In India, generally Ph.D. Mathematics program runs over three years and students needs to submit a thesis within 12 months of the end of the program. Many universities includes some capstone projects which may enhance the program duration to four years. Generally Five Courses are offered during the first year and minimum three courses are required to be completed. The topics offered in the first year is as follow, it may vary college wise.
4. Discrete Mathematics
5. Differential Equations