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June 7th, 2009, 12:07 PM   #1
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Joined: Apr 2009
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An Introduction to Pure Mathematics

Yeah, I was a graduate student and was totally clueless. Then I got introduce to this book Mathematical Quantization, by Nik Weaver. It is a truely a honest, to the point book. I would like to write what I understand from my perspective, starting from the back:

"Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can [possibily access the realisation of] determine quantum analogs of variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued "functions," we can transfer these constructions to the quantum realm, giving rise to 'C*- and von Neumann' algebras."

I believe these are true. This book are also filled with ideas which perhaps tell the author particular perspective on the topic.
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