Question

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.

Answer 1

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.

Answer 2

77 videos on Category theory.

Answer 3

For what it's worth, my own University of Toronto 2009 course on Algebraic Knot Theory.

Answer 4

Federico Ardila's (full-semester) courses on polytopes, combinatorial commutative algebra, Coxeter groups, combinatorial Hopf algebras, and matroid theory. 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, and matroid theory.

Answer 5

The lecture videos of Introduction to Abstract Algebra, taught by Benedict Gross at Harvard, can be downloaded here.

Answer 6

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

Answer 7

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

Answer 8

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.

Answer 9

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 .

Answer 10

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

Answer 11

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/

Answer 12

Gilbert Strang's course on Linear Algebra at MIT.

Answer 13

A bit borderline since its only nine lectures, but a mini course on Additive Combinatorics taught at IAS by Boaz Barak, Luca Trevisan, and Avi Wigderson.

Answer 14

The entire master course at ICTP:

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

Answer 15

Lectures on Real Analysis, from Bilkent University (Assoc. Prof. Dr. Alexandre Gontcharov): http://courses.bilkent.edu.tr/videolib/course_videos.php?courseid=12

Answer 16

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

Answer 17

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.

Answer 18

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

Answer 19

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.

Answer 20

The San Francisco State University hosts large number of course videos on various subjects including:

$\cdot$42 videos on Coxeter Groups

$\cdot$41 videos on Discrete Geometry

$\cdot$18 on Dynamical Systems

$\cdot$16 on Lie Algebras

$\cdot$43 on Matroid Theory

$\cdot$28 on Real Analysis I and II $\ldots$

All you need to do is click on the drop down menu "List all courses".

Answer 21

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.

Answer 22

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

Answer 23

Multivariable Calculus by Edward Frenkel at Berkeley:

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

Answer 24

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

Answer 25

The Fourier Transform and Its Applications, taught by Brad Osgood at Stanford.

Answer 26

Introduction to Algorithms, taught at MIT by Charles Leiserson and Erik Demaine.

Answer 27

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.

Answer 28

David Forney's course on Coding Theory at MIT.

Answer 29

Differential Equations, taught by Arthur Mattuck at MIT.

Answer 30

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