I'll take you through writing a ray tracer in the order I do it, along with some debugging tips. By the end, you will have a ray tracer that produces some great images.

You should be able to do this in a weekend. If you take longer, don't worry about it.

I use C++ as the driving language, but you don't need to. However, I suggest you do, because it's fast, portable, and most production movie and video game renderers are written in C++.

Note that I avoid most "modern features" of C++, but inheritance and operator overloading are too useful for ray tracers to pass on.

Is math related to science?