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Absolutely it is possible to get a good high level picture of a field without taking any particular class. Moreover things like "convex optimization" can be done in the footnotes of a serious maths course. But on the other hand until there are again 300+ people functional analysis classes like in the old soviet union, this is perhaps the best there is.

Yup, Kolmogorov and Fomin -- NICE book. I never learned from it, but I believe that eventually I got a copy, looked through it, and liked it.

If Boyd has some nice engineering applications, terrific!

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