Mathematical Programming

Often, we come across functions that we do not know how to evaluate without having qualitative knowledge of the input value. For example, sin(x)\sin(x), max(x,y)\max(x, y)1 , and x|x|.

For example, how do we compute min(x,y)\min(x,y) without knowing beforehand what xx and yy are, using only a basic calculator2?

This question, along with many others, will be answered in this short course.


  1. max\max stands for maximum. max(x,y)\max(x,y) will always return the larger value out of xx and yy. Similarly, min(x,y)\min(x,y) (minimum) returns the smaller of xx and yy.

  2. For the purpose of this course, we will assume our calculator to have the following capabilities:

    • Addition, Subtraction, Multiplication, and Division
    • Exponentiation
      • including square roots
    • Floor and Ceiling

    These basic capabiities will enable us to construct other, more complex capabilities.

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