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All the Mathematics You Missed

That is, a book that covers the motivation and important ideas of various fields of mathematics at the graduate/professional level (Measure Theory, Functional Analysis, Representation Theory, Algebraic Topology, Stochastic Analysis, Harmonic Analysis, Number Theory etc.)? I know there's the Princeton companion, but it is a massive book and not exactly suitable for light reading while commuting say.

Thank you.

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    $\begingroup$ What's wrong with the Princeton companion? It's exactly what you're asking for. Get an electronic version if portability is an issue. $\endgroup$ – Potato Jun 10 '15 at 10:25
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    $\begingroup$ I don't have anything to read electronic books and I don't intend to buy one just to read one single book. $\endgroup$ – Project Book Jun 10 '15 at 10:32
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You might have a look at Zeidler: Quantum Field Theory I and see whether you like that. There are also two more volumes. In many parts of the books there a great explanations from a motivational point of view, for instance on cohomology.

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  • $\begingroup$ If I carry 1000 pages around, I might as well carry the Princeton Companion, but thanks anyway. $\endgroup$ – Project Book Jun 10 '15 at 13:12
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    $\begingroup$ It would be good training ... Think of a 24 kg kettlebell instead. $\endgroup$ – Martin Peters Jun 10 '15 at 13:39
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    $\begingroup$ Professional trainers hate him! One weird trick to get that 6-packs! $\endgroup$ – Project Book Jun 11 '15 at 3:10

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