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Comment by robertakarobin | Hacker News Reader

This is really interesting! I started my Stanford undergrad as an engineer. After my first Calculus class, I switched to American Studies because it was one of the least engineering-y majors available. Then I dropped out in my Junior year. That was over 10 years ago. Now, ironically, I work at Google as a software engineer — the only one on my team without an engineering degree, let alone without a degree at all.

I never thought of my disillusionment with engineering in the context of other students, but rather just as an absolute: "Engineering is too hard for me." Taking Calculus at not-Stanford may have led to a very different result.

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Having watched the Gladwell talk a couple of times now - I think your experience is really the most indicative of what he was trying to say. Many self weed themselves out of Engineering and into generic liberal arts studies - even though they were top of their high school class in STEM and specifically chose the highly selective school for STEM.

And perhaps not all have the mental fortitude to stick with it in the background like you did - which is a net loss for society.

anecdote: I took Multivariate calculus and differential equations while in high school at the University of Nevada. I was easily the top student in my classes. I had to retake them at Stanford (figuring out how to transfer the credit was too complicated). Despite having "taken" the "same" material before and the fact that the average grade in the class was probably a B or B+, I was below the median in the class on the exams and got worse grades in the classes at Stanford. Of course this is anecdotal, and the University of Nevada is not that great of a school, but no doubt my GPA would have been much higher at a school like that...

I think that's sort of what he's talking about. Had you not had the experience of calculus and diff eq at a university and your only exposure to it was at Stanford with middling grades - perhaps it'd probably lead to more existential questions of whether you really wanted to do STEM in the first place.

Right, I quickly made peace with being a mediocre student at Stanford (and, still ended up getting into MIT for a physics PhD, where I was also a mediocre student but by then I didn't care :) ). I think the people who probably suffer the most at are probably premeds, where it really might be easier to get into med school by going to an "easier" school.

If there are dull students at Stanford, i am 100% sure they are not taking advanced math classes or higher physics classes.

In the grand scheme of things, I was probably pretty good at math as I got through a rigorous Mech E program. But I struggled with the more math intensive classes (Fluids/Navier-Stokes) and I'm pretty sure I could have dealt with an undergrad in physics/math--much less a grad program--about as well as I could have flown by flapping my arms in the air. But things ended up fine.

I don’t suppose you took Math 51H/52H/53H? That series is ridiculous.

(I suspect we met, at least briefly, somewhere along the way. Hi!)

Hah, no, I took 51H and suffered through it for some reason, but just took normal 52 and 53. (And I think I slept at your place when I was visiting MIT as a prospective grad student).

At least my 51H prof had the decency to try very, very hard to scare the students away. It was ridiculous but fairly effective.

I hope your visit was fun :). Your Antarctica beard on your website threw me for a loop.

Should be mentioned that classes within the same school can vary from year to year, completely depends on the person at charge. The first time I took Calculus 3, I got a D. IIRC, the fail rate was over 50%, and average grade was a weak C.

Two years later, I re-took the class to improve my grade. Ended up with a B - and the class average was round B at that time, with only around 15% of class failing the final exam.

> Taking Calculus at not-Stanford may have led to a very different result.

Thomas Sowell, in Inside American Education, argues that promoting students to more difficult colleges while ignoring SATs is not doing those students any favor. A firehose-pedagogy accepted by those with SAT scores 200-300 points higher can completely demoralize someone who could have done perfectly well at a moderately-paced school. However, the competition to practice AA leads, he argues, those more advanced schools to ignore SAT scores in admission for the schools' benefits, but not the benefit of the students so admitted.

> Taking Calculus at not-Stanford may have led to a very different result.

I doubt it. As my professor used to say, math is math. Plus, intro-level undergrad math courses are pretty standardized across the US. Similar textbooks, similar problem sets, and similar past exams.

There's nothing wrong to feel calculus is hard even if you're the top of your high school class. Most people hit a wall at certain abstraction level. Malcolm wrote in his book about smart people simply not being able to grok organic chemistry. Some of my smart classmates could not really understand the concept of limit intuitively. Some of them dropped out of abstract algebra course. I myself dropped out of model theory as I couldn't get why I should even bother with the course. None of these failures prevent people from finding success in other areas.

> Some of my smart classmates could not really understand the concept of limit intuitively.

that's because the way it's presented is silly. limits aren't the key idea, the continuity of the reals is.

but limits are a key idea, their invention allowed a whole class of mathematical problems to be solved

sure. and despite all the trouble people have, their definition is quite simple. the crux of the problem is understanding continuity. if you truly understand the continuity of the reals (which is the "real" invention), limits can be derived almost effortlessly.

in most calculus teaching, continuity is quickly stated and then there's a bunch of rules and these seemingly contradictory discussions involving delta and epsilon. they're not contradictory if continuity is understood and internalized.

Do you prefer the Dedekind cut construction of the real numbers over the identification of Cauchy sequences of rational numbers with common limit? In ZFC, they coincide, but in constructive mathematics, one can build a model wherein they differ (see https://mathoverflow.net/questions/128569/a-model-where-dede... ).

I used limit as an example. It could be other concepts, simple or sophisticated.

I don’t think it’s about how professors teach, but about that people simply can’t get some abstractions. Have you seen kids in high school who can’t do algebra even if you find the best teachers for them?

I disagree, I would say limits are the key idea.

1. How do you even express the idea of continuity if not through limits? (Sure, there's the topological definition and the epsilon-delta criterion but those are merely an abstraction or a different way of phrasing the same idea.)

2. The key difference between the rationals and the reals is that the latter are Cauchy-complete. How do you even define (in an intuitive way) what that means without referring to limits?

3. The reals are typically constructed as (equivalence classes of) Cauchy sequences, i.e. by their very definition they are the limits of their Cauchy sequences.

i think, for the purpose of introducing the continuity of the reals, for the purpose of introducing limits, one could skip any discussion that involves constructing the rationals or building the reals from them, at least to start.

instead go directly from integers to reals by introducing countable vs. uncountable infinities.

>Malcolm wrote in his book about smart people simply not being able to grok organic chemistry.

I adjusted majors in no small part because of intro organic chemistry. Just didn't connect.

I think a contributing factor for organic chemistry is not everyone teaches the mindset needed to do well. Good teachers will help students explicitly build a heuristic mental model for what the electrons might do in a particular bonding environment. Not everyone thinks naturally that way, but I think it’s a lot more effective than the raw pattern matching approach many people seem to bring to organic chemistry

Do you have any actual empirical evidence? In my undergrad, even different STEM departments (e.g., math, EE) had differing rigor and workload based on the average scores they required of admissions. Almost all grading was done relative to other students anyway, so even with the exact same course, things would be very different.

As an example, we had to prove all continuous functions on a closed interval are monotonically continuous on that interval, in Calculus I. Which we had in our first semester with no choice. I doubt this level of rigor is at all common.

Advanced freshman math, the kind for the top few students, varies extremely widely. As far as I can tell, if you made it all the way through the series at Harvard or Stanford, then you are an excellent student regardless of whether you get a good grade. I’m sure a couple other schools are like that. Many schools that you might expect to have similar classes don’t.

Sadly the universities with courses like this seem to me mediocre at advertising that, no, if you are not specifically very very good at math (and very very good at following a very fast paced course and you don’t have a strong background), then that’s not the class for you and you should be in the other honors math class.

Unfortunately many ostensibly good schools also have notoriously poorly taught introductory math and science courses.

Stanford's introductory CS sequence has a good reputation however. Consider this course (for example) which teaches students bare-metal programming (and real-world interfacing) on a raspberry pi: https://cs107e.github.io/schedule/

> Taking Calculus at not-Stanford may have led to a very different result.

I don't know. Calculus (and a lot of CS nowadays) is pretty standardized across schools. Same textbooks, similar problem sets and curricula.

People dropping out of engineering isn't anything new [0].

[0] https://www.youtube.com/watch?v=mJbE-CukPsU

> People dropping out of engineering isn't anything new [0].

What is new is: students were told all their life that “they’ll make it” in life.

Spoiler alert: not everyone does. Most will never make 7 figure compensation as a SWE, for example.

I think if the average person thinks the goal for making it in life as a 7 figure comp, 99% of people will never be happy.

I feel like Stanford is a little different. Despite being as selective as Harvardm Harvard has a very unique international reputation as the world's best university (or at least america's best university for the oxbridge lovers)

Oooh, I know a lot of Stanford (and Berkeley) students who would be extremely upset to hear you say that. :)

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