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purplecthulhu at 11:40am on 30/04/2003 | If I were a Springer-Verlag Graduate Text in Mathematics, I would be Frank Warner's Foundations of Differentiable Manifolds and Lie Groups. I give a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. I include differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provide a proof of the de Rham theorem via sheaf cohomology theory, and develop the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find me extremely useful. Which Springer GTM would you be? The Springer GTM |
I'd be interesting to know which text
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overconvergent since he's probably capable of writing one of these books by now, and would understand more of the words above than I do.
(no subject)
If I were a Springer-Verlag Graduate Text in Mathematics, I would be J.L. Doob's Measure Theory.
I am different from other books on measure theory in that I accept probability theory as an essential part of measure theory. This means that many examples are taken from probability; that probabilistic concepts such as independence, Markov processes, and conditional expectations are integrated into me rather than being relegated to an appendix; that more attention is paid to the role of algebras than is customary; and that the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.
Which Springer GTM would you be?
The Springer GTM Test