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by knzhou 2231 days ago
Gilbert Strang's linear algebra course blew my mind back in high school, and I still use insights from it every day. Strang has a particular lecturing style where he approaches every topic several times, often beginning many lectures before the main treatment. At first I thought it was a bit confusing, but later I realized it helped build fluency, just like a language class.

I'm really thankful to MIT OCW for putting his lectures out for free -- in fact, I think I'll go donate to them now.

5 comments

+1, I was very grateful to MIT OCW because when I learned Linear algebra, I could not have afforded it. Later when I got a job, I donated to OCW and I bought his book full price from his own site [1] just as a tribute to the guy.

[1] https://math.mit.edu/~gs/linearalgebra/

Hey me too! ( All of it )
Of course it is up to you what you do with your money but, they have a $17.5B endowment so there may be more needy causes if you were so inclined.
OCW opens up top-notch education to anyone and everyone, regardless of social or economic background. I wouldn’t take it for granted even with MIT’s eye-watering endowment, and I doubt donations to it are going to be paying cafeteria lunches for the students.

I hope you’re donating and actively contributing to many non-profit projects and that your comment comes from being tired of the world’s injustices rather than from callous impertinence, although I suspect it does not.

Most money which comes into MIT passes through overhead. That means if a foundation donates to MIT, a bit over 1/3 of that money might ends up with whatever they donated to. A bit under 2/3 might go into the general budget (overheads vary by funding source, but the numbers above are from one specific project).

On paper, overhead is used for costs of running the place. In practice, it's used for things like upscale faculty clubs, million-dollar executive salaries, $200 million buildings, etc. MIT has among the highest overheads in the academy. Ironically, MIT claims its ocean yacht makes money rather than losing money (which could very well be true).

If you're okay with the majority of your money going to graft, donate to MIT. With a project like OCW, which has such a huge cost:benefit ratio, accepting the graft with the donation may be a rational decision, if you subscribe to a system of ethics like utilitarianism.

Personally, I almost never donate to a charity where the highest-earner makes more than I do. I think if everyone did that, MIT might lose some of the graft and corruption which has built up there over the years.

MIT’s current overhead rate is 50.5%, but that’s pretty standard.

Here’s a scatterplot showing lots of research institutions’ rates. When this was published, MIT’s rate was slightly higher (54%). https://www.nature.com/news/indirect-costs-keeping-the-light... showing actual and calculated rates.

This also applies to federal research grants and is meant to cover costs associated with actually hosting the research (rent, utilities, support staff). Foundations can (and often do) negotiate lower rates. I’m not sure how donations are handled, but I don’t think the same F&A rates apply.

The article quotes 56%, as the negotiated rate on NiH projects, not 54%, but the rate varies by funder and by project. The 2/3 number is from an actual project I had insight into as the base overhead rate.

What's a little bit hidden there is that MIT dips into these funds multiple times, in pretty complex ways. For example, a sponsor might pay overhead and graduate student tuition (which just flows into MIT's general coffers). Or graduate student tuition might be waived, and the sponsor pays just overhead. Or a donor might pay overhead when the money comes in, and again on specific purchases. Or capital expenditures might waive overhead. Etc. The level of complexity is high, while the level of transparency is low.

I'm not claiming any of this is unique to MIT by any means. It's just where I have the most visibility.

What's cute is that MIT claims to lose money on everything. In the article you cited: "'We lose money on every piece of research that we do,' says Maria Zuber, vice-president for research at the Massachusetts Institute of Technology (MIT)." You'll find similar statements about educating undergraduates and tuition. And just about everything else. I've worked through the numbers at some point, and MIT only loses money with clever accounts; it's good PR to say MIT subsidize everything it does, but it's often not a reality.

I think his point is there are plenty of other noble causes that could use the money a lot more.
Malcom Gladwell made a similar point on his podcast http://revisionisthistory.com/episodes/06-my-little-hundred-...
Is there a better way to incentivize educational institutions to offer free content?
A modest proposal: ban donating to them so they need to radically increase their student body (online or offline) to earn their keep with tuition, instead of relying on the donations of the extremely rich parents of legacy admissions students.
What problem do you think drastically increasing the student body will solve?
I'm mainly thinking of elite institutions. I'd first invert the question and ask what problem places like Harvard, Yale, MIT are currently solving. (This small set of elite universities is absorbing the vast majority of donations.)

As the number of student has exploded over the decades around them they've kept their student numbers the same as before even as they collect more and more money which they hoard with no concern for opportunity-cost-of-capital whatsoever. This has created an intensifying zero-sum battle for the admissions slots in these universities. Meanwhile the state systems are increasingly overwhelmed and sketchy private universities are increasingly scamming students on the edges.

By keeping their numbers so low, the Ivy League retains comfortably small classes, no major change in their overall mission and professorial lifestyle. At the student level they function to perpetuate privilege across the generations, especially via legacy admissions which seems like a gilded age concept I can hardly believe is still a thing in 2020.

I'm saying if the Ivy League were to change its mission to serve America and the world as much as they could instead, it would do a great deal to help the vast mass of striving students who are barely not making the cut, as well as the economy over the long run, and even reduce tensions in American democracy. And that change of mission probably can only happen if they start to ignore what their biggest donors think they should focus on.

I'm in an online Master's program now. With way more students than I feel they can handle. I'm sure they're milking the tuition just fine, but when projects and papers aren't graded in time to determine if you should withdraw or soldier on, it's less awesome.

While your view makes sense in the theoretical, once again human failings cause it to not work well in reality.

+1. Since I took the OCW course, whenever I multiply a matrix and a vector or two matrices by hand, I hear his voice saying, "combinations of columns." Strang must have said those words hundreds of times in it. His lectures stick like nothing else.
This is very well put. Knowledge has a hierarchical (or perhaps even cyclical!) structure and it's unrealistic to think that a body of knowledge can be taught or learned sequentially.
In High school?
Yes. Linear Algebra is an extension of what is commonly called Algebra 2 or Precalculus in high school.

LA and Calculus can be studied independently in any order and then fruitfully combined later.