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

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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Sets, Counting, and Probability, taught by Paul Bamberg at Harvard.

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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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Differential Equations, taught by Arthur Mattuck at MIT.

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

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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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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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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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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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This collection has a mixture of French and English, but here you can find videos given at the Bicentennial of the Birth of Evariste Galois (Bicentennaire de la naissance d'Evariste Galois) at the Institut Henri Poincaré in Paris.

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Steven Miller's ongoing lectures on complex analysis are very stimulating

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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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The YouTube channel of The Institute of Mathematical Sciences, Chennai has several such courses, such as "Effective methods in Diophantine Analysis" by Yuri Bilu, "Soergel modules and Kazhdan-Lusztig theory" by Ben Elias, a course on von Neumann algebras by Sunder, Lie groups by Raghunathan and many more:

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

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A Computability Theory course by Bart Kastermans. These lectures followed Robert Soare's new book, which is not yet published, so they are temporarily behind a password; however, Bart's website indicates that the passwords are available upon request. (In any case they will be open to the public eventually, I think.)

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Andrew Ng at Stanford offers videos of various courses.

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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