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USC is not well known internationally, it is a very local school. USC doesn’t rank very high on the international rankings
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Sorry, but this is simply not true.
Check out the Times International Rankings, which are based solely on reputation (how well a school is known globally):
https://www.timeshighereducation.com/world-university-rankings/2016/world-ranking#!/page/1/length/25
USC #68, ND #108
I can’t say for sure about its’ reputation in Europe, but the Times is a UK paper.
In China, USC is known (though not as much as the UCs). I work with college bound students (undergrads and grads). Notre Dame has never come up even once. (That doesn’t make USC better than ND - we’re just talking about being well known in other countries.)