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I would like to check if my mathematics paper is worthy of publication.

Is there any guide on the quality and form required for paper to be of publication quality?

Is there organization which will evaluate my paper for free?

How should I determine if my work is substantive enough to be grounds for pursuing PhD thesis?

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    Your edited question has a very easy answer: Ask your advisor. – Tobias Kildetoft Dec 12 '14 at 7:46
  • I am not having any advisor and i am not doing Ph.d. I am doing M.phil and I wish to know about it.@TobiasKildetoft – David Dec 12 '14 at 7:47
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    If you are not doing a PhD, then in the systems I am familiar with, the answer is simply "no" then, regardless of the quality of the work (I am mainly familiar with the Danish system where it is not sufficient to hand in a good dissertatio to obtain a PhD). – Tobias Kildetoft Dec 12 '14 at 9:07
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Regarding the Ph.D. part of the question, only a school can grant a Ph.D., and no school will grant you a degree if you are not enrolled as a Ph.D. student. Your best bet is probably to contact the mathematics department at a nearby research university and ask if a faculty member would be willing to look at your work. If you have really been doing original research on your own, then you can probably be admitted as a student and begin working toward a degree.

Regarding the journal part of the question, most journals do not charge fees to authors (they make their money from subscription fees). Most journals have web sites that explain the format and process for submitting a paper. See http://en.wikipedia.org/wiki/Academic_publishing#Publishing_process for a description of how this works.

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