I've recently taken a basic numerical analysis course in university and the subject intrigues me so much. I know Pascal and C++ fairly well, not very good like a professional programmer, but just to tell you how good I am, I've coded several programs for numerical integration using trapezoidal method, Simpson's rule, midpoint rule and Gaussian quadrature rule. So my main question is, how far I could go forward doing amateur research in numerical analysis? I've seen that when I try to do arithmetic on large numbers things go wrong and with my limited knowledge of CS I guess a buffer overflow happens. So I guess I need to know some professional programming to be able to get some fascinating results. For example can I approximate pi up to 1000 decimals on a PC? Can I approximate e up to 1000 decimals? Things like that. I feel I have very little information about the subject, that's why I can't explain myself very well, but I think I've somehow tried my best to tell you what my intention is, I leave the rest up to the reader that helps me what I should do. My goal is to do amateur research in numerical methods of computing math. operators by computer. What things do I need to know? What limits will I face? etc. Thanks in advance.