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  • I agree it certainly wouldn't make sense to try and lay out everything; that's what a textbook is for. I do think we can make recommendations though; but perhaps we need more information about the problem domain. In my case I'm working on speech and NLP related problems, so situations like the above are quite common. It is of great practical use to be aware of these simple log identities. Maybe a better way of asking would be to ask about problem domains and things one 'ought to have an inkling of'. Commented Jul 9, 2011 at 2:55
  • @blackkettle: If you specify a problem domains (which often implicitly selects a set of solution methods by virtue of the fact that's the only way we know how work those problems), you might be able to focus on some kinds of optimizations. But even problem domains can have many solutions and there many optimizations; you wouldn't do a lot better if you narrowed this discussion to "scientific computation" and its solution methods. You mean diff eqn solvers? Relaxation systems? Computational fluid dynamics? Protein folding? .... Pick a very narrow solution area and you might have a chance. Commented Jul 9, 2011 at 3:44