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58,000 Sign Up for Stanford AI Course (nytimes.com)
225 points by mhb on Aug 16, 2011 | hide | past | web | favorite | 94 comments

I am most excited about the machine learning course, since I could use the structure to go through Andrew Ng's lectures; also the ones from 2008 are already out of date.

As for the AI course, I'm skeptical, frankly. Sign-up right now has meant putting your name and email address. There is a big difference between spending 2 second to fill that in, and spending the amount of time necessary to finish the course. You come to a website that sounds like making robots and turns out the class is about developing pruning heuristics for search trees, do you stick with it? Maybe...but I'm going to save my awe for how many people complete.

I praise Stanford (CS) for thinking up this idea. Like Khan, they are going to reach a lot of people, and I think its particularly useful for motivated learners who, for whatever reason, are stuck in a place that you can't take a good AI course or can't afford one. Ultimately, though, the course is going to require drive that a lot fewer than 65,000 have.

If 1% of sign ups complete the course .. that's still 5800 people. Which is pretty good reach. And then add in all the people who didn't complete, or look at the materials afterwards, or who are otherwise affected by the project... These people don't have enough drive to get the full benefit, but they do get some benefit for sure.

Nice try, but 1% of 58,000 is 580.

Yeah, that's a pretty stupid mistake. My bad!

I still stand by my other, less retarded point, though.

Did you take the prereqs? :)

And if 0.1% complete the course, that's 58 people. Despite what you may have heard, there are numbers less than 1%. Many people who buy advertisements in publications with, say, 100000 readers have learned this lesson the hard way.

"there are numbers less than 1%" WTF!?! Hmmm, all the online marketers I know are going to be very disappointed about this news. LOL.

btw, just worked my way through your ROR tutorial - thanks for YOUR contribution to online learning. A big reason I am signing up for the Stanford courses is because of the great fun I had working my way through your Rail Tutorial. Online learning is awesome!

... 580 people ...

I'm really curious what affect this will have on Universities with relatively poor teachers in these areas. I remember taking algorithms with a very nice but not altogether great teacher, so in the evenings I would follow up class with the appropriate lecture of from the MIT OCW algorithms course.

I've worked in higher-ed awhile and been a student for many, many years and noticed that independent of the quality of the school there are always smart, ambitious students to be found (the density just changes). I can imagine a relatively near future were the brightest students start class having already finished the course material at Standford, smiling and nodding at a relatively clueless prof. I've heard that there are highschools that assign their students the khan lectures for homework and in class do the exercises together, it would be interesting to see universities start to go this direction (where poorer profs would essentially become long distance TAs for Norvig et al.)

It's absolutely a revolution in education. None of what you mention was possible ten years ago when I was in college.

Maybe a bit farther than 10 years. I watched CS lectures online back in 2000 for my USC classes.

Fair enough. It was when Quakeworld was extremely popular, so a little more than ten years. ;)

I'm curious if any of the Stanford students who are paying thousands for this course are worried about the diminished return they might get from their professor. Don't get me wrong, I love this idea as the free recipient, I'm just curious if students who are paying, and obviously getting lots more, have any views on this.

The scrutiny that this course will attract because of its popularity might actually encourage a higher standard of teaching for this course than many others that are offered. It could be a win for everyone.

They can also use the data the crowd is generating, these are big data guys.

Also, students are going to be trying harder because they are going to be competing against the world. Imagine if no in-class student was in the top 1,000?

The professors' actual interaction will be limited. Questions from free students will be aggregated and ranked and only the top ten or so answered and posted online. And I doubt the profs will reduce their office hours to make time for this. More details like on the QA section of the announcement site. As far as the paying students are concerned, this probably won't be much different than the profs' other research.

Not sure why you were down voted. This seems like it would be a legitimate concern to me if I were a "regular" Stanford student enrolled in (and paying for) this course.

A regular Stanford student can expect to spend about $50,000 a year [1] or about $200,000 for a four-year degree. In four years, I believe that there will be at least one company that will offer trustworthy certification for a lot less, like maybe $20,000 or $2000. If the primary benefit of a Stanford education is the certification, then in a few years Stanford grads may be like owners of $200,000 cars-- obviously wealthy, but not possessing any significant advantage in transportation over owners of $20,000 cars.

[1] http://answers.yahoo.com/question/index?qid=20090416220215AA...

The level of in-person interaction, office hours, etc. won't come close.

Also - you're paying for the grade & the transcript, not the content.

> you're paying for the grade & the transcript, not the content.

How much is the grading and transcript worth? How much does it cost? I think there's a great opportunity for a startup to just focus on offering transcripts. The hardest part of education is the course content. The grading and transcript part is easy.

I love the concept of open education. But it seems to me that universities who do this are self-destructing. Does Stanford really want to base it's value proposition on its administrative staff? "Anyone can get the knowledge for free. But if you want certification from the Stanford administration staff, that will cost you $150,000. Come to Stanford and get a diploma!"

I don't know how things work in the US, but I went to one of the top engineering schools here in Brazil, and there's an agreement between me and my classmates that the best thing school got us was access to people, i.e., the other students.

I just listened to a talk[1] by Ori Brafman in which he mentions that one of the most important factors in professional collaboration and friendship is physical closeness. MIT dorm students were twice as likely to be best friends with their immediate dorm neighbor (6 meters away) than with the dorm neighbors two rooms down (12 meters away). Professional collaborations followed the same pattern. Y Combinator likes to see founders share an apartment. There's probably a lot of value in simply being physically near other people with similar interests.

[1] http://ecorner.stanford.edu/authorMaterialInfo.html?mid=2683

not at all - I took both the ML and AI course equivalents, and I think it's awesome more people can benefit from the great instruction I've been lucky enough to receive. I do agree that I also became more familiar with the material during office hours and other interactions with the course staff, and I think the classes are already designed well enough that making the resources like videos and assignments available will not put too much additional burden on the instructors.

Perhaps crowd-sourced questions will help improve the overall quality. The relative anonymity and impersonal nature of the Internet could encourage more people to ask questions so that the professors are much more aware of areas that are unclear and require further explanation.

I'm looking forward to this.

I think an interesting challenge scaling the class won't be the professor's time but the TAs'. I'm assuming that assignments for free students won't be graded as rigorously depending on problems sets (time consuming) vs coding assignments (potentially automated).

Why would they? It's not like you're getting a degree from Stanford. It's very similar to MIT OpenCourseWare (and no way they will grade the assignments with so many students taking the course).

Government should sponsor this kind of thing, seems like there are a lot of people out there that want to learn more and these kind of quality courses should scale fairly well. Sure it won't replace the real course but it will teach a lot of people a lot of things.

Really the only thing holding this kind of thing back from dramatically improving education efficiency is the old thinking rigid degree requirements.

I have often marvelled at the wastefulness and inefficiencies of the current teaching system. If you have an exceptionally good teacher they should be teaching millions, not a year-group of 100. If online learning took off I think it has the potential to dramatically improve education for people everywhere in the world, for a fraction of the current costs.

Having said that, there are numerous issues which would have to be sorted out. Academic education is (I believe) extremely scalable. Children's emotional, social and physical education is less so. The results of such an education are extremely dependent on the child's attitude and willingness to learn.

At the very least, online learning has the power to completely change adult learning in the near future, where we can assume the above issues do not apply.

Some variation of this happens in HK, where everybody wants to learn English (because they can't learn as well from their peers, unlike other subject) and English lecture/tutoring places pops up all over the place, and the top teachers teaches, via video conferencing, hundreds of pupils at once. I'm told the top teachers gets paid in the millions.

Why should the government be involved? Can't 60k folks pay two guys they want to learn from?

The appeal here is that the course is free, ergo, _anyone_ with a basic internet connection can take it.

If you require payments, you then have credit card companies and Paypal restricting who (i.e. which countries) gets access to it.

Income from donations isn't guaranteed, and thus provides a weak incentive for universities to provide these kinds of courses. I'd also wager that donations would fizzle out as this sort of thing became more commonplace.

US Government grants would provide guaranteed incentives for American universities to offer these kinds of courses, which would educate your populace and bolster the appeal of your higher education institutions to potential overseas students. The latter point would lead to many knock-on economic benefits (e.g. immigrant students deciding to stay in the US).

(oh, but rabble rabble gubment rabble bad rabble rabble because this is HN where libertarian capitalists roam free)

The top 10% of this class would be ideal candidates for Google/MSFT/etc.

Besides students or government paying, there are several other business models that could be considered, including employers sponsoring in exchange for exposure to the best students.

That said, governments already subsidize education in many countries. We should be demanding that the investment get us a better return!

> The top 10% of this class would be ideal candidates for Google/MSFT/etc

I really wonder if this is true. I've looked at the text and it seems pretty intro-level. What would the certificate of completion look like on a resume?

Wait you are saying the key advantage of US taxpayers funding this is people overseas in paypal blocked countries (Libya, North Korea...) get it for free?

You can get Teaching Company DVDs from a lot of libraries. Basically the same idea but lower tech, and government subsidized.

But then, I am a big believer that a great teacher on tape is far better for the students than a good or OK teacher in person.

Government subsidized? You mean the library? Because IIRC the courses retail at a fortune (but are always on sale.)

It's not really. The most useful thing a teacher can do is give feedback. That said, one student among 300 doesn't get a lot of feedback.

How about "great lecturer or speaker" over "great teacher"? Because a 300:1 lecture by an ok lecturer is much less useful (bordering on worthless) than a recorded one by a great lecturer. And that mediocre lecture is what you will get in most schools for intro classes.

... which are often the ones with 300 students, and no useful feedback. I agree.

"Government should sponsor this kind of thing"

Maybe 60% of the budget of Stanford is from research grants from the US Federal Government. For the students, there are also scholarships, e.g., from the NSF, NIH, etc., which is more "government" support.

Be not at all in doubt: Look at the Stanford campus with all its buildings, lawns, people, equipment, etc. and know that nearly all of it is paid for by the US Federal government.

Research for the US Military was/is an important source of funding. To be clear, it's not like the government is getting nothing in return.

Gifts from successful alums are also a big source now: http://facts.stanford.edu/finances.html

Yes, since the US military, yes, mostly via NSF and NIH, have been tossing Stanford ballpark $1 billion a year, it's nice to have some alums kick in a few million a year, maybe $10 million now and then?!!!

Yes, I can believe that the Stanford alums have especially good reason and ability to be 'grateful'! Good for Stanford; thank you, thank you, thank you Dean Terman!

Still, nearly all the world's top research universities are in the US, and the main reason is that right after WWII Ike and others concluded that research in math, physical science, and engineering were just crucial for US national security. Congress has gone along. Any significant claim that the US is falling behind in research will open Congress's funding for the usual suspects NSF, NIH, DoE, DARPA, etc.

Net, no way, not a chance, will Congress permit US research universities to fall behind: From Congress all it takes is money, that is easy for Congress to vote, and actually in the big picture it doesn't take very much money.

Also, all things considered, the money is relatively well spent. Evidence: Getting those grants is DARNED competitive. Want to get promoted at a top US research university? Get a grant!

And there is a secret -- hush, hush! About 60% of the grant money, for math, physical science, and engineering, goes to 'overhead' which ends up good for the English, modern dance, French literature, and art history departments! Likely helps pay for the university theater, art gallery, string quartet concert series, etc.!

Don't tell anyone that Federal taxes are supporting string quartets!

Also looked to me that the Stanford lawn was in nice shape!

I bet ~5% will complete the course

here is the number of views for Andrew Ng's Intro to machine learning course on youtube (http://www.youtube.com/watch?v=UzxYlbK2c7E )

lec 1, 206612

lec 2, 91234

lec 3, 49000

lec 4, 36823

lec 5, 27782

lec 6, 26347

lec 7, 22075

lec 8, 20713

lec 9, 15665

lec 10, 14142

lec 11, 16573

lec 12, 14296

lec 13, 12401

lec 14, 15022

lec 15, 12290

lec 16, 10760

lec 17, 8986

lec 18, 13639

lec 19, 10219

lec 20, 11373

These lectures are also available on iTunes U. It would be interesting to compare the number of YouTube views to the number of iTunes downloads. I watched the first two classes on YouTube, and downloaded the rest on iTunes, though admittedly I'm still only on lecture 6.

This sort of thinking is supported also by the fact that the number of views is not strictly decreasing.

thats a ton more people than the usual number of stanford enrolled students, it's a win for education in my book.

and just like any math based course at a community college 3/4ths will have dropped by the midterm.

Most likely the percentage will be much higher. I'm saying that as a former dropout :) I've decided to go through the Machine Learning course (the web version) few months ago but it's really too math heavy. It's not that I'm a total noob but having to parse formulas spanning 2 rows and containing half the Greek alphabet is about as exciting as reading an organic chemistry textbook.

Nevertheless I signed up! But I hope some day there will be a AI/machine learning course that will have code examples for every concept and every math formula, just like this: http://www.cleveralgorithms.com/nature-inspired/index.html Maybe it's just me but code is way easier to read and understand.

I suspect more will drop out since they have even less necessity driving them than someone at community college.

I think it's safe to say at least 3/4 will not do any work. Another 3/4 of the remaining will drop out after trying, and another 3/4 will not understand a thing.

900 is still a decently large university class.

That's still 14500 who won't.

I don't think you belong here. You're supposed to whine and bitch bitterly about "Kids these days".

I figure the future of education looks like this. Where anyone can sign up for courses, and if they don't get it, they can either drop it or hire a tutor.

1 teacher per subject per 300 students is an anachronism. It should have gone away when textbooks became ridiculously cheap to print.

We should run a betting pool for this. I'd bet at even money than more than 90% of online signups fail to complete the course. Give me decent odds and I'll bump that up to 95%

I think you're being way too optimistic. I'm guessing about 5% of sign-ups will ever actually follow the course once it starts, and of those, I'm guessing less than 5% of those people will complete the course.

Do you think they'll makes the numbers public?

HN readers may find another free Stanford course of interest: EE380, the Stanford EE Computer Systems Colloquium. The Colloquium meets w4:15-5:30 throughout the academic year and moves re-runs during summer quarter. Lectures can be seen live, viewed in real-time over the web, viewed on-demand over the web, and eventually find their way onto YouTube, iTunes, and elsewhere. http://ee380.stanford.edu.

Official registration hasn't opened yet, right? I haven't received any additional info since I initially submitted my name and email address a few weeks ago.

Correct, the real headline was "58,000 Want Course."

Kind of sensationalist of mhb to change it like that, unless NYT secretly updated the article, which I've heard they're fond of doing.

Most likely NYT updated it. Easy mistake for someone not familiar with this topic to make.

It would be an interesting twist if someone were to sign up an AI bot, using machine learning to work its way through the course.

That's the homework for their machine learning class (ml-class.org). ;-)

54.000 entries? I'd bet someone did that.

I really love this experiment. When I was in High School I was fortunate to be able to audit some University classes for which there wasn't an equivalent in my school district (numerical analysis and fortran programming). That allowed me to 'bank' time which would have nominally been wasted waiting to reach 'college age' or 'post HS diploma'. This is much more common today and my kids have all benefited from it.

This experiement is sort of the next step. If we can combine that with free access to a syllabus of seminal papers (vs paying $36 each from some Journal publisher) it will allow a lot of people more time to do great things.

I think this is a great idea, but I'm not sure emphasizing the number of sign-ups at this point is smart.

They don't even have a CAPTCHA and don't verify the emails besides basic email@doman.tld. So hopefully they are removing bounces from the counts.

In fairness, these are AI experts. Surely they, more than anyone, know how to reliably distinguish people from non-people?

that's what they said about financial experts ...

Uh, in "AI", the "I" is mostly just a hope or goal and not yet an accomplishment!

We have AI as a field mostly just because of long, aggressive funding by DARPA, early on especially of the MIT AI Lab. Since then DARPA has funded the prize where computer controlled cars chase across a desert. It appears that some people at DARPA are hoping that something good happens from their funding. Tough to say something good will never happen! If something okay leaks out of the research, then some lives of some US soldiers might be saved and, by now, may have already. In that case, good. DARPA is likely some of the very best money spent, even if for some years the work looks weak. At least with the money so far, a lot of quite bright people have TRIED to make progress in AI.

Some years ago, I was one of three researchers in an AI group that did some of the world's best AI work. I had two conclusions: (1) For the practical progress desired now, just use 'traditional' approaches of (A) see problem, (B) analyze problem, (C) find assumptions can make about the problem, (D) do some math starting with the assumptions, (E) take the conclusions of the math as progress on a solution, (F) use the best of what have to wrap up the best solution can see. (2) For the AI part, so far "We dance 'round in a ring and suppose while the secret sits in the middle and knows.".

iTunes U was a big step in the proliferation of higher-quality education to the masses. It's nice to see Universities like Stanford spearhead revolutionary innovations to give the opportunity of learning from world class academicians to people who would have otherwise never dreamed of it. Bravo!

iTunes U was a big step in the proliferation...

A big step backwards, from what I can tell.

Sharing video recordings of class lectures on the Web is easy: record video, upload to Web. Why is there a need to do it through iTunes? AFAIK, iTunesU is just a way for Apple to try to get campus lock-in. I know this sounds kind of rant-ish, but I'm being 100% serious and honest.

My school started using iTunesU, which didn't seem to have any advantages over just putting video online, except that I couldn't use it, since I can't run iTunes on my computer (Linux).

I'd honestly like to know what benefits iTunesU has for anyone besides Apple and Microsoft, in the sense that if it became truly widespread, it would prevent any widespread movement to adopt Linux on campus.

You can use TunesViewer [1] to view iTunesU media and podcasts in Linux.

[1] http://tunesviewer.sourceforge.net/

Thanks, good to know about.

While I agree that iTunes is a very cumbersome piece of software and it is more difficult to use on Linux, the amalgamation of educational videos is the big step forward. The technology has been around, like you said, for a long time to post videos online - but what good is it if those videos are hosted on a thousand different websites? iTunes U aggregates them all into a platform that can easily be searched, as well as enforcing a minimum level of quality in order to provide a higher quality learning experience. Is Apple truly that magnanimous? Probably not. But it's an ad-hominem fallacy to dismiss the quality of iTunesU on the basis of it's creator.

While I agree that iTunes is a very cumbersome piece of software

That's not what I said.

and it is more difficult to use on Linux

That's a sloppy way to put it. AFAIK, there is no Linux port of iTunes. It may be possible to use with virtualization, but that's beside the point.

The technology has been around, like you said, for a long time to post videos online - but what good is it if those videos are hosted on a thousand different websites? iTunes U aggregates them all into a platform that can easily be searched, as well as enforcing a minimum level of quality in order to provide a higher quality learning experience

I wasn't aware that iTunesU aggregated videos other than those from the particular university at which you are a student. That's how it was billed at my school. Still, if it does do so, it's a strage way to go about it. The same thing could be accomplished in a much more accessible way with a YouTube clone for educational videos.

Is Apple truly that magnanimous? Probably not. But it's an ad-hominem fallacy to dismiss the quality of iTunesU on the basis of it's creator.

Right, which I didn't do. In fact, quite the other way around. I have great respect and admiration for Apple and Steve Jobs. That respect went down a bit when I realized that (and here's my real point):

There is no business case for Apple to have iTunesU except to block Linux from getting a foothold on university campuses.

Now, maybe that statement is too strong. I would be delighted if someone could prove it to be wrong.

Now, just to be clear, I don't think there's anything morally or legally wrong with acting to block your competition. But still, I'd rather see Apple selling great products that people love, which is what they normally do, rather than giving away products with the sole (apparent) intention of blocking the spread of other great things (Linux).

There is clearly value in organizing the content into an iTunes-like UX.

I see your point about not having access to the iTunes content on Linux. Fair point that should be addressed.

That said, I'm a big fan of iTunesU. I like the ability to download courses on my iOS devices and listening to the lectures on trains or at the gym. Also, they must save a lot on bandwidth by letting people download the videos (I go through the lectures a couple of times at least).

You are saying this as if you cannot download videos and view them on an iOS device from any other source. I believe it is possible to just download a video and start watching. How does the iTunes software help to make that process better? Also many people do not have an iOS product.

The iTunes software sucks quite badly. Don't get me started.

However, the end-user experience for downloading videos from iTunesU and playing it on an iOS is excellent. It is almost a one-click experience. This is just my opinion as a user.

I'm curious, on a vanilla iOS device, what application would you use to download a video on a website and have it cache onto your device?

I agree that if you don't have an iOS device, this doesn't work.

Well, guess we should all go buy iOS devices, so we can have a great one-click experience watching lectures produced by public universities that are paid for by taxpayer dollars and ought to be freely accessible.

(Sorry if I'm rubbing it in too hard, you've been very gracious in this discussion.)

I don't think it's the downloading anyone objects to.

I don't think iTunes U has anything to do with this.

What did iTunes do? I'm not really up-to-date on all things Apple.

iTunes U (as in U for University) is a section of iTunes where you will find a whole host of University courses to download and watch. I mention this to many people and there seems to be very little awareness that all this high quality content is available on iTunes.

There are some great courses available (most for free), in fact I have just finished the Stanford iPhone programming course by Paul Hegarty which I highly recommend.

Thanks for the reply. While I do have an iPhone I try to avoid iTunes (I used it twice to update my phone since I got it two years a go). The programming course does sound interesting though I could use a good course to supplement my self-thought knowledge of the platform.

Any reason on why they are compacting the courses during the Fall quarter? It could be interesting to have AI and ML separated in Fall-Winter quarters.

Anybody knows if they plan on doing something similar in future quarters?

I love the idea, and I am excited to see the results of this methodology.

I just found it through the database course and signed up. Just got a taste of machine learning etc via http://blog.saush.com/

Hoping not all of it will go over my head!

What is the name of the Stanford Course on compilers? I WANT I WANT!

So is this the eventual commoditization of a university education on the horizon or what?

Learning is not a spectator sport. For material that is solid and clearly presented in a book, for a good student with good preparation and good motivation, it is enough for the student to study the book independently or nearly so. Indeed, such is nearly necessary.

E.g., in 'research', how do you think the necessary background material is obtained? By signing up for 'courses'? Nope! Instead, the researcher gets the background materials, learns what is needed, and then gets on with the research. A researcher can't get paid just for getting the background material; instead, the researcher has to just do that seemingly effortlessly! Well, students, once they reach a suitable level of educational 'maturity', can too!

E,g,, here on HN are many thousands of programmers who use computer hardware and software they never saw in a course. So, HN readers learned on their own. Such self-education has long been a central feature of the US computer industry.

Net, researcher, HN reader, or serious student, all can learn solid material without a course, and do.

Actually, learning outside a course is sometimes in academics considered almost 'cheating'! So, if a course is to be a 'filter', a competition, a 'stress test', then for a student to have worked carefully through solid texts on the material before the course lets them in the course effortlessly blow away all the students who started with the material only in the course. So, can get comments such as "Best student in the class by a wide margin, but apparently knew most of the material before the course.". So, there's commonly no doubt that it's possible to learn the material outside the course and to learn it well enough to lead the class in a corresponding course. Indeed, such self study can move forward at the student's own pace, faster some places, slower others, and, net, learn without gaps or wasted effort.

Net, course or not, the actual learning is mostly or entirely from what the student does with the material alone in a quiet room.

Of course, again, to get this good situation of self learning, need solid material clearly presented in, say, a book. Some subjects, sadly, are so vague that no such book can exist; in that case, maybe a course is 'needed', i.e., so that a student can soak up nonsense that couldn't be written down in solid form! For such, wander over to one of the 'humanities' departments and take one of the courses in 'political correctness'!

Certainly nothing beats a good book, but often a good lecturer can give some intuition or motivations that are not customarily written down. I think a great example of this would be material on convex optimization released by Stephen Boyd (http://www.stanford.edu/class/ee364a/videos.html), also from Stanford - certainly his style is not as precise as e.g. Bertsekas, but probably much better at helping students to get a sense of how to actively work with those ideas.

"Certainly nothing beats a good book, but often a good lecturer can give some intuition or motivations that are not customarily written down."

You are correct on both points. Early in my learning, I found both points to be important. And, for a beginning student, both points can be crucial: Without the second point, it is far too easy for a student to get into some not very good material or into some good material but, still, lost.

Eventually I got away from your second point.

Still, there is a version of your second point that lasts: For research, seminars and conferences are good, fast ways to keep up, see the forest for the trees, pick new research directions, etc.

When my company is successful and I retire, I will return to mathematical physics and, maybe, attend research seminars in, say, Boston.

Is Boyd still talking about convexity?

Convexity is an important concept, and the world is just awash in rock solid treatments.

So, for some positive integer n, consider n-dimensional Euclidean space. Suppose C is a closed, convex subset and point x in the space is not in C. Then there exists a closed half space that covers C and omits x. The boundary of this closed half space can share a point with the boundary of the closed half space so that the plane of the half space is 'supporting' for C. So, this is a 'separation' result. Yes, it generalizes past finite dimensional Euclidean spaces! Yes, it's a darned useful theorem! E.g., can ask for the point in C closest to x -- the point has to exist since C is closed. Then the plane through this point and perpendicular to the line to x is supporting for C. So, can get a nice projection result and use it for optimization and best approximation.

Okay, my point: This result is one of the most important about convexity but is standard in 'analysis'. I first saw the result in the 'advanced calculus' book, Fleming, 'Functions of Several Variables'.

Bigger point: Convexity pops up frequently in analysis. E.g., there is Jensen's inequality. With it can easily knock off a nice list of otherwise difficult to prove inequalities. E.g., in the L^p spaces, we can use Jensen's inequality to get Holder's and Minkowski's inequalities.

When we start with optimization, we should start with convex sets and also convex functions. E.g., there is a nice list of theorems of the alternative that are separation results for cones and polyhedra that can be used to establish some otherwise tricky results about duality in linear programming and are also key to the Kuhn-Tucker conditions in non-linear programming. Of course, the feasible region in linear programming is a convex set.

In non-linear programming maximization, there is a non-linear dual that is to minimize a convex function, and that can be the core of the powerful technique of Lagrangian relaxation.

When we have a norm on a vector space, the locus of all points distance 1 from the origin is convex.

In facility location we can be minimizing a convex function and doing so by constructing a sequence of planes supporting the hypergraph of the convex function.

Alas, I never heard a lecture from Boyd!

There are plenty of rock solid, highly polished books where the role of complexity is made clear!

Absolutely it is possible to get a good high level picture of a field without taking any particular class. Moreover things like "convex optimization" can be done in the footnotes of a serious maths course. But on the other hand until there are again 300+ people functional analysis classes like in the old soviet union, this is perhaps the best there is.

Yup, Kolmogorov and Fomin -- NICE book. I never learned from it, but I believe that eventually I got a copy, looked through it, and liked it.

If Boyd has some nice engineering applications, terrific!

So how many signed up for the DB course?

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