I am physics master's student in India. I wish to do my PhD in theoretical physics in the Applied Maths department at Cambridge (DAMTP). Can I apply for a PhD and do Part III as a part of it (akin to 1 year of coursework before PhD in India or Master's + PhD in US) or should I do Part III and apply for a PhD in DAMTP separately by the end of it?
Even though I have good grades in all my courses, I am not confident with my skills. My institute is one of the very best in India, however I am not satisfied with my understanding of most of the subjects (and mathematical rigour in general) and there are a few topics, e.g. Advanced QFT, Advanced GR/Cosmology, which are not offered here. I believe Part III would help me in fixing these holes and I want do this before my PhD (in Cambridge or elsewhere).
From the Cambridge website: "Part III is a 9 month taught masters course in mathematics. It is an excellent preparation for mathematical research and it is also a valuable course in mathematics and in its applications for those who want further training before taking posts in industry, teaching, or research establishments."