I recently completed my undergraduate in engineering from India. Somewhere along the line last year, I realized that I did not want to continue in the field of my major (which is completely unrelated to Math, except for Engineering Mathematics courses in the first 4 semesters) and wanted to shift to studying Math. I wanted to choose a degree in Math for my undergrad, but somehow messed up and ended up with a stream I do not like.
In order to make the shift to pure math, I started preparing for IIT JAM - Mathematics less than a year ago. IIT JAM is the entrance exam to premier Indian institutes such as IITs, IISc, etc. This required me to also study the syllabus of B.Sc (Math), along with preparing for the entrance exam. I appeared for the exam, and its results were recently announced. I expected to do better on the entrance exam. My rank is in the top 10% of applicants, but is not good enough to get into an institute (typically have to be in the top 1% of applicants). I am pretty set on doing my M.Sc. (Math) because it will provide me with a formal education in Mathematics which I have sorely missed.
Since I have missed out on getting into the universities that I wanted to, I need advice on what to do next. Eventually, in all likelihood, I would want to go to foreign universities to pursue another Masters degree in Applied Mathematics or a PhD (if I am able to carry out research successfully). Following are the options I could come up with:
1. Take a break for a year. Prepare again for IIT JAM. This option is what I am pursuing now because I believe that I just did not have enough time to prepare as compared to other students (6months v/s 3 years). Having said that, I think I made a decent effort and hope to do better on the JAM next year.
2. Try to join a regional state university for M.Sc.(Math). Ideally, I could have gotten into a regional state university in India with my score. However, because my undergrad is not in Mathematics, I am not eligible to apply to most places.
I also came across this Diploma course in Mathematics (https://london.ac.uk/courses/mathematics). I am thinking of doing this alongside my entrance exam preparation. Are courses like these beneficial when trying to gain a formal education or connecting with professors at universities?
The ideal scenario would be that I am able to crack the entrance exam this time around, and is my primary aim. However, I am looking for a backup which could help me get an education in Mathematics. Even instances or references of people who have made a similar switch would also be helpful.
tl;dr - Need guidance on making a late career switch to Mathematics.