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## Main Question or Discussion Point

I think most students develop their mathematical background up to classical tensors before digging into the physics of general relativity.

I think this approach is good, but once this "Introduction to General Relativity" is finished, then the student should refine his mathematical background further and study tensors (with the modern coordinate-free approach), differential manifolds, point-set topology, differential topology, group theory, fiber bundles, etc... and then

I think this approach is good, but once this "Introduction to General Relativity" is finished, then the student should refine his mathematical background further and study tensors (with the modern coordinate-free approach), differential manifolds, point-set topology, differential topology, group theory, fiber bundles, etc... and then

__study general relativity again__with a more mathematical general relavity book. This way, he gets a strong taste of general relativity from the both the physicist's and mathematician's point of view, with which he can then decide upon how to specialize. What do you think?
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