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Not an essay or book, but there is a rather informative and clear video address by Timothy Gowers (a Fields Medalist) in 2000 on the "Importance of Mathematics" for an audience containing non-mathematicians in Paris. He specifically addresses the issue of the (enormous) benefits that mathematics yields on a (very small) investment, its intrinsic cultural ...


3

Be careful of what you wish for... Bernt Stigun's book "Towards a Formal Science of Economics: The Axiomatic Method in Economics" probably goes above and beyond of what you had in mind when asking for rigor. He starts with mathematical logic (first-order languages)... http://www.amazon.com/Toward-Formal-Science-Economics-Econometrics/dp/0262192845/ Also I ...


1

You can use the following function for calculating floor: $$f(x)=x-\frac{1}{2}-\frac{\arcsin(\sin(\pi(x-\frac{1}{2})))}{\pi}$$ Then, for your purpose, you can simply use: $$\frac{f(xN)}{N-1}$$ If it helps, then you can also use the following function for calculating ceiling: $$f(x)=x+\frac{1}{2}+\frac{\arctan(\tan(\pi(-x-\frac{1}{2})))}{\pi}$$ If ...



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