gromov wrote:Given you had background in a different field, you should carefully consider what sorts of mathematics you would like to pursue, and work towards mastering the fundamentals for that at the least. A good subject GRE score seems almost required for internationals applying to most strong US schools, so it may not be a huge boost. In places like Canada, you likely may not even need a score to apply.
If you pursued an applied mathematics PhD, you could use your past background as an advantage.
My advice is to figure out why you failed the attempt and be open to spending some time securing good background for your interests. But I confess to knowing little of PhD admissions in India.
Feedback on entrance exam results:
I did miserably in abstract algebra-went horribly wrong in word problems involving rings and isomorphisms and vector spaces.I amazingly fared badly in multivariable calculus.The positives are that I scored high in linear algebra and topology.I was trying to pass an exam which required 1 year prep work,I had 4 months.
Sorry for not making it clear,I did my bachelors and masters courses in automotive engineering.I dont have a phd in applied math...yet.But,as you say,if I use my past background as leverage,it looks like applied math seems more connected to my field.But,the problem is I like pure math subjects equally.This is where I am at a dilemma,to take-up a masters course in pure math or applied math??One professor suggested I take-up a integrated phd program since I'm already 24.In the meanwhile,I will keep working on my basics as you advised.Thanks again.