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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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    $\begingroup$ Some list can be fetched from the ancient post here:mathoverflow.net/questions/1714/best-online-math-videos $\endgroup$
    – Unknown
    Feb 5, 2011 at 19:00
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    $\begingroup$ +100 if I could. I always wanted to have them in summers. $\endgroup$
    – Unknown
    Feb 5, 2011 at 23:11
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    $\begingroup$ I'm voting to close this question as it is just a request for collating information that could be found and hosted elsewhere $\endgroup$
    – Yemon Choi
    Feb 13, 2019 at 20:46
  • $\begingroup$ I add as comment a collection of 19 videos for the course Introduction to Loop Quantum Gravity by professor Carlo Rovelli, it's from the official YouTube chanell Quantum Gravity at CPT Marseille. I don't know these videos of Physics, but I've read several scientific dissemination books about loop quantum gravity, and this is a topic with very interesting mathematics. I hope don't bother with my comment, many thanks. $\endgroup$
    – user142929
    Dec 30, 2022 at 18:14

91 Answers 91

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Ted Chinburg has videos of his lectures for what is going on a 2 year course in algebraic number theory online( direct links to videos: semester 1, semester 2, semester 3, semester 4), and from there you can also get lectures from various seminars at Penn.

Also, there's the MSRI database for all the things that go on there, they're all over the website at each program's site.

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    $\begingroup$ Chalk and board presentation... Am I alone who can't stand them anymore, no matter the merit? $\endgroup$ Feb 13, 2011 at 2:22
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    $\begingroup$ You probably are! I can't stand anything other than chalk and board! $\endgroup$ May 16, 2012 at 22:22
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    $\begingroup$ Anyone know the status of these? I recently pointed a student to these, only to find all of the links were down. $\endgroup$ Jun 3, 2014 at 14:20
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    $\begingroup$ @CamMcLeman I just attempted to open up the first video of semester one and it seems to be working fine now. $\endgroup$
    – Alec Rhea
    Feb 5, 2018 at 20:41
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    $\begingroup$ The links on Ted's videos no longer seem to be working in 2020. $\endgroup$ Oct 25, 2020 at 3:00
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77 videos on Category theory.

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  • $\begingroup$ what order should this stuff be watched in ? $\endgroup$
    – galois
    Apr 22, 2015 at 19:29
  • $\begingroup$ They have a link for the order on the webpage. Honestly I watched all of their videos but got sick of them pretty quickly. They aren't bad, but they aren't great to watch in one sitting either. $\endgroup$ Aug 15, 2016 at 22:07
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    $\begingroup$ @William, I find their videos pretty dull and unfocused tbh $\endgroup$ Dec 7, 2016 at 12:35
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    $\begingroup$ They certainly are not designed to be watched in one sitting! They are 10 minute, bite-sized videos. Brent Yorgey's has a Catsters guide where he suggests an order to watch them in. (He was trying to watch two per week.) $\endgroup$ Jul 30, 2018 at 13:06
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The lecture videos of Introduction to Abstract Algebra, taught by Benedict Gross at Harvard, can be downloaded here.

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Federico Ardila's (full-semester) courses on polytopes, combinatorial commutative algebra, Coxeter groups, combinatorial Hopf algebras, matroid theory, and enumerative combinatorics. They include lecture videos and lecture notes. See http://math.sfsu.edu/federico/teaching.html

Now they are also on YouTube here: polytopes, combinatorial commutative algebra, Coxeter groups, combinatorial Hopf algebras, matroid theory, and enumerative combinatorics.

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    $\begingroup$ the links to the course notes are broken, but the YouTube videos are still there. $\endgroup$
    – Colin Tan
    Oct 13, 2022 at 15:53
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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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For what it's worth, my own University of Toronto 2009 course on Algebraic Knot Theory.

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  • $\begingroup$ Great content, but frankly poor video... so many board diagrams are too blurry to read. $\endgroup$ Mar 20, 2020 at 2:01
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Gilbert Strang's course on Linear Algebra at MIT.

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Algebraic topology by Prof. N J Wildberger of the School of Mathematics and Statistics, UNSW

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    $\begingroup$ I'd steer clear of these. Besides his nontraditional views, they're just not very good (they're elementary, not really very rigorous, and due to the above don't cover the same material as you'd see in a normal treatment of the material). $\endgroup$
    – Julian
    Jul 21, 2013 at 3:44
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    $\begingroup$ Being nontraditional isn't a bad thing. He clearly explains his approach and covers interesting, engaging content. I also don't think that an undergraduate algebraic topology course at the level he is going for (covering in fact a large chunk of material) needs to have ever thing detailed in a grad style level of rigor. Very few undergrads get most of the material he introduces. $\endgroup$
    – Zach Haney
    Aug 9, 2015 at 4:34
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The Fourier Transform and Its Applications, taught by Brad Osgood at Stanford. Lecture notes here.

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Miles Reid's lectures on Algebraic Geometry and Algebraic Surfaces.

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  • $\begingroup$ Are they as much filled with side blows as his book? $\endgroup$ Feb 7, 2011 at 18:16
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    $\begingroup$ I like very much his books (including side blows). The lectures are witty.. $\endgroup$
    – pi2000
    Feb 7, 2011 at 18:45
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    $\begingroup$ how do I view these lectures? I'm unable to open them. $\endgroup$
    – john
    Dec 30, 2011 at 12:02
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    $\begingroup$ You can watch them with Windows Media Player. $\endgroup$
    – pi2000
    Jan 15, 2012 at 9:43
  • $\begingroup$ thanks. can one download? $\endgroup$
    – user 1
    Jan 11, 2015 at 16:52
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At my YouTube site Insights into Mathematics. 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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Geometric Representation Theory Seminar - Fall 2007 by John Baez and James Dolan

This fall, our seminar is tackling geometric representation theory — the marvelous borderland where geometry, groupoid theory and logic merge into a single subject. The seminar is jointly run by John Baez and James Dolan. Besides explaining well-known stuff, we'll report on research we've done with Todd Trimble over the last few years.

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  • $\begingroup$ Is anyone else having trouble getting audio from the videos? I'm pretty sure that the audio worked just fine for me back in '07 when I originally watched these, but now I don't hear anything. I tried streaming the videos in Chrome, in Firefox, downloading and opening with the standalone QuickTime application, as well as opening with VLC. The video shows up just fine but no audio from any of them. Running Windows 7. $\endgroup$ Sep 14, 2011 at 21:08
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Coursera offers not just the videos, but entire courses: I'm currently following Probabilistic Graphical Models, which has weekly exercises and programming projects (which are marked by an autograder), plus community discussion boards and a wiki for collaborating with other students pursuing the course at the same time. Although you could presumably just create an account towards the end of term, archive off all the videos and then watch them at your leisure rather than trying to match the (reasonably demanding) schedule.

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    $\begingroup$ I took a Cryptography course there and it was good! Also, it seems like it is growing quite fast with more and more courses added. Definitely recommended to take a look. $\endgroup$ Jul 19, 2012 at 2:29
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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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This might not fulfill the requirements of being a mathematics course, but I think that it is close enough. In 2006 the Clay Mathematics Institute hosted a Summer School in Arithmetic Geometry. The videos are great if you have a solid foundation in algebraic geometry already and wish to continue in the direction of arithmetic geometry .

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Three courses by Stephen Boyd at Stanford: Introduction to Linear Dynamical Systems, Convex Optimization I, and Convex Optimization II.

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  • $\begingroup$ There are no videos on that page $\endgroup$ Aug 15, 2020 at 23:51
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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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Introduction to Algorithms, taught at MIT by Charles Leiserson and Erik Demaine.

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Graduate course on Computational Complexity and Quantum Compuation given at Cambridge University by Timothy Gowers.

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Richard E. Borcherds has posted videos for courses on group theory, commutative algebra, classical Algebraic geometry and scheme theoretic algebraic geometry.

Link

Connecticut summer school in number theory (CTNT) has short courses on different topics, like modular forms, elliptic curves, p-adic numbers, sieve methods, etc.

Link

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Multivariable Calculus by Edward Frenkel at Berkeley:

http://www.youtube.com/view_play_list?p=07CF868151394FE3

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

Here is the link: http://www.newton.ac.uk/webseminars/

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MIT's Open Courseware is a very good source of this http://ocw.mit.edu/index.htm.

I personally recommend the differential equations course they have.

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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 entire master course at ICTP:

http://www.ictp.tv/diploma/index2.php?activityid=MTH

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A great collection of combinatorics videos

Igor Pak’s Collection of Combinatorics Videos

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Here is an ongoing series of videos covering Point-Set Topology that is planned to continue indefinitely.

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  • $\begingroup$ Not going to continue? $\endgroup$
    – Max
    Aug 13, 2018 at 16:30
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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 forms the bulk of a book titled "Representation Theory: A Combinatorial Viewpoint" (Cambridge University Press, 2015) by the lecturer.

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MSRI's online videos. These do not consist of courses, but each semester is themed so the videos offer good exposure to many areas of current research.

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    $\begingroup$ This duplicates part of Verma (on the other hand, Hill had a better MSRI link at first). What should I do...? $\endgroup$ Jan 6, 2013 at 23:01

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