Getting into Harvard or Yale, undergrad, as an Asian is very, very difficult. Top US colleges use race/ ethnicity quota system in admitting students. So, Asians (koreans) are competing against Chinese, Indians, etc for about 20-30% of the class at each top U.S. college. Getting into Harvard college as an Asian would mean that you got in despite an admission rate of 2-3%.
Getting into top schools at master levels (master in engineering, humanities, etc) is much, much easier than undergrad. Most American students don’t even apply to masters programs, and these programs are mostly filled by chinese / indian international students.