Video Lectures for Upper-Level Mathematics

Sankaku

Hello all,

I am looking for video lectures for upper-level mathematics courses. In general, late-Undergraduate and early-Graduate courses of any kind. If you post in this thread, please do not link videos for Calculus I, II, or III, or first courses in Linear Algebra, ODEs, Complex Variables, or Discrete math. There are plenty of other threads for them. Also, this isn't the place for seminar videos. Please stick to whole courses.

Here are some I have found (I have only viewed a few of these so I cannot vouch for quality):

Ted Chinburg (UPenn): Algebra and Algebraic Number Theory
http://www.math.upenn.edu/~ted/noframes.html

UCCS Archive: Real Analysis, Functional Analysis, etc.
http://www.uccs.edu/~math/vidarchive.html

ICTP: Many
Warning : Strong accents and strange filming.
http://www.ictp.tv/diploma/index2.php?activityid=MTH

NPTEL: Math video links missing?
Warning : Strong accents.
http://nptel.iitm.ac.in/courses.php?disciplineId=111
http://www.youtube.com/user/nptelhrd

N J Wildberger (UNSW): Basic Algebraic Topology
http://www.youtube.com/watch?v=kdpbfOzkJzI

MathDoctorBob: Representation Theory
http://www.youtube.com/watch?v=9rDzaKASMTM


My personal wish list (at the moment) would be for good quality videos on Galois Theory, Category Theory, Topology and upper-level Complex Analysis. I am more interested in pure math but if people want to post applied math courses, I am sure there would be lots of interest here on PF. As well as links, any comments on quality of instruction and filming would be appreciated.

Thanks!

sponsoredwalk

Random I: http://calvino.polito.it/~salamon/V/
Random II:http://videos.najah.edu/courses (Many in English, not all of them though)
Real Analysis: http://courses.bilkent.edu.tr/videol...hp?courseid=12
Abstract Algebra: http://www.youtube.com/watch?v=y03Fog8q-40
General Topology: http://www.youtube.com/watch?v=yWi2_H-JUqY
Algebraic Geometry: http://www.mathnet.or.kr/new_VOD/sub...WCU+project%29
Classical Mechanics I: http://www.pa.msu.edu/courses/PHY233...oLectures.html
Classical Mechanics II: http://www.pa.msu.edu/courses/2010fa...VideoLectures/
Electricity & Magnetism: http://www2.pa.msu.edu/courses/2011s...VideoLectures/

Sankaku

1) Your first link is broken for me.

2) It does look like there are videos on Real Analysis II and PDEs in there but it will take a bit to dig through stuff like Arabic Rhetoric.

3) These look like solid Analysis videos. Good find.

4) 5) Thanks for the link to ohubrismine's youtube channel.

6) I think I may have run across this before. Thanks for the reminder. Unfortunately the asx files seem tempermental under linux. Do they work for you?

7) 8) 9) If it is possible, I would like to keep this thread to Mathematics and not Physics. If someone would like to start a separate physics thread, that would be great.

Thanks for a good start.

Sankaku

I found another interesting youtube link:

mathematicalmonk: Very quick graduate Probability Theory
http://www.youtube.com/watch?v=Tk4ubu7BlSk

sponsoredwalk

Link works fine for me, as for the physics videos I posted them specifically because it says
they were made with more of an emphasis on the mathematics than the physics.
Some of the good Najah videos, like Real Analysis II, Abstract Algebra I & II, are in English.
The .asx files aren't working for me either at the moment unfortunately, they worked fine in August.
Most of the good NPTEL videos wont be ready until 2012 (e-mailed them a few months ago about it).

PDE's: http://ee.eng.usf.edu/people/snider2.html (Other Stuff Too)
What is...?: http://vimeo.com/23635470 (Playlist has introductions to topics like Modular Forms, Elliptic Curves, P = nP)
More Topology: http://www.youtube.com/user/ThoughtSpaceZero
Category Theory: http://www.youtube.com/user/TheCatsters
Numerical Methods: http://numericalmethods.eng.usf.edu/videos/
Quick ZFC Set Theory Intro: http://www.youtube.com/watch?v=xalFtiY-JoQ
Logic, Set Theory, Number Systems: http://www2.latech.edu/~schroder/videos.htm (Other Stuff Too)

Sankaku

They don't even look like upper-level physics, let alone upper-level mathematics.

I forgot that Snider might have some PDE videos. Thanks.

Having just made a quick look, this seems to be more of a "one-off" type series - Seminar Style. We should probably keep them to another thread as there are a billion math seminar videos online.

Looks like "Khan does Topology." Worth a look, I think.

This is great! Eugenia Cheng and Simon Willerton of the University of Sheffield.
Although it isn't a whole course, it is certainly better than the big fat zero I had found for Category theory so far.

Not really my thing, but very useful for others I am sure.

Interesting. Looks like it is more oriented around Lambda Calculus and Computer Science. Lambda Calculus always seems to be one of those things that one should eventually get around to reading about.

I did like Schroder's complex variables videos, but basic set theory hardly qualifies as 'upper-level' does it?


Edit: Sorry, multiquote makes this post hard to read. I will try to do it differently next time.

Sankaku

I just watched his 3 Lambda Calculus intro videos and, while I admire his efforts, it is just painful (coming from mathematics) how he doesn't define any of the objects or operations he is using. I still got something out of it, but it could have been so much better.

xristy

Benedict Gross course in Abstract Algebra at Harvard. Uses Artin "Algebra".

Sankaku

Yes, Gross' Abstract Algebra videos are very good. I didn't really think of it as upper-level but he moves along quickly enough that it probably would work better as a second course.

I was too quick to judge this one. He gets through some decent abstract algebra in this course, up to Ring and Field theory. Thanks again for the pointer.

Sankaku

I wanted to mention that there are Videos in the "wild" from the University of Washington's master's program in applied mathematics (AMATH5xx). I have seen some of the Complex Analysis course by Mark Kot and they were very good. Although it wasn't really an "upper" level course in a pure-math sense, it was solid and I am sure that the more numerical courses in the series are at a high-level.

However, they are not free. It is unfortunate that a public university would be reluctant to share its excellent teaching with the rest of the world. Oh well, such is the commercialization of learning.

DIOGYK

http://www.youtube.com/user/MathDoctorBob

He has videos on:
Abstract Algebra
Complex Analysis
Matrix Theory & Linear Algebra II
Representation
and many more...

Sankaku

I had linked to the Representation Theory videos in my first post, but it looks like he has put up a lot more videos in the last month and a half.

Thanks for the pointer!

Sankaku

More YouTube mathematics:

Multi-linear Algebra (Tensor Products, etc.) by "mlbaker"

http://www.youtube.com/playlist?list=PLB7041DC6FDA5452C

Sankaku

The start of some Galois Theory videos, by "mimrir":

http://www.youtube.com/playlist?list=PL6F9E61DB693E565C

He has a few others that aren't in that playlist.

sponsoredwalk

What better way to start the summer than with some video lectures?

Harvard Lectures Following Hubbard's Differential Forms Book:
http://isites.harvard.edu/icb/icb.do...icb.page424494

More Differential Forms (I think mainly Following Bachman's book!):
http://www.youtube.com/playlist?list...9&feature=plcp

Milnor Giving 3 Lectures on Differential Topology:
http://vimeo.com/29434116
http://vimeo.com/29434762
http://vimeo.com/29436993

Yes, I know...

battousai

is the benedict gross algebra video lectures good for self study (first exposure to algebra)?

Sankaku

Thanks for the interesting links. I will have to take a look.

The Gross lectures are very good, but they do move quite quickly and cover a lot of ground. Try them out, but you may find it helpful to have another slower course first, depending on your mathematical maturity. You could also try something like the UCCS videos (Math 414, Fall 2007), which are pretty gentle to start with.

http://www.uccs.edu/~math/vidarchive.html