Both common core math and mathematical finance depend critically on recursion. This is one reason that a math finance guy is a good guide to learn common core math.
Green’s functions in finance are a method for doing recursive calculations.
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I have had over twenty years experience in teaching recursion and basic finance on Wall Street, to actuaries, computer programmers, and so forth.
They and you would do well to start by learning the proof of the associative law of addition of whole numbers using recursion. The same techniques can then be used in probability and in pricing financial instruments.