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Calculus Revisited - a complete self-study calculus course from MIT OCW (ocw.mit.edu)
332 points by stiff on Feb 24, 2011 | hide | past | favorite | 44 comments

I also recommend Prof. Strang's book http://ocw.mit.edu/resources/res-18-001-calculus-online-text... and series of lectures http://ocw.mit.edu/high-school/courses/highlights-of-calculu... He explains Calculus in a way that make it really easy to understand.

His linear algebra intro lectures are the best I've seen anywhere too... plus his book is probably the best intro on the topic to date.

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.

Funny, I have always found a very high correlation between "amazing teacher of math" and "just a really fun, likable guy".

(My experience also includes "musician" and "bridge player".)

Great resource, thanks. Another great resource is, of course, the Khan Academy. See their precalc videos here:


And their calc videos here:


I just wrote a short blog post on different kinds of places to find math online: http://inperc.com/blog2/2011/02/24/math-online/.

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).

I dug out my old calc textbook last weekend because I need derivatives for my latest hack. Every time I get stuck Khan Academy saves the day.

just sayin'.

Any chance you'd want to share some details about that?

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...


Another recommendation -

Keisler's Elementary Calculus: An Infinitesimal Approach http://www.math.wisc.edu/~keisler/calc.html

(pulled from this old slashdot thread) http://books.slashdot.org/story/04/03/04/028253/Five-Free-Ca...

If you've never read it before this book is a very intuitive introduction (and refresher): http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

This book is currently out of copyright (published 1910):


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

It seems to be a rather nifty book.

Anyone know of a resource like this where you can take problem sets and/or tests? For the way I learn, it just doesn't stick unless I can do problems and correct my mistakes.

Just get a book, like Concrete Mathematics, and do their problems. Post your solutions in a blog, if you want people to criticise them. You can ask on HN, if nobody reads your blog otherwise.

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.

Some like `Concrete Mathematics' come with solutions to nearly all the exercises anyway.

Most books have problems and most have solutions guides for about half of the problems. I'm surprised nobody's mentioned Spivack yet: http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098...

There are exercises (with solutions) that accompany the video series: http://ocw.mit.edu/resources/res-18-006-calculus-revisited-f...

Enjoy the scanned typewritten materials.

I kid you not, just this morning I was thinking "I want to brush up on my calculus", then I go for my morning dose of HN and see this. I like reading prescient web sites.

If you go looking it isn't too difficult to find material like this. Many of the posters hear have jumped in with their favorite resources. But, where do you all go when you want to ask potentially dumb questions as you would an instructor in class or of classmates? Khan Academy has a nice Q/A section for each video, but the best I've seen is PhysicsForums. Anything better?

Thanks for this - just watched the first video. Clearly spoken and well explained. Will be going through the rest of the course.

What are the Calculus applications for startup people?

Anything related to engineering.

Games, robotics? Linear algebra is perhaps more important, but mostly as a way to get the computers to do the calculus.

It makes it easier to calculate tips at restaurants in Palo Alto.

Aside from iTunes U, is there any other method to download an offline copy of the modules (inclusive of a/v content)?

There's no bundled zip file that you can download like in other courses, however you can find the videos at http://ia700300.us.archive.org/15/items/MITRES18_006F10/

Quick wget script to download everything from that directoy:

    wget -erobots=off -Pvideos --random-wait 1 -nH -nd -N -r -l 1 "http://ia700300.us.archive.org/15/items/MITRES18_006F10/"
And then just download the study materials from http://ocw.mit.edu/resources/res-18-006-calculus-revisited-f...

Awesome! A great refresher. {nostalgic of the simpleness of life back in highschool...study and learn}

Hope this is how the future of education looks like. Curses like these are too valuable to be locked in the ivory towers of ivy league schools. Kudos to MIT for releasing it and hope many other premier schools follow this lead.

Do you think releasing stuff like this might be bad for the university since the students have the possibility to learn without actually enrolling, thus depriving the university of some potentially good students?

Or is the effect opposite - good word, good press, good marketing.

Or, maybe I am completely of track and one has nothing to do with the other?

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.

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.

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.

> So in that sense it's been possible to 'mooch free learning' off of universities for some time.

They are more stingy with grading your exercise questions, because that takes time. But if you are genuinely interested, you can probably find someone to grade your stuff; or if you are advanced enough, just try to write a paper. Professors will probably help you, even if you are not in a university. (Just offer co-authorship, if necessary.)


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?

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