Separating Monte Carlo methods from math theory is an odd distinction to make. There's a lot of sophisticated theory underlying Monte Carlo methods as well. MC

Separating Monte Carlo methods from math theory is an odd distinction to make. There's a lot of sophisticated theory underlying Monte Carlo methods as well. MC also is more of a loose term referring to a class of techniques, rather than any specific algorithm. In that sense, there aren't really any [specific] tools or software you would use. A textbook on MC applications to your area of interest is probably the best place to start, there are a ton in practically every field. If theory-heavy presentations aren't your flavor then you can likely find a text or blog series to match.