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They seem to agree on one thing: from a workaday perspective, math is essentially useless.

I would love it if someone had resources on how mathematics could actually be used as a tool by programmers.

What kind of problems would mathematics as a tool help me solve better/faster/more efficiently than the other tools in my programmer toolbox?

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There are plenty. The analysis of basic algorithms involve math (e.g. QuickSort, binary search, etc). Programming a user friendly website can involve advanced mathematics, for example you want to recommend to your users a product that might interest them (Collaborative Filtering)

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