[bjourne]

> Lesson Six: You must measure up to a very high level of performance. I can imagine a propective student or parent asking, "Why should I (or my child) take calculus at MIT rather than at Oshkosh College? Isn't the material practically identical, no matter where it is taught, while the cost varies a great deal?"

Is there any truth to this? Because it seem like classical university jingoism to me. "My institution is better than yours." Anecdotes like "All MIT graduates I've met were dumb" or "All MIT graduates I've met were smart" does not count.

Because I looked at the DE course he taught (18.03) and I completed harder math courses than that in my non-MIT education. I'm sure many other HN readers have too. I wonder if there is some test you can take to see if you are just as good as an MIT graduate?

The EU has done great work in this area by trying to standardize the university curriculum across the union. What that means is that a master's degree in computer science from the university of München is mostly comparable to one from Madrid, so name-dropping your university "does not work." It also means that it is trivial for a Spanish student to study one year in Germany and then come home to Spain (see Erasmus). The US system, where some colleges are rated higher than others for irrational reasons, is strictly worse.

[csa]

I can't speak for MIT, but I can speak for a couple of Ivies.

The content covered in the curriculum and the speed at which it is covered is one potentially challenging aspect of one school over another.

The more important aspect, imho, is your peers. Speaking for myself and what I have heard others experience, peers can push your thinking to more sophisticated levels -- this can be in terms of something like elegance in problem solving (which has valuable real-world applications), the ability to apply the knowledge in a wider range of contexts, etc.

This is also often reflected, rightly or wrongly, in the assessment stages. If you take a class with wicked smart peers, the test is usually going to be much harder just so that the test can evaluate differences in knowledge.

I remember showing my $IVY calculus final to a friend of mine who set the curve in what was supposed to be the same class at $STATEU, and his mind was blown. It took him a few minutes just to realize that the test covered the same topics, while I thought the test was merely "hard" pedestrian content. Once I talked him through the problem, he realized how cool it was, and then he realized one of the key differences between our schools -- the boundaries of my thinking on topics were challenged and stretched much, much more aggressively.

To be fair, some non-elite schools are equally or more rigorous than elite schools, but this is usually on a department level and is the exception rather than the rule.

[akhilcacharya]

> It took him a few minutes just to realize that the test covered the same topics, while I thought the test was merely "hard" pedestrian content. Once I talked him through the problem, he realized how cool it was, and then he realized one of the key differences between our schools -- the boundaries of my thinking on topics were challenged and stretched much, much more aggressively.

Well as long as you were able to demonstrate that you were better than him, it's all OK.

[csa]

Neither I, my friend, nor any of our peers doubted who was better at STEM subjects -- he was and is.

The whole thing was a pitch to get him to transfer (I think he would have easily gotten in), but he didn't want to leave our home state.

My point was merely that the school I went to pushed the boundaries of my thinking, while his (at least in that class) did not.

Did that make my school better? For my personal goals, it did. For his personal goals, it did not.

[bjourne]

Then one should prefer the universities in Singapore, Hong Kong, Taiwan and Japan. Students from those countries outclass everyone else on every level of the education system. Just look at PISA results and TIMSS -- it is almost scary how good they are. In fact, one should avoid all American colleges since American students are quite a bit below the international average on those rankings!

[csa]

Hmmm... Im not sure I should respond given your straw man response, but just so others can keep the record straight...

1. PISA is a widely administered test for 15 year olds.

2. TIMSS is a widely administered test for 4th and 8th graders (Advanced TIMMS does "last year of secondary").

3. We are talking about university -- specifically elite universities.

4. I am extremely familiar with education in East Asia (most familiar with Japan), and their teaching of the fundamentals of math in junior high school and high school are in fact excellent. Sadly, this does not translate well into creative thinking. The best math people in Japan are largely limited to a small number of schools (3 or 4 elite ones and maybe a handful of others that have some players).

5. While you are correct that the average quality of education in the US is lower than other places (there are lots of US-specific reasons for this), the education at US elite universities and the US high schools that feed into elite universities is quite a bit higher than the US average. It's tough to find hard statistics on this because it would reveal a class bias in the US (gasp, there is one!), but spending some time in these classrooms and talking to and working with the students from these schools is fairly convincing anecdata.

I'm not sure what you have against US schools and/or US elite universities, but I encourage you to open your mind -- there is a reason why we have a lot of world-class top-rated (by any measure other than cost) universities here.

[bjourne]

1-2. I know the tests are administered to school children. But academic success in school translates to academic success later in life.

3. What makes you think that MIT would be more elite than elite universities in other countries? Talent follows a normal distribution and if PISA and TIMMS show that the American mean is below the average, the American elite must also be below the average. So, if the most gifted American students are admitted to MIT and the most gifted Singaporean students are admitted to the Nanyang Technological University (NTU), the latter university will contain the more gifted students. And if it is true, that you claim, that the quality of the education is dependent on the skill level of your peers, then NTU must be (much) better than MIT.

4. You can't measure creative thinking and the "Asians may be good at math, but they aren't creative" thing is a cliche.

I don't have anything against US schools or elite universities. Rather it would be you who have something against non-elite universities because you are claiming that you can't acquire the same education at other non-brand name universities. My claim is merely that one can excel at any university in any country as long as one puts in the time and effort. Especially when talking about math. You need a book, pen and paper and solitude and you're set.

I would be happy to put my money where my mouth is and run down to my local university with your hard calculus final. :)

[jcranmer]

You make a big deal about how secondary school rankings show that Americans are idiots and use that to guess that university rankings should similarly show that American universities are poor quality.

Which is obviously why only 12 of the top 25 schools, and 4 of the top 4, are American. I'd cite the logic failures in your argument as well, but I think letting actual statistics speak for themselves works better. And FWIW, I'm citing the university rankings that's published by a non-US publisher lest you think it's merely patriotic bias.

[bjourne]

Secondary school rankings show Americans are below the average. I never claimed that the quality of the alumni correlated with the quality of the school. The GP did. My point is that if you want to rank schools by how smart their students are, then no American institution would rank in the top 10. So you need to find a better metric if you want to claim that MIT is best of the best.

[rueynshard]

Students in elite American universities (ivy-plus) come from the top 1% of all American students in their cohort, not to mention other countries. However dismal American performances in PISA/TIMSS and other tests have been, the top 1% of roughly 3 million students every year are still bound to be generally smarter and more motivated than the average Singaporean or Japanese student.

[bjourne]

What makes you think other countries does not also have "elite" universities? China and India has five times the population of the US and several universities which are harder to get into than MIT. Fwiw, I don't believe in the theory of the GP. Math is a subject best done by yourself so what your peers know or not doesn't matter, imho.

[ep103]

Scroll through, and just take note of how many are American, vs other. Choose any international university ranking, I leave the following on just as an example.

https://www.timeshighereducation.com/world-university-rankin...

[bjourne]

Such rankings are bullshit and easily gamed.

[walshemj]

And I have a suspicion that PISA is gamed to save face I suspect if it was taken by a representative sample of all school age kids the scores would be different

[Leaning_Tower]

https://www.unzcloud.com/wp-content/uploads/2016/12/PISA-201...

[neltnerb]

As an MIT alum, I don't see a ton of value in competing over whose classes were the hardest. I've met super impressive people from everywhere from community colleges to Rhodes scholars and do not subscribe to the idea that MIT alums are uniquely good.

But having taken some physics and math courses at multiple universities MITs went much deeper in a shorter period of time. This isn't necessarily reflected in the syllabus because the topics may be the same but the devil is in the details.

MIT had absolutely fantastic problem sets that took me 10+ hours a week per class to finish and were rarely changed from year to year. This is because they've been tuned over so long that whether you get the answer correct is almost besides the point, the useful part for learning was the process of banging your head against them. This was true to an extent at other universities I've been at but usually the expected proficiency required to excel in a course was not quite so severe.

I ended up getting a PhD (in materials science), spent many hours working as hard as I could in lots of classes, and despite honestly knowing my stuff quite well I never got an A in an undergraduate physics course at MIT. Those were only gotten by the students who were obviously frighteningly talented, often with research experience in the course material already. Don't take that as sour grapes or anything, I am super proud of my B's in these courses. But MIT grades harshly, which may be part of why it's "harder".

Most MIT students stop caring about grades freshman year. Most MIT students interact with one another in class as fellow masochists struggling together against a common foe (learning the material) rather than competing against one another for grades. This is what I would personally call the weirdest and most advantageous aspect of MIT versus Ivy Leagues, but I actually think state schools are awesome at this too.

I'd have put that environment on the list of lessons way before any of the ones on there. Learning the value of close collaboration with people, regardless of whether you may think (probably wrongly anyway) that they're "better" or "worse" than you. Learning that when it comes to the real world, on a team you're all up against a way bigger opponent than each other, you're up against the laws of nature. And that success against that opponent is far more satisfying than any grade.

[KGIII]

As a fellow alum, you summed it up nicely. I did my full eight years there, so I can't compare. But, what mattered to me was that I was always encouraged to question, always encouraged to excel, and always allowed to discover.

I think that mattered more than difficulty and speed, at least to me. Having smart people able to answer very specific questions and being encouraged to check their answers really helped with how I continue to view the world and to learn.

[bjourne]

> As an MIT alum, I don't see a ton of value in competing over whose classes were the hardest.

There are many schools around the world with much harder and more technology intensive curriculum than MIT. If you disagree with that statement, then you do see "value in competing over whose classes were the hardest." If you do not disagree with that statement, then you must agree that the "MIT experience" you describe can be gotten in many schools other than MIT. F.e, I also worked 10+ h/day 7 days/week year round at university and also felt that getting A grades were impossible.

I think the professor is making a great point by comparing math to sports. Yes, you can go to a sports university but you don't have to. The way to get good at it is by busting your ass of (and having good genetics). It's your own effort that counts, not the name of the institution, imho.

[neltnerb]

I think you're misunderstanding what I was trying to say. I am explicitly saying that lots of other schools are fantastic, and also that schools which aren't pitched as the "best" produce fantastic alumni. So, as you say, I agree.

Yes, I think that there are schools around the world with harder curricula than MIT, with the caveat that every university has different strengths. I could go into my accomplishments in undergrad, but it's truly besides the point.

At some point it's truly ridiculous to compare as if it's a linear ranking. It's counterproductive to worry about rankings, and causes completely unnecessary friction between institutions. Pride and insecurity get in the way of solving problems, and all of us are ultimately struggling against a much more interesting challenge than each other.

I think the professor here is really not making a compelling argument, to be honest. None of the listed things are unique to MIT for sure, though strictly speaking he doesn't claim that they are -- he says that they are lessons of an MIT education, rather than unique aspects of an MIT education. He's a mathematician so this may be intentionally precise.

[zmb_]

> The EU has done great work in this area by trying to standardize the university curriculum across the union. What that means is that a master's degree in computer science from the university of München is mostly comparable to one from Madrid, so name-dropping your university "does not work."

It matters very much whether you got your CS Masters from a place like Cambridge or ETH Zürich versus some small university in a small member state. In my experience (having studied and taught in multiple European universities, both before and after the standardization) Lesson 6 very much applies to the EU.

The main achievement of the EU standardization is that a Bachelor degree from any accredited university from any member state will technically qualify you to the Masters programs in all member states -- before the Bologna Process some countries didn't even have separate Bachelor and Masters degrees.

The Masters programs themselves are standardized at the level of nominal effort, but vary wildly in topics offered, actual effort required, and quality of the teaching. No standardization can change the fact that the top people will seek out the top universities, which then heavily skews the skill distribution between the universities.

The structure of the programs is standardized in the EU, not the quality of the programs.

[taysic]

As an MIT grad, what I particularly found challenging was the fast pace of work and the tough scoring on exams - not so much the subject matter. I wasn't impressed with this aspect of the education because I like taking my time with subject matter until I really understand it but I didn't feel like there was time to do so while there.

That method seems to encourage superficial understanding unless you're willing to devote a large chunk of your time to working. And by that I mean nearly all day. There is a strong culture of pushing those boundaries. For me, MIT helped me realize the importance and value of life/work balance more than anything. I do my best work when self-directed and moving at my own pace - not cramming for exams. But I am just one data point. I'm sure it worked well for others.

[zaptheimpaler]

My experience is that the curriculum and what is taught is the same in many places but the assignments & exams are much more difficult at top schools. My bar for what "learning" something meant became much higher after constantly being beat down by insanely hard assignments/exams. Now I think testing is just as important as teaching in determining how much someone learns - hard tests expose sloppy learning very quickly and give you feedback on what you didn't learn as well as you thought.

Not to say that non-elite universities can't be as rigorous - some certainly are, and some students will be better than others. The brand is definitely a part of it too.

[csa]

> hard tests expose sloppy learning very quickly and give you feedback on what you didn't learn as well as you thought.

This is stated very well. I will be using this verbiage (specifically the "expose sloppy learning" part) in the future in my occasional defense of hard tests.

Thank you.

[BeetleB]

>What matters most is the ambiance in which the course is taught; a gifted student will thrive in the company of other gifted students.

As someone who went to both a very average university and a top ranked school, I fully agree. There were only two differences between the two:

1. The top university packed more material in a course (not a good thing, in my experience).

2. The top university had more peers which drive you to be better. This I really felt a lack of in the average university. All the motivation had to come from within, and although it was somewhat beneficial, it was also very aimless and inefficient. Synergy really is a thing.

(As an aside, the quality of instruction was not very different - perhaps slightly better in the average university. In my experience the role your peers play is much more impactful than the role your teachers play).

[mcguire]

The next two paragraphs go into more detail:

"One answer to this question would be following: One learns a lot more when taking calculus from someone who is doing research in mathematical analysis than from someone who has never published a word on the subject. [...] But this is not the answer; some teachers who have never done any research are much better at conveying the ideas of calculus than the most brilliant mathematicians.

"What matters most is the ambiance in which the course is taught; a gifted student will thrive in the company of other gifted students. An MIT undergraduate will be challenged by the level of proficiency that is expected of everyone at MIT, students and faculty. The expectation of high standards is unconsciously absorbed and adopted by the students, and they carry it with them for life."

I'm going to look funny at the claim of "expectation of high standards"; I suspect he's delusional.

But there is, in my experience, a considerable difference between "someone who is doing research" and "someone who has never published a word on the subject"; I've never met any "teachers who have never done any research [that] are much better at conveying the ideas." Further, the "ambiance" bit is right; being surrounded by people who are deeply interested in a topic beats the pants off people who are just there to get a grade.

[mathattack]

Within the US there is tremendous variance in academic quality both between schools and within schools.

[dagw]

I completed harder math courses than that in my non-MIT education.

Just looking at the curriculum doesn't really tell you anything useful. How well the material is taught and to what depth matters much more. Something simple like "learn matrix multiplication and determinants" could either be covered in 45 minutes or take up several lectures going deeper and deeper into the subtleties of what those things actually mean on a fundamental mathematical level.

Then there is of course the personal additions a lecturer can add to each course beyond the curriculum, which in many cases can be more interesting and educational than anything on the curriculum itself. Basically you can have a dozen lecturers covering the same curriculum using the same textbook and get a dozen very different educational experiences. You can probably, to a lesser extent, even have the same lecturer lecture to a dozen different groups of students and get a dozen different outcomes.

That being said I have no idea if MIT is actually better in this regard

[ThenAsNow]

I enjoyed most of Professor Rota's comments, but couldn't disagree more with his Lesson 6 and think it is pretty destructive.

In my view, the ultimate proof as to whether you deeply understand something is when you can engage in rigorous synthesis using that thing, or correctly explain it to others without using terminology as a crutch.

Getting to that level of understanding is not merely a function of the recognized accomplishment level of your peers or your instructor. What imbues people with a deep understanding varies from person to person, and many really benefit from a deliberative, instruction and discussion/conversation-focused instructor. My casual observation of MIT is that the level of instruction can be far from the best I've seen, because the students are so bright or so fast that they don't need much from the instructor in order to immediately see the conceptual space.

Imagine however that you are no intellectual slouch, but maybe are a more contemplative and deliberate thinker. You may be penalized in an environment like this, which bears no representation on whether or not you can get to the same quality and depth of understanding as your peers. I once had an MIT-educated professor say, "I know how to grade these exams. My 'A' students will finish the exam in the time allotted, my 'B' students will finish most of the exam, the 'C' students less so." This infuriated me then, and infuriates me now. The counterpoint was a (well-known) UMich-educated professor, one of the best I had, that gave challenging exams with no practical timelimit. He inspired me to be very ambitious as the lead on a free-form semester group project, so much so that it was clear we wouldn't finish during the semester. He saw how ambitious it was, and gave us an incomplete until we could turn it in the next semester. We did, and it was a really nice body of work.

I've seen similar patterns in the rest of my education. I've always gotten the most not from the best-credentialed professors, but from those who themselves understand deeply and make the material and themselves open to the interested learner.

This is ultimately what teaching and learning should be about, and can easily take place at any good institution, not just the MITs of the world. In my field of engineering, there is no significant correlation between those who were educated at MIT or Stanford, and the impact of their contributions to what is in the field and has truly advanced the state-of-the-art.

[home_boi]

> Because I looked at the DE course he taught (18.03) and I completed harder math courses than that in my non-MIT education. I'm sure many other HN readers have too. I wonder if there is some test you can take to see if you are just as good as an MIT graduate?

My experience at an okay school was that all upper level classes were graded and taught to scale with the student's intelligence. I and many other students passed through the curve. Many of us would not have passed comparable (by name and subject matter) courses at the top schools with a different curve and more in depth material.

[stonemetal]

In general the answer he gives sounds like bullshit to me. Really, "unconsciously absorbed" "ambiance" is what going to MIT is about?

>a gifted student will thrive in the company of other gifted students

This I put a little more stock in. It is competitive to get in. So all of the people in your calculus one class had calculus in high school, and they are all particularly gifted at math. This means they are able to cover more, and go deeper in to the subject because there is no time "wasted" educating an "average" student.

[csa]

> This means they are able to cover more, and go deeper in to the subject because there is no time "wasted" educating an "average" student.

Sort of.

Even in a class of motivated and gifted learners, there are some learners who are more motivated and/or gifted.

One of the most frustrating experiences for me at Ivy schools was having to slow the discussion down for the less-talented folks. Don't get me wrong, they were still (mostly) smart and knowledgeable, but there was a palpable difference in discussions that accommodated the slower people and those that didn't (e.g., office hours, some seminars, informal round tables, etc.).

In short, and imho, there is still time "wasted" educating an "average" student at these schools, it's just that the "average" is usually quite a bit higher.

[swiley]

I looked at the OCW stuff when I took calculus at a community college. They cover the same material but a lot of the homework and exams are made of word problems which makes it (arguably unnecessarily) very hard. After that I only used OCW for lectures and book suggestions and never for worksheets/exam/practice problems because if I want to study calculus then I'm going to focus on that.

You can take it either way. It's hard, but not in a way that makes you better at the subject.

[sinab]

I think I would disagree. One of the aspects of an MIT education (c/o 2017) was the fact that we were forced to decipher problems from statements in a similar way that one would be forced to do so in real life. Problems should (and almost never do) come packaged in a neat and nice way that is easy to solve, hence why I believe that word problems and sometimes confusing problem statements are beneficial.