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<p>Just to add, Stanford math is rated higher than Princeton is in CS/engineering. For example, in [url=<a href=“http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-science-schools/mathematics-rankings]this[/url”>http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-science-schools/mathematics-rankings]this[/url</a>], Stanford and Princeton are tied with Harvard for #2. In [url=<a href=“http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-science-schools/computer-science-rankings]CS[/url”>http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-science-schools/computer-science-rankings]CS[/url</a>], there’s a larger difference. But you’re right the differences here are minimal and both are excellent for what she wants to study.</p>
<p>I chose Stanford over Princeton when I was a senior, largely for Stanford’s strength in my field (in STEM). Your D seems to like aspects of Princeton that I ultimately didn’t like (e.g. the eating clubs). One thing she should definitely consider is what she’s interested in within math or CS. Both of them are very broad fields, and Stanford and Princeton do have many different strengths within them (although there’s a lot of overlap).</p>
<p>I don’t think that the median ‘intellectual capacity’ at Princeton is higher. Sure, there’s a difference of 30-40 points on the SAT midpoint (which doesn’t mean the average or median is actually lower; that’s estimated), but that says nothing about their intellect. In fact, Stanford has traditionally required more essays than Princeton, including the “intellectual vitality” essay. I think in general Stanford probes for different kinds of intelligence (esp. for that oft-discussed “passion”), which is why it often makes decisions that just seem “odd.” I’d also say Stanford is a little bit more selective - not so much because its acceptance rate is lower, but more because its yield is much higher (in past years, a spread of ~25% or 15 percentage points). I’ll add that usually Stanford takes the majority - around 2/3 - of the [url=<a href=“http://mathacle.blogspot.com/2010/10/hypsm-cross-admits-for-2002-2014.html]cross-admits[/url”>Mathacle's Blog: Stanford's HYPSM Cross-Admits for 2002 - 2010]cross-admits[/url</a>] with Princeton. IMO the student bodies are definitely comparable.</p>
<p>What else is she looking for? Perhaps certain extracurriculars? Class variety? Department/program variety? Interdisciplinary programs? Does she like the idea of being able to take graduate-level classes?</p>