Adventures in Tech

We are all accustomed to deterministic algorithms; we work with them every day, and feel comfortable in knowing that the results of running them are predictable, barring a coding error of course. The idea of randomized algorithms feels remote and uncomfortable, despite their usefulness and elegance.  There are a couple of great examples in the introductory chapters of the book " Probability and Computing " that are an eye opener. One is verifying polynomial identities: how can you tell that two different representations of polynomials are the same? For example, if we have two polynomials $P(x)$ and $Q(x)$, both of degree $d$ described by the following formulas: \[ P(x) = \Sigma_{i=0}^{i=d} a_i x^i \\ Q(x) = \Pi_{i=1}^{i=d} (x-b_i) \] how can we determine that they are the same polynomial? Intuitively we first check that the degrees are the same, then we could try to transform one form into the other, either by multiplying out the terms for $Q(x)$, collecting like t...