Ok so there was a thread around here that mentioned a lot of the members here were mostly self-taught.I wanna ask-can you share some sources for learning the math or whatnot to become proficient in more advanced techniques like most real-time global illumination techniques that require a knowledge in working with spherical harmonics and reflective shadow maps.Any specific books that you might suggest?I mean I can mostly understand the logic behind academic papers when I read them,but implementing them seems impossible,when I'm not proficient in the math they require.

If you want a book for Direct3D stuff by Frank Luna is good.

Although I acquired a lot of my maths and physics knowledge through conventional education (I studied Physics at University), I learned to program on my own very early and was implementing rendering techniques well before I studied the relevant math. My advice would be that practice makes perfect, both in math and programming. I'm strongly in favor of getting as good an education as you can, but meanwhile there's a lot to be gained in just programming stuff. Start out small and progress from there, and try to do things which you understand rather than simply copy code and algorithms you don't.

I agree with MrJoshL. I know this won't answer all your global illumination questions,
but good sites with explanations and discussion on implementation are worth gold.
Look at Hugo Elias' pages on CG, for instance;
http://freespace.virgin.net/hugo.elias/radiosity/radiosity.htm

He's great at describing and supplying visual references, too.
We should have a resource links sharing section here at gd.net...

thanks,Nvidia also has fully working global illumination system with source code provided: https://developer.nvidia.com/nvidia-graphics-sdk-11-direct3d,but without knowing the full math behind it,working with it is hard