Schools What are the following schools known for

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The discussion centers on the reputations of various prestigious universities, highlighting their perceived strengths in specific fields. Harvard is associated with law and medicine, Yale with law and politics, and Stanford with computer science and mathematics. Oxford is linked to philosophy, while Princeton is noted for mathematics and political science, among other areas. Berkeley is characterized by its focus on physics and a countercultural vibe. The conversation emphasizes that these institutions are not solely defined by one discipline, as many have top-ranked programs across multiple fields. Additionally, it suggests that prospective students should consider the overall environment and student demographics of a university, alongside its academic rankings, when making their choices.
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(The way that Pepperdine is known for buisiness): Harvard, Oxford, Yale,
Berkley, Standford, Princeton ?
 
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My Impressions:

Harvard: Law
Yale: Politics
Stanford: ?
Oxford: ?
Princeton: Mathematics
Berkley: ?

Of course, I'm in no position to judge accurately.

Why are you asking?
 
My perceptions (heavily influenced by popular culture):

Harvard: Law, Medicine, Will Hunting types.
Oxford: Philosophy.
Yale: Law, Politics, Mr. Burns.
Berkeley: Physics, Hippies.
Stanford: Computer Science, Mathematics.
Princeton: Physics, Snobbery.
 
Those are all very major research universities. Not one of them is known only for a single thing. For instance, four of Princeton's graduate programs are currently ranked #1 in the country (mathematics, economics, history, political science).
 
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Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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