The summations as for loops is what got my attention, as I am guilty of that. Also the idea of math as more manipulable than programming is intriguing.
The best tip I have, one that helps me not be intimidated by "real math," is to find a method of forcing yourself to slow down while reading. I've found that I get intimidated and frustrated only when I'm trying to rush through something. The best method I have for slowing myself down is to keep a notebook open, and write down definitions as I go (and lemmas, and theorems, but from here on I'll just call them definitions). I try to write a definition that is more clear (likely only to myself) than how it was presented in the text I'm reading. I also try to write down important implications of the definitions.
I think the procedural way of thinking about mathematics is natural for someone without much exposure, and is indicative that you're still trying to work out minor details of each definition you encounter. That's fine. If you have to think about a summation as a for-loop to understand it, go for it. After seeing a bunch of summations, eventually they'll carve out their own mental space. I think that writing down definitions will also help to solidify the declarative nature of mathematics, and definitely helps me to move through math more fluidly.
When I'm learning new math, I find that I'm least frustrated when I plan on moving very slowly. I feel that I'm making good time through a mathematics text if I read a page an hour. Next time you encounter some "real math", grab a pen and paper and really dig in to the text.