rate this textbook a 10 out of 10, and I think most mathematics books are god awful.  It’s incredibly clear.  With most math books, I find myself reading and re-reading, and re-reading the definitions and concepts, and slog through the “proofs” which never make any sense.  This book isn’t like that at all.  I just sat down and read it and it all made sense to me from the get-go.  And then I went to work the problems and since everything was explained so well, I pretty much immediately knew how to work the problems.  If you search online you can find a complete solutions manual.

For fun I’ve been reading the Feynman Lectures on Computation.  This is a collection of lectures Richard Feynman gave toward the end of his life on computers and digital electronics.  It covers things like what’s computable and what isn’t, Turing machines, Shannon’s Theorem, reversible computation, the thermodynamics of computation, quantum limits of computation, and the internal structure of digital devices and their limitations.  Very cool book.

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I’ve also been doing a lot of running — roughly 8 miles each day.  I may well be in the best shape of my life!

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