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from the I-can-really-learn-my-maths-and-sciences-now dept.
If you ever wanted to learn General Relativity, now here's your chance. The caveat is that first you must learn differential geometry. But it's not difficult, really. Only lots of hard work, but not difficult. I was attending this February such a course. This course is fully documented: there are recordings of all lectures, and of tutorials with solutions (also the .pdf files with practice questions). For easier access you can also visit the The WE-Heraeus International Winter School on Gravity and Light YouTube channel.
You should know though that this material on the internet is not everything we were doing there, the biggest omission are the advanced tutorials, which were done in groups and couldn't be filmed. Also their solutions were too difficult to be "quickly" filmed like the tutorials that have videos. However there's hope that advanced tutorials will also be put online some time later this year (as promised by the organizers). In that case I'll submit a follow up story.
I must tell you that attending this course was really a great experience, and Prof. F. P. Schuller is in fact on of the best lecturers I have ever met.
(Score: 2) by PizzaRollPlinkett on Tuesday April 07 2015, @06:27PM
No, you must RETAIN differential geometry. That's the problem with casually being interested in math. I love d.g. and topology, but I don't have the time to study it at the level I'd need to learn it to be any good at it. This kind of math needs deep immersion to develop any facility with it. These areas of math require a huge background in different subject areas to be able to follow them. The only way to keep all that in your head is be constantly immersed in it. I can't find the time for that. I get discouraged and leave it alone.
(E-mail me if you want a pizza roll!)
(Score: 4, Interesting) by Hartree on Tuesday April 07 2015, @06:56PM
"No, you must RETAIN differential geometry."
Exactly. It's been 20 years since I've used that and taking a look at an advanced text is like being a stroke victim. You can kinda sorta remember it, but being able to actually use it again takes a lot of rehabilitation.
(Score: 2) by FatPhil on Tuesday April 07 2015, @07:44PM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by boristhespider on Tuesday April 07 2015, @07:55PM
It's all just differentiation though! Don't give up, it'll click into place. So long as you know a partial derivative (and the Greek alphabet), GR is not beyond you. And also don't worry; anyone who claims they understand intuitively what's happening in GR is a liar. We evolved to swing from trees, chuck spears, and tell each other where the fruit/angry lion are. We did not evolve to understand four-dimensional spacetime and anyone who pretends they can visualise it in full generality is either misguided, an idiot, or an out-and-out liar.
(Score: 3, Interesting) by FatPhil on Tuesday April 07 2015, @08:45PM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by hendrikboom on Thursday April 09 2015, @08:59PM
I'm in the first lecture now. I find it easy because I recognise it from 50 years back. I don't think it'll stay that easy when I get the the differential geometry.
There's another way of viewing topology in which open sets are *not* fundamental, but instead you use an apartness relation. I find it easier to understand, because one of the basic concepts is the inherent limits of practical computation. See Frank Waaldijk's book Natural Topology, at least for the first chapter or so. See http://www.fwaaldijk.nl/mathematics.html [fwaaldijk.nl] for context and links. It's constructive math.
I'm curious how much of what they do would still go though with the so-called natural topology.