Calculus Revisited - a complete self-study calculus course from MIT OCW

I couldn't agree more! His linear algebra lectures are amazing if you need to brush up on your eigenvalues and matrix decompositions. Direct link to the videos: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...

It really is. Prof. Strang is an amazing teacher of math plus he's just a really fun, likable guy.

I noticed you included planetmath in your list of encyclopedias. They used to be an excellent source for definitions and theorems in pure math. But for the past 3 years, their search has been broken and their rendering has been slow (each page view lands on a yucky page of unrendered typesetting syntax, which is replaced by a blank page for more than a few seconds before some 'jsmath' plugin does something?). They hemorrhaged most of their users during that period. I found some notes from their board meetings, and they've know about these issues, they discuss them continually, but they've done nothing for 3 years. It's really sad, because it could have been an alternative to wikipedia for pure mathematicians.

Another hidden gem for academic mathematics is york university's ask a topologist: http://at.yorku.ca/cgi-bin/bbqa . Regulars on this forum routinely answer and discuss graduate and research level questions (in algebra and geometry too, not just topology).

sure - I want to teach myself market analysis, so I'm scraping craigslist for data and fiddling with it. I did some curve fitting so I thought it might be cool to calculate velocity to, you know, figure out what time the velocity of people selling macbooks maxes out by city...

derp.

Also available at the Gutenberg project, here: http://www.gutenberg.org/ebooks/33283

It seems to be a rather nifty book.

Interesting. I'd like to do this, but I assumed that textbook authors / publishers would get annoyed.

The obsessive part of me wants to go back through my textbook collection and do all the exercises.

Don't think it matters. The information has never really been locked away, and the value added by the university environment (personal contact with top lecturers, working closely with like minded students, formal qualification, the chance to meet all sorts of cool people) is still enough to draw students.

It's a dry old world if you only focus on access to the material.

Well, most (all?) public universities let you check out books from their libraries without being enrolled. And many professors will let you sit in on lectures if you're polite and not a disturbance. So in that sense it's been possible to 'mooch free learning' off of universities for some time.

But this takes away the barrier of having to actually visit a campus. I think of it as 'freemium' marketing, but for academia.

Right now in the USA I have to imagine there is actually a glut of students. While many of them really do want to learn, I would argue a great majority are enrolled in college because "that's what they're supposed to do." I don't think an institution like MIT is at any risk of running out of potential students any time soon.

No.

Students need to be graded. You're paying for assessment as well as education.

I seriously doubt it will hurt universities. The fact is, to accomplish anything mainstream, you are still 'required' to have a degree. You can certainly accomplish a lot without it, but the barrier to entry is increased significantly without one.

There are of course exceptions, i.e, most technology jobs and on the opposite side; medicine.

The university needs to have enough demand to keep their price high -- and MIT is NOT losing applicants because they can listen to Gilbert Strang for free. Or even if MIT is losing applicants, it probably doesn't impact the number they admit each year.

On the other hand senior professors (not universities, at least to the same degree) trade in fame, not enrollment; Gilbert Strang's career has almost surely only benefited by the fact that we all know his name. MIT probably benefits as well.

However, crappy on-line universities (National, etc) might really be taking a hit from these things -- though, again, one pays for certification not (just) learning.

It's probably more that more knowledge, education and information is good for everyone, especially universities. It's not like you can go around talking about your MIT degree because you took a calc course online, but you are more likely to support higher education, research and its corresponding political necessities if you've got some education. You're also more likely to be productive and consequently more wealthy, and a bigger tax payer as a result.

I think it's an investment in society.

What's to say you can't just walk into pretty much any university and sit in on their lectures?