Math magic

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Years ago, I enjoyed reading books about how to do arithmetic mentally and quickly (there are several of them - one good one is "Math Magic" by Scott Flansburg). There did not seem to be anything equivalent for more abstract math, i.e. algebra and calculus. For some reason, I cared so much that I actually took the trouble to write a couple of books about it ( http://hilomath.com/ ). To figure out what to write, I actually sat down with an old algebra text book, and while solving the problems in my head, very carefully observed what I did and how... then wrote down how it all worked, using words and images. This process was about a hundred times harder than it sounds; had I any clue how hard it would have been, I probably never would have started. Anyway, for doing abstract/symbolic math mentally, the method I came up with defines three le…