The only real prerequisite is curiosity - to have sufficient interest to find out about something (real or imagined) that one is willing to spend the better part of a day or night or week on a problem for no other reason than the pure joy of it.
Access to a computer with a programming environment installed helps, but is not strictly required. Even very basic knowledge of programming concepts and a programming language is also very useful. Sophistication is not required, most problems described here can be programmed in a very simple manner. (Understanding the code samples may require some intermediate knowledge of the languages and libraries used, but is never required - all problems can be and should be developed from scratch.)
A college science education is certainly helpful but not strictly required, provided one is willing to accept some results on "faith". Some of the subjects discussed are quite advanced and not part of a usual undergraduate syllabus, but should be accessible to anyone with sufficient interest.
The biggest concern is the level of mathematical sophistication. So many questions in science (and physics specifically) are so naturally expressed in the language of Calculus and Vector Spaces, that it seems a disservice to attempt to do without. Throughout, I will assume familiarity with elementary transcendental functions (i.e. the trigonometric functions, as well as the exponential and the logarithm). I will also assume that the readers have seen derivatives (including Taylor's Theorem) and integrals before. I will also use vectors in two- (and sometimes three-)dimensional real spaces freely. Rarely will we require more sophisticated tools, such as complex numbers, Fourier Transforms, differential equations, etc. Finally, I will make sure that the results are clearly stated so that they can be used by everyone, even if the derivation was not fully understood.
(The first volume of the Feynman Lectures in Physics contains a few chapters which will cover all of the frequently required math in a form expecting little or no previous knowledge.)