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

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

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Carmen Rovi's DailyMotion website has 160+ videos on the topology of manifolds in general, and surgery theory in particular, of lectures either given at the University of Edinburgh or at conferences elsewhere. Some of the lectures are courses, and some are one-offs. The November 2012 Edinburgh course of 12 lectures by Rob Kirby on high-dimensional manifold topology is a particular highlight.

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Here you find the videos of the conference "Orbits, Primitive Ideals and Quantum Groups", Weizmann Institute, Israel.

1. Finite W-algebras, by I. Losev
2. Adapted pairs in a biparabolic subalgebra, by F. Fauquant-Millet
3. Hopf Algebra and Root Systems, by H-J Schneider
4. Quiver Grassmannians, by M. Reineke
5. Quantum quasi-Shuffles, by M. Rosso
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My school, the University of Colorado at Colorado Springs, has a video course archive on some subjects. 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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If it's not too gauche to plug my own course at CMU,

23 lectures on Analysis of Boolean Functions (one lecture by John Wright):

http://www.cs.cmu.edu/~odonnell/aobf12/

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

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HERE IT IS A GOOD RESOURCE OF VIDEO LECTURES CONDUCTED BY IIT'S & IISc'S. http://nptel.iitm.ac.in/courses.php?disciplineId=111

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Master Class on Wall-Crossing. Lectures given by Maxim Kontsevich.

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says "404 not found" for me –  Dima Sustretov Apr 18 '12 at 13:57
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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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Here are some of my favorites :

1. Sidney Coleman's Quantum Field Theory

2. Shiraz Minwalla's String Theory

3. MIT OCW

4. Videos to short courses at some workshops can be found at IAS and MSRI

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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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Plenty of short courses given at workshops can be found in the Newton Institute archive at newton.cam.ac.uk.

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Why don't you make that a hyperlink? –  Quinn Culver Jul 22 '11 at 2:15

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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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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At my YouTube site Insights into Mathematics (http://www.youtube.com/user/njwildberger?feature=mhee) I have playlists on

Rational Trigonometry

Linear Algebra

Math Foundations

History of Mathematics

Universal Hyperbolic Geometry

Algebraic Topology (this was mentioned above)

Elementary Mathematics (K-6)

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David Gay gave a graduate course on Morse Theory at the University of Georgia this spring and the videos are compiled together in a YouTube playlist at Morse Theory: UGA 2012. Notes for his course are also online on the course website.

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http://nptel.iitm.ac.in/video.php?subjectId=122104017 -here are a good series of video lectures from IIT kharagpur

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nice videos about Quantum Mechanics (By J.J.Binney -Oxford), total 27 videos with about 1 hour duration, and QFT (By David Tong - Oxford). Those videos about QM are really great here.

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Would you mind giving a link ? :-) –  DamienC Dec 5 '12 at 9:18

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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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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Nine lectures by me 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 last two deal with polynomial representations of GL(m). Assignments and notes are available on the course website.

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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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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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