Lecture 1: Topology (International Winter School on Gravity and Light 2015)
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As part of the world-wide celebrations of the 100th anniversary of Einstein's theory of general relativity and the International Year of Light 2015, the Scientific Organizing Committee makes available the central 24 lectures by Frederic P Schuller. Titled "A thorough introduction to the theory of general relativity", the lectures introduce the mathematical and physical foundations of the theory in 24 self-contained lectures. The material is developed step by step from first principles and aims at an audience ranging from ambitious undergraduate students to beginning PhD students in mathematics and physics. Satellite Lectures (see other videos on this channel) by Bernard F Schutz (Gravitational Waves), Domenico Giulini (Canonical Formulation of Gravity), Marcus C Werner (Gravitational Lensing) and Valeria Pettorino (Cosmic Microwave Background) expand on the topics of this central lecture course and take students to the research frontier. Access to further material on www.gravity-and-light.org/lectures and www.gravity-and-light.org/tutorials
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This professor is EASILY one of the best I've ever seen - every student should be so lucky to study from such an articulate, patient, and clear instructor at some point in their academic career!
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This is the most self-contained lecture which introduces Topology very gently & yet profoundly highlights very fundamental axioms that are at heart of Relativity.
Thank you very much. Especially, Mr.Schuller, for his teaching techniques. -
this guy is good at drawing cartoon clouds yo
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Awesome lecture, very clear and well motivated!
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The method of using board is amazing
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SUPERB SIR SUPERB
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I'm an Electronic Engineer, and I allways want to take a Course where you see Topology, Differential Geometry and Gravity, thenx, by the way, all those asking, what you need to know to understand this course, is just Set Theory and Read and Do Proofs, all the rest is explain.
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I cannot get over how great his presentation is. The ideas are so crystal clear, the notation and board work so pretty and suggestive of the ideas they represent, all of it organized, and even balanced like a painting.
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Ah, the Eintein's view on gravity (as opposed to the Feynman view).
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Can such f() be defined that maps M to N and also the chosen topology on M to another topolgy on N?
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what is the difference between U(alpha) and U? Is U(alpha) a set of all UєO?
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at 23:18, the equation should be ∀p∈M since Bᵣ is only defined for p∈ℝⁿ.
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Thank you for posting this! It's very helpful!
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Great lecture! Wished I had such a competent professor when I studied math. I never really got it, cause lectures were bad. This here is explained easy and one can follow.
What I like so much about topology is the fact that you don't need these annoying delta-epsilon-calculations to proove continuity :) -
If anyone is interested in other lectures by him
https://www.video.uni-erlangen.de/indizes/person/alpha/s/48/id/829
two of them are in english, the other two in german. -
Does anyone know where to get the problem sets for this series? It looks like the original site is gone.
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What mathematics should I know prior to starting this course?
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Point set topology is just a matter of language.
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absolutely superb.
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brings back good memories of my undergrad years :-( I'm a tired old hag now
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