Really need advice for the next year.

> It's not possible for me to attend graduate level classes, since my college doesn't allow it.

What exactly do you mean by this? Are you just not able to officially schedule them? You can try auditing a graduate class then, do all the coursework/ exams and get to know the professor. You'll have one recommendation letter set if you excel in the class.

If you mean that you aren't even allowed to audit classes then try auditing classes at another university, maybe a nearby university. I'm doing something like this, which is possible since many classes are through video calls because of the of the pandemic. From what you said you're background is at the moment you shouldn't rush for them to be graduate classes.

> I really want to pursue a Masters in Pure Math from a good university abroad, and I think I am seriously under-prepared for it.

>I would be really thankful if you guys could tell me what I should essentially focus on in the following year to improve my chances at a Masters. Any help would be much appreciated. Thank you so much!

If you're serious about this, then let me share my advice. I am applying to graduate school this November, I'm from a subpar unknown school located in developing country as well. The first thing you have to acknowledge is that you're at a huge disadvantage in getting in compared to others. So because of that you have to really excel. It's great you're taking the initiative already and self learning the topics will probably be a struggle at some point for you, but you have to put in all the work to reap the benefits. You also have to be able to prove and back up your hard work. I disagree with arkaghosh since you're intent on pure math, doing internships or a project on applied math will do nothing for you. I would recommend for you to apply to REUs overseas (preferably in a school you have in mind, if you have none then at least in the country you have in mind). This will be a great opportunity for you to get research experience, build connections and possibly get a recommendation letter from a professor there if you do well. Do a thesis if you're school has the option. If you become interested in a field that none of your professors are experts in then I would recommend reaching out to professors from other universities, check with you're dept if they would allow that when the time comes. And lastly check if there are other students from you're school who are also interested in pure math, they don't have to be you're classmates or from the same year as you. Try to form a study group with them. Seeing other people's way of thought, communicating ideas to others and working with others is very beneficial.

/r/math Thread