Good (preferably free) Beginner Software for Part Creation?
I don't have a heavy math background, but enjoy using such skills when applicable.

If you've not yet explored OpenSCAD, you may find that it meets your qualifications. It's more or less a scripting/descriptive language "compiler" that takes ordinary text and converts it to your model design. I use quotes, because I'm not skilled enough to qualify it as a true compiler, although it works in a similar manner and may indeed be a compiler.

It meets another qualification of yours in that it's free and there's quite a supportive mailing list/forum for any questions or difficulties that arise. If you look on Thingiverse using OpenSCAD as a search term, you'll find others' code available for examination and integration into your own models.

For the folks who are not so much into the math and text and logic, there's a GUI of sorts for OpenSCAD called BlocksCAD that allows drag and drop of various modules in a manner akin to Scratch programming. 

I'd been using OpenSCAD long enough that I found BlocksCAD to overly complicate the creation of models by obscuring details. It may be better suited for younger model makers in that respect.

Syntax and punctuation errors would be eliminated with BlocksCAD, while it's far too easy to create such errors in the editor for OpenSCAD. One gets used to it and error count quickly is reduced.