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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]I’m just happy that people aren’t putting 3 at the top. There’s too many PhDs coming out of the Ivy league, let alone the rest of the T50, to even begin suggesting that there’s some extreme difference in education. Unless your kid is on the bounds and is highly highly intelligent (like top 0.001%) where they need specialized/accelerated instruction to the level of grad school near freshman year, you’re probably receiving a very similar education to others.[/quote]
Even a standard freshman course like math 2230 at Cornell will exceed the level of rigor of any freshman math course at most lower ranked universities[/quote]

Cite?[/quote]https://math.cornell.edu/lower-level-courses (scroll to bottom)

https://pi.math.cornell.edu/~allenk/courses/14/2230/

Compre this to the freshman math options at most other lower ranked schools (e.g. any VA school besides UVA)[/quote]

I don't think this is true.[/quote]

DP. Why do you doubt it? The most elite schools are known for having more challenging coursework, stem and humanities. Any professor will tell you that. Professors have written about it. Not cornell, but one student of ours takes second semester calculus at a different ivy versus one taking the equivalent at a non-flagship in VA: they are night and day. They both are equivalent to BC calc, are the “regular “ versions (the ivy has an even more difficult proof based version) and they cover almost the same topics, yet the ivy has several topics not in the state school curriculum, and the psets /quizzes/exams are much different, with the ivy much more difficult . For people who study math or are in mathematics-heavy fields, it is not subtle how much harder the ivy is. I do not have one at UVA to know where uva falls on the spectrum of difficulty. [/quote]

Where is the actual evidence?[/quote] The commonness of extremely rigorous proof-based math courses intended for first semester students at top universities, compared to their rarity elsewhere. Just about every T20 has one.

You can also look at the finals for the lowest level, easiest math courses (which are often several levels below the most rigorous freshman classes):

Precalc final at Princeton: https://exams.math.princeton.edu/syllabus/mat103/precalculus

One-semester combined calc 1 and 2 final at MIT: https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/pages/final-exam/

Calc 2 final at Princeton: https://web.math.princeton.edu/~nelson/104/F02ans.pdf[/quote]

DP. We reviewed syllabi when our first was applying to colleges, at the urging of our college professor family member who has taught at T10s and T55-60. The course offerings are more rigorous, indeed as pointed out by other posters above and on other threads , at almost all T20s. Not sure why this is surprising to anyone. The student body makeup skews much further to the top-1% students; these students are the future of intellectual thought in whatever fields they choose. Of course the top schools need these courses, and their “regular “ intro courses are also more rigorous. The vast majority of professors are about the same—it is the student level that determines how hard the professors can push the pace and depth of coursework [/quote]
You'd be surprised by how underwhelming the math talent is at most T20s. It's just that Princeton swallows all the students interested in math academia and MIT the competitive math students. Harvard has math geniuses, but they're 2% of the math students. The rest are very very average.[/quote]
You’re missing the point. 
The average student in average math are not “average”. I have kids at ivies and spouse and I went ourselves. The average student has gotten much smarter since we attended. It is very different than what our siblings and nephews have experienced at lesser schools that are not close toT30. [/quote] You're missing nuance. UChicago is not in the Ivy League yet their honors analysis sequence (which is formally open to qualified freshmen) is graduate level and at least on par with if not harder than math 55.

On the flip side, UMD is outside the T30 but still has the type of proof based calc 3+ linear algebra courses (340+341) that Cornell does (2230+2240)[/quote]
Some people in this thread don’t get how many paths there are to coursework at any college, not just ivies. If you come in with BC calc, you have a lot of options at most colleges in the US[/quote]PP here, I wouldn't say "most" - outside the top 100, I haven't found a single proof based linear algebra + multivariable calculus freshman sequence like UMD and UVA have, and outside T30 I've only seen them at large state flagships which have both a large student population and a significant minority of extremely strong students who are often there for the in state tuition.[/quote]

There are 3000 colleges in the US. Rigor of course offerings is correlated to student body: when 1/3-1/2 come in with exposure to post-BC calculus, as they do at the ivy/plus schools, those colleges have to offer more depth. Same with physics and chemistry and foreign languages. The syllabi and course progression differences is evident in many subjects. It is no surprise that T100 level schools do not offer the same education as the elites: the vast majority of the 3000 colleges do not. Kudos to UVA and UMD and other top large flagships for covering the math need and many other needs of the topmost students who attend. There is a reason academically highly gifted students chase the ivy-plus schools: the course depth and intensity plus smaller class sizes compared to the large top flagships is the best fit for a significant subset of them. DCUM seems to think it is all about finance career networking and wealthy peers(with less than 50% full pay now, the wealth is quite diluted compared to the 90s). For many it is about the specifics of the education.[/quote]

"There is a reason academically highly gifted students chase the ivy-plus schools: the course depth and intensity plus smaller class sizes compared to the large top flagships is the best fit for a significant subset of them."

The depth, intensity and class sizes at top flagships is plenty challenging for highly gifted students. They place out of the large, introductory courses and into 300 and 400 level classes by sophomore year at the latest, and they are often offered graduate level courses by junior and senior year. All you have to do is look at lists of the top people in any field to see that students at state flagships are well prepared for any career. My favorite website for this has 12 careers listed. Here's the list for medicine to start.

https://lesshighschoolstress.com/medicine/
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