Function Vs. Method a Programming and Mathematical View

I have been thinking about how Mathematics and Programming are basically the same recently, because of the use of the word: Function vs. Method. In C/C++ which is the language I started out learning in, we would call sub programs Functions. While in languages like C# and Java they call them Methods. I remember reading some place that mention that Methods was more of the correct way of describing sub programs.

I of course highly disagreed. I consider programming and mathematics very similar, where in math a function is very similar if not exact to what we have in programming. A function in mathematics can be viewed as a black box where values going in are changed and/or the output may be different. When programming all we do is take in variables and either change them or output a different variable/value that needed the use of these variables.

Now going off topic,
So recently, thanks to digg, I found this website, actually a blog, that deals with mathematics and programming concepts. I like it so far, my math isn't the greatest, since I don't use it often enough.

http://epsilondelta.wordpress.com/2006/01/29/programming-like-a-mathematician-i-closures/
- and -

http://epsilondelta.wordpress.com/2006/01/31/programming-like-a-mathematician-ii-learning-new-languages/

I'll probably check on this guy's blog more often, especially since I like to keep my mathematical sense a-live while trying to become a better programmer.