Do you think I can get into Columbia?

http://www.studentaffairs.columbia.edu/admissions/ Here's the admissions page for Columbia with all the requirements and everything.

Honestly your best bet is to start looking things over on there and then start contacting the university and getting some feedback from them.

Do your homework first. Millions of people want to get into these universities and they have little patience for people who want to get in without doing the work such as reading the admissions page and want someone to do it all for them. (Not insulting, just telling you how they view it and where it will put you and what you need to shoot for. )

If you do your homework and look everything up, when you write them you can ask them your specific questions if their page does not answer your questions. You may even contact their receptionists for faculty in your field and tell them you're interested in sitting in on aclass or are interested in their work and would like any advice they could give on what you should do to better prepare.

The competition is stiff but you'll actually be ahead of the curve by studying the admissions page and reading all you can there and poking around and becoming really familiar with everything. You'll also have an idea if you need to do anything extra to boost your standing. Many people apply without reading these or getting to know them and they suffer as a result and often don't get to where they want to go. (Be prepared!)

Lastly I reccomend two books (pick one) "The complete idiots guide to college planning" and "College for dummies." These just give a great host of things to consider that I don't have space to write here and really are helpful!

Congrats!