Poll: What level of math is programming roughly analogous to?

Programming a first person shooter requires linear algebra. Programming crypto-algorithms require discrete math.

The problem arises, in that I adored maths, and had amazing teachers , and my father is an engineer and would sit me down every week and teach me more about maths, so how much can be attributed to programming, is hard to say. All I know is that variables introduced in the classroom made the class look at me funny when I pointed out how they worked when programming, in grade 6!

I think it's analogous to math in the sense that a programming language is a formal system, just like any logical system. The syntax is defined by formal rules, it semantics if not defined formally is strictly defined by the compiler implementation or hardware.

Actually, the link between programming and proving as been characterized by the "curry-howard isomorphism" that says that a program is a proof of his type. In that sense, programming = writing a proof.

For instance, in ML : the program "fun (x,y) -> x" is a proof of the proposition "A and B => A". This idea can be extended to more complex types/propositions (see the Coq proof assistant for instance).

That being said, writing programs usually require different set of skills than doing mathematics. The best programmers are not always the best mathematicians and conversely. To me difference shows especially for big complex software, rather than smart algorithms in programming contests for instance.

While I know the definitions of each term, I'm unclear on what exactly 'Pre Calculus' would be in this case. Also, is Trigonometry higher than Algebra or Algebra 2, if that question even makes much sense? Finally, what are the differences between Algebra and Algebra 2, and Geometry and Geometry 2?

Pre-Algebra / Discrete : Basic variable substitution and functions

Geometry : Drawing 3d figures and graphics

Calculus & Trigonometry : Physics engines