They don't all teach the same things. As an example, here are the course catalogues for a BS in Computer Science at MIT and at Caltech

http://catalog.mit.edu/degree-charts/computer-science-engineering-course-6-3/

https://www.cms.caltech.edu/academics/ugrad/ugrad_cs (link at the end of the page for the course catalogue PDF; page 571 onwards in the pdf)

Not to mention the professors/lecturers, as well as the equipment and facilities also play quite the role

Here are some of the differences at "top" schools:

• Many professors are luminaries in their field. You'll be taking a class from the person who wrote the textbook everyone uses. Your next class is taught by the person who literally invented/discovered the technique you're learning that week.
• The students are more highly motivated, on average. You're surrounded by "people who wanted to go to a top school", rather than "people who wanted to go to college".
• For better or for worse, you're surrounded by wealth. Some of your classmates will have wealthy parents and connections.
• The schools have a lot more money for fancier equipment and labs.
• Companies love the prestige of hiring from top schools. You'll be recruited heavily.

It doesn't necessarily mean you'll actually learn more. Really that's mostly up to you. I do think there's a difference in difficulty and expectations for courses, but it may be that's more due to the average caliber of students being higher rather than the school actually teaching more.

Also, not all top schools prioritize teaching quality. Many small liberal arts colleges have 100% of courses taught by full professors who care about teaching, while many top universities don't prioritize teaching, especially lower-level classes, and many undergraduate classes are taught by grad students who don't have any teaching experience.

How much you learn is mostly up to you. You can learn just as much and have just as many opportunities at an average school, but you might have to work harder and seek them out. At a top school, it's harder to get in, but once you get in you'll have more opportunities.

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They may have similar courses (with some notable exceptions), its more a about who's teaching it and what kind of resources they have to teach with. Top universities bring in the top experts and teachers in the world, and have amazing resources to allow students to use top level equipment, tools, libraries, etc to facilitate top level learning. These schools are also usually conducting amazing research that even undergraduate students can often participate in, accelerating their careers. When a university has all these things, they gain a good reputation, allowing for students to find easier and better jobs upon graduation. That alone makes a university "better" in the eyes of most.

Generally, school prestige is a holdover from way back then. A little bit of private school elitism. A little bit of education not being as standardized. Harvard, Yale, etc cemented their reputation as Hugh class institutions long before college became widely available.

At a practical level, the math you learn at your state university is the same as at Harvard. The value of a high class institution is not necessarily in the actual education.

As prestigious universities, their degrees carry weight and they also have lots of connections. As the adage goes, it's not just what you know, it's who you know. So prestigious universities open more doors simply because they have better connections.

In terms of education, it is true that prestigious universities intentionally try to draw some of the top scholars who are doing cutting edge research. However, most of the time they're doing research and even if they do teach it is rarely undergrad classes. Top scholars usually only matter for people doing postgraduate study as they will join in their research.

So while there are some academic advantages, the real difference between prestigious universities and Podunk State down the street is social.

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