1. Do you think you’re going to learn calculus better than you would at flagship state U? - No. There might be a small difference but I would not claim to have received an education that is significantly better than any state university. I was able to take very specific grad-level classes and learn basically whatever niche subject I wanted to - which might be an issue at schools which do not have comparable funding. But overall, not significantly better than a state U.
2. Do you think you’re going to work with famous professor there? - In my experience every student who was competent and wanted to work on a research project was able to - even as soon as their second semester in freshman year (might not get the exact professor and project you want - but in my experience all professors have an incredible reputation and you will gain a lot out of whoever you get to work with)
3. They will hand off all your classes to adjuncts and grad students. - In all my classes, grad students have been responsible for grading assignments and exams, but never for teaching - only the professors teach.
4. Don’t waste your money on a fancy brand - I didn't. Coming from a low-income household, Cornell covered all my expenses and I have not paid a single cent my entire 4 years (and no loans). It is significantly more likely for an Ivy League university to provide full financial aid as they have the endowment to do so.
Additionally, the biggest advantages for me with regards to the brand name were: 1. Recruiting - recruiters from FAANG and other top companies come to you - pretty much everyone I know was going into FAANG or a top fintech company their sophomore or junior year internship. 2. Networking - Since there are so many alumni already at top firms, it is significantly easier to get referrals.