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I have completed by B.Tech (Bachelor of Technology) in Electrical Engineering from India, and I have since then been teaching Mathematics to the students aspiring for the IIT-JEE examination for almost 3yrs now.

I now want to pursue a PhD in Mathematics from a top university in the US. I have worked on some papers on alternative proof of Pythagoras theorem and another paper on new perspective into Catalan Numbers (which are yet to be published).

Please guide me and provide some valuable suggestion which would help me to become eligible for PhD programs in top universities in the US. Thanks in advance!

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    According to Cambridge dictionary "pass out" means to become unconscious for a short time, for example when ill, badly hurt, or drunk or to leave a military college after successfully finishing the course. Did you leave a military college? If not, you probably want to avoid using this phrase. Vote to close as it depends on the individual institute. – scaaahu Jul 22 at 8:10
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You are eligible to apply to any doctoral program, but acceptance is a different matter. Everyone seems to want to join a top university's doctoral program according to many questions here. Think about that for a minute. You have thousands of competitors for relatively few slots. Many, not all, top institutions have relatively small math programs.

Like anyone else, if you make an application it will be evaluated. If you show clearly that you are likely to succeed in the program, then you will be considered. This means your application will be moved to a large pile of those that need further scrutiny. But many of the applicants are coming from good (maybe "top") mathematics programs and so have all of the "expected" courses.

I don't mean to discourage you, but the task, given your desire for a "top" program, is very hard. If you want to study for a doctorate in math, pretty much anywhere, don't focus too much on a narrow set of universities. Cast a wide net. Apply to several universities, including a few "top" institutions, but not only those. Make sure you meet their stated requirements and make sure, in the US that you have very good letters of recommendation.

The fact that you have been trying out some research ideas in math will certainly be a plus. But the individual admissions system will have to judge whether they have sufficient merit to move your application to the "further consideration" pile, and then what occurs thereafter. Make your case, but cast a wide net, also.

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  • Thank you very much! – Euler Jul 23 at 4:24

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