I am not sure who told you that you can't do mining engineering in Columbia University, but according to their website there is a department that deals with it. Here's the link: http://www.seas.columbia.edu/earth/hksm/default.htm
Hope that helps.
Let's start by understanding that mechanical engineering is much broader than petro. or mining engineering. You can apply mech. engineering in both of these. As for electrical engineering, it is such a common job that in some countries it is simply not required. Personally I believe that an...