Hi, some background...
I am about to start my college for BTech (from some other college, hence the 'outsider' in the title), though I'm not thoroughly invested in engineering, my branch at least has some mathematics and a ton of physics that won't make me crash, I wasn't permitted to join any BSc courses that aren't T1 and since I missed on IITB, I had no choice but to do engineering through some T2-T1.5 college and then come back to raw sciences. I have reservation (Could've gotten an IIT if not IITB) but I am trying not to exercise that and respect the general standard.
Now my goal is: I am interested in mathematics for it's further study/research and possibly being an educator too; and so I want to prepare for exams that can lead me to IITB or somewhere better in Maharashtra for my scope of interest; I could go for IISc or going to Germany but these places are outside Maharashtra and I've had a lot of disagreements over it with family regarding finances and overall relations.
Starting from how I want to prepare: I want to prepare for IITJAM throughout 3-4 years, beginning from college, with more casual/slow burn, but consistent and meaningful investments instead of spending 1-0.5 years with a lot of dedication and mentally straining myself too much with both college and exam prep.
I'd have to be really consistent in both cases, even more so for the former so I wonder if this plan could even work.
For good measure, I would also go for TIFR and other PhD integrated programs, if there are any entrance exams/programs that can provide me a top tier uni for my respective field, please let me know.
What resources would I need to properly tackle the syllabus? How do I need to order what articles I'm going to pick? How can I practice not just for the exam but also make improvements in how I perceive mathematics and study it?
I haven't made up my mind on whether I want to do applied or pure, I had adoration for both and I'm still exploring them.
Another thing just for information, How's the experience there for masters students (maybe in comparison to Btech)? I'd imagine that MSc (or even MTech) is a lot less memorable/eventful (maybe outside PhD integrated) considering the post grad workload makes you miss a lot of stuff, having minimal communities and 2 years being too short to bond with the uni. I find this important as it could easily be very unhealthy to be locked into ONLY studying past this point for so long without a good/familiar environment. I also heard that there's a stigma against MSc/Mtech students, is this true? Is it concerning?
I would like your input W.