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Tips for international undergrad student.

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Hello everybody! I am a freshman at an university in Poland. I have a dream to get accepted into prestigious grad school in US. I tried to get in for undegrad but all of 15 universities I applied for rejected me despite summer schools at really presitigous institutes all over the world and strong (in my opinion) academics I had. I study Computer Science, but at high school I was involved in math and physics activities. My university is top in the country, but doesnt exist in world rankings. For grad school, I would like to do sth related to math and/or physics, maybe with elements of computer science. I would be ok with working interdisciplinary. Quantum Information Theory is kind of a mix of all of that and really excites me, but there is not a single course about it at my university. The problem is I only had math classes at university during the first semester and I will never have math again during my undergrad (I cannot adjust courses list). I also cannot go for any sensible exchange, partner universities are no-names. I am top of my class with high GPA. I am involved in some research in bioinformatics (publications may appear in the future), but I am not particularly interested in this area(I have no other sensible research opprotunities). Could you advice me what to do in my situation to improve chances for grad school? I know I should take up Math GRE and General GRE. I feel ok with it, even now Math GRE is not so hard for me, and I learn English intensively. Is it still crucial to volunteer or should I focus on academics? I practise algorithms a lot, try myself in competitions, but I am a beginner for now and to get into the top I should probably dedicate all of my free time to it. Isn't it a blind alley maybe? Would publications be more important? Thanks in advice for sharing any tips!

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