I want to do P.hd in maths through correspondense which university is offering this ?

Answer 1

The best way to do correspondence/online programs, in my view, is to take them at good, campus based, non-profit universities that also offer the same programs on campus.  There are a number of these universities that offer MS degrees in mathematics online.  Among the best, in my opinion, are the following:

http://www.cvn.columbia.edu/deg/app_math...

http://www.amathonline.washington.edu/am...

However, I have never seen a Ph.D program in mathematics at this type of university.  

It is possible to take a Ph.D in mathematics at the University of South Africa, but it operates by distance education only.

http://brochure.unisa.ac.za/brochure/sho...

You should be aware that to take full advantage of a Ph.D program in mathematics, you need to be on campus.  You can certainly do the required coursework and write a dissertation away from campus.  But you will miss the seminars and colloquia,  interaction with other graduate students and faculty,  instruction of undergraduates, close supervision from your adviser, and opportunities to collaborate on research papers.  These things are all essential to your success as a professional mathematician.

You might do better to take the MS by distance, and then do the Ph.D on campus.  Note that even taking MS level courses from a distance is a challenge.  Some of the deeper concepts in pure mathematics graduate courses can be difficult to master without the help of the instructors' office hours, special problem sessions and student study groups.