It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some universities do that (albeit to a very limited extent), and I hope we can compile here a list of all the mathematics courses one can view in their entirety online.

Please only post videos of entire courses; that is, a speaker giving one lecture introducing a subject to the audience should be off-limits, but a sequence of, say, 30 hour-long videos, each of which is a lecture delivered in a class would be very much on-topic.

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Some list can be fetched from the ancient post here:mathoverflow.net/questions/1714/best-online-math-videos –  Unknown Feb 5 '11 at 19:00
+100 if I could. I always wanted to have them in summers. –  Unknown Feb 5 '11 at 23:11
Please, share these videos also on MathOnline, in the video section! :-) mathonline.andreaferretti.it –  Andrea Ferretti Apr 8 '11 at 11:39

Search iTunesU for "Mathematics": It turns up many courses (I couldn't see how to count them easily), including the Gilbert Strang course already mentioned.

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The Eilenberg Lectures at Columbia. So far, the topics have been:

• Benedict Gross, on number theory and representation theory
• Edward Frenkel, on Langlands program and quantum field theory
• Sergiu Klainerman, on the mathematical theory of general relativity
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Eleven lectures by Amritanshu Prasad on representation theory, the first two on generalities, the next five deal with representations of symmetric groups in the semisimple case, going up to the calculation of character values using Frobenius' formula. The next two deal with polynomial representations of GL(m). The last two are on the hook-length formula and Frobenius's characteristic function respectively. Assignments and notes are available on the course website for the first seven lectures.

This content is going to form the bulk of a book titled "Representation Theory: A Combinatorial Viewpoint" by the lecturer.

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David Forney's course on Coding Theory at MIT.

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Differential Equations, taught by Arthur Mattuck at MIT.

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Thirty lectures from the course Wavelet Theory given at the University of Maryland by John Benedetto.

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A real analysis course from Harvey Mudd College. An early course for math majors, so it also covers a bit of good proof writing techniques, induction proofs, logic, etc.

(Disclaimer: Filmed by me. So you know who to blame for the bad camera work.)

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Might as well plug my own course on Diophantine Geometry. It's in Portuguese, so that will restrict the audience a bit, but I am having fun and it's nearly finished (last class on Nov 8th 2011). IMPA has a bunch of other videos as well, just follow the links.

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A course on Lie groups taught by Erik van den Ban at Utrecht University.

The parent directory contains a few more bachelor level courses, but these are in Dutch.

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The courses of the summer school Poisson 2012 (that took place in Utrecht), as well as lectures of the conference that followed, are available online: http://www.youtube.com/user/poissonutrecht

The courses are:

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My rather standard course on ordinary differential equations, at http://drorbn.net/index.php?title=12-267.

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There are many good quality math lectures (mostly in Russian but sometimes in English) http://www.lektorium.tv/ they are groupped by courses (for example http://www.lektorium.tv/course/?id=22876)

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I would recommend those from Simon's Center for Geometry and Physics. Here is a list of all workshops at SCGP.

Videos from all of their workshops are available online. Here are all talks from Random Tilings Workshop last February.

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The University of South Florida has a whole series of lectures devoted to numerical methods here: http://numericalmethods.eng.usf.edu/videos/

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Very, very introductory lectures in complex analysis: http://adamglesserf09math481.wordpress.com/page/3/

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LMS Durham Symposia have archive of videos online which can be found at http://www.maths.dur.ac.uk/events/Meetings/LMS/

For example, 2009 conference on model theory of fields has videos of the talks by Hrushovski, Kazhdan, Macintyre and Zilber, among the others.

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Twenty-four lectures from a course on algebraic combinatorics, taught by James Propp.

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Here a summer school on representation theory for $SL_2(\mathbb{R})$:

http://www.math.utah.edu/vigre/minicourses/sl2/

Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry":

http://www.uni-math.gwdg.de/aufzeichnungen/SummerSchool/

Algebraic Quantum Field Theory - the first 50 Years

http://www.uni-math.gwdg.de/aufzeichnungen/AQFT50/

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Andrew Ng at Stanford has a machine learning course. (This is related to, but not the same as, the Stanford/Coursera online machine learning course.)

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My alma mater, the University of Colorado at Colorado Springs, has a video course archive on some subjects (mostly undergraduate). These include

Calculus I, II, III

Algebra (elementary and abstract)

Analysis (Real, Functional, but no Complex)

Geometry (mostly Euclidean)

There are several more.

For each class here, the entire semester was recorded. To download the videos, you have to create an account, which merely requires a name and email address.

Here's the webpage: http://www.uccs.edu/math/student-resources/video-course-archive.html

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There are lots of links to various pages filled with online video lectures here:

http://www.ims.cuhk.edu.hk/geometry/

Go to "Links" on the left hand side.

Some of the links are broken or out of date, but there's still a ton of good stuff here.

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Eight recent lectures by Emmanuel Candes on compressed sensing are linked to from here: http://www.newton.ac.uk/programmes/INI/iniw04p.html

More generally, the Newton Institute has been making a large archive of talks available.

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Here is an interesting choice

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If you happen to know Italian, on Massimo Gobbino's home page there are videos (tablet pc screencasts + audio) of several courses (Calculus I and II for engineers, honors calculus/analysis) and lots of high-school Math Olympiad training material.

Highly recommended: I find tablet screencasts an excellent medium, and on top of that Massimo is a great teacher.

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A master course by Benoit Fresse on operads and Grothendieck-Teichmüller groups (in french), at Université Lille 1, given this semester (Winter 2012). The course has a really nice and complete introduction to the subject. The principal reference is a preprint (in english) writed by Fresse.

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Here is a summer school on Berkovich spaces

http://www.diffusion.ens.fr/index.php?res=cycles&idcycle=490

(there are more courses at http://www.diffusion.ens.fr/ but unfortunately they are not broken into catergories; one has to fish for mathematical courses more or less via manual search)

http://bogomolov-lab.ru/SHKOLA/courses.html

a summer school for undergraduates (topics include number theory, metric geometry, anabelian geometry)

has a huge collection of videos, including recordings of summer school courses both for undergraduates and graduates.

http://blip.tv/pifagorov/ and http://www.lektorium.tv/ are examples of a similar effort

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All Master Classes given at QGM and the previous CTQM are online here: http://qgm.au.dk/video/ and here: http://www.ctqm.au.dk/news/special_events.html.

It is quite an extensive list of 17 Master Classes in total. The courses are on a variety of different subjects, given by among others Maxim Kontsevich, Nicolai Reshetikhin, Nigel Hitchin, Vaughan Jones, Tom Mrowka, Gregor Masbaum, Dylan Thurston, Robert Penner and many more.

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