Video Lectures for Upper-Level Mathematics

  • Thread starter Sankaku
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  • #1
Sankaku
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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 [Broken]
http://www.youtube.com/user/nptelhrd

N J Wildberger (UNSW): Basic Algebraic Topology


MathDoctorBob: Representation Theory



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!
 
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Answers and Replies

  • #2
sponsoredwalk
532
5
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/videolib/course_videos.php?courseid=12 [Broken]
Abstract Algebra:
General Topology:
Algebraic Geometry: http://www.mathnet.or.kr/new_VOD/su...lgebraic+Geometry+by+Miles+Reid+(WCU+project)
Classical Mechanics I: http://www.pa.msu.edu/courses/PHY233B/VideoLectures.html [Broken]
Classical Mechanics II: http://www.pa.msu.edu/courses/2010fall/PHY321/VideoLectures/
Electricity & Magnetism: http://www2.pa.msu.edu/courses/2011spring/PHY234B/VideoLectures/
 
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  • #3
Sankaku
708
11
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.
 
  • #4
Sankaku
708
11
I found another interesting youtube link:

mathematicalmonk: Very quick graduate Probability Theory
 
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  • #5
sponsoredwalk
532
5
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:
Logic, Set Theory, Number Systems: http://www2.latech.edu/~schroder/videos.htm [Broken] (Other Stuff Too)
 
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  • #6
Sankaku
708
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...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.
They don't even look like upper-level physics, let alone upper-level mathematics.

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

What is...?: http://vimeo.com/23635470 (Playlist has introductions to topics like Modular Forms, Elliptic Curves, P = nP)
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.

Numerical Methods: http://numericalmethods.eng.usf.edu/videos/
Not really my thing, but very useful for others I am sure.

Quick ZFC Set Theory Intro:

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.

Logic, Set Theory, Number Systems: http://www2.latech.edu/~schroder/videos.htm [Broken] (Other Stuff Too)
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.
 
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  • #7
Sankaku
708
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Lambda Calculus always seems to be one of those things that one should eventually get around to reading about.
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.
 
  • #8
xristy
Gold Member
116
2
Benedict Gross course in Abstract Algebra at Harvard. Uses Artin "Algebra".
 
  • #9
Sankaku
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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 did like Schroder's complex variables videos, but basic set theory hardly qualifies as 'upper-level' does it?

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.
 
  • #10
Sankaku
708
11
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.
 
  • #12
Sankaku
708
11
http://www.youtube.com/user/MathDoctorBob

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

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!
 
  • #15
sponsoredwalk
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  • #16
battousai
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is the benedict gross algebra video lectures good for self study (first exposure to algebra)?
 
  • #17
Sankaku
708
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What better way to start the summer than with some video lectures?

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

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

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
 
  • #18
glb_lub
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Sankaku;3922981 http://www.uccs.edu/~math/vidarchive.html[/QUOTE said:
Are the lectures on this website available for free like MIT OCW ?
Or do we have to pay for them?

I noticed it needs registration. Does it mean the lectures are available only at request ?

Thanks.
 
  • #19
Sankaku
708
11
Are the lectures on this website available for free like MIT OCW ?
Or do we have to pay for them?

I noticed it needs registration. Does it mean the lectures are available only at request ?

Thanks.

They are free. Hence the link that says "Register Free" when you click on a course.
 
  • #20
dimension10
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0
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  • #21
Sankaku
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NPTEL doesn't really have a strong accent.

Certainly some, like Balakrishnan's physics videos, are superb. However, many of their other presenters do have strong accents. I don't mind too much, but some people might find it harder to watch.
 
  • #22
sponsoredwalk
532
5
Some differential geometry videos:
http://www.toldo.info/vipsschool/index.php?option=com_content&view=article&id=50&Itemid=55 [Broken]

Some seminars & a hardcore video course on algebraic topology:
http://www.youtube.com/user/arichar6

Tons of stuff:
http://www.perimeterscholars.org/317.html [Broken]

Tons of fantastic videos (in class diary section) organized around the topics in the Topic Files pdfs
http://www.math.umn.edu/~adams/FM500x/
 
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  • #24
Sankaku
708
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I think you guys are missing this excellent set of lectures from Harvey Mudd on Real Analysis. They cover the first half of baby Rudin. Check it out. Chu is a fantastic lecturer.

http://www.youtube.com/playlist?list=PL04BA7A9EB907EDAF&feature=plcp

Yes, Francis Su is very good. I guess I hadn't thought of those as "upper level" but they are well worth mentioning in any thread on good mathematics videos.

Here is the companion webpage:
http://www.math.hmc.edu/~su/math131/

Personally, my rough definition of "upper level" is something you would do in the final year of an undergrad degree or anything grad-level. However, if it is easier to make the thread for anything that isn't a basic first or second-year course, then that is probably fine. It looks to me that HMC considers that Analysis course something around a second-year level.

Edit: Perhaps it is better just to give up and post anything that isn't the basic calculus sequence, intro linear algebra or ODEs?

Except, if it is here, then it probably doesn't need mentioning:
http://www.infocobuild.com/education/audio-video-courses/mathematics/mathematics.html

...unless someone wants to do a good course review.
 
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  • #25
WiFO215
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Sorry, I meant Su, not Chu.
 
  • #26
dimension10
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Certainly some, like Balakrishnan's physics videos, are superb. However, many of their other presenters do have strong accents. I don't mind too much, but some people might find it harder to watch.

Maybe I don't realise that because I'm Indian myself...
 
  • #28
Sankaku
708
11
http://www.youtube.com/user/litsky
this guy does some nice lectures

Nice. I think I had stumbled on his channel a while back but he only had a couple videos at that point. I just watched the Semi-Direct product one and I think he teaches well (although he jumps around a little bit).

For others wondering, at this point he has videos on:

Group Theory
Multilinear Algebra
Introduction to Advanced Mathematics (Basic Analysis)
 
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  • #29
sponsoredwalk
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Does anybody have any concrete (!!!) information about the upcoming NPTEL stuff & when it'll be released or what's coming sooner rather than later etc...?
I'm quite frankly too excited to wait for all of this, the quality of their lectures is literally unmatched by what exists on the internet & it'd be among the great tragedies of my life if I have to wait until Christmas to view their approach to some of the courses they have planned.

Statistical Mechanics
http://atomlaser.anu.edu.au/honours_em_downloads.html [Broken]
Statics, Mechanics of Materials...
Engineering Mechanics
 
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  • #30
WiFO215
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Here, take my glasses and read the title again: this thread is for upper level math.
 
  • #31
Sankaku
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Harvard Lectures Following Hubbard's Differential Forms Book:
http://isites.harvard.edu/icb/icb.do?keyword=k80478&pageid=icb.page424494

I have now had a chance to look through this course. Unfortunately, it is (mostly) just the first half of the Hubbard book and so doesn't get into differential forms. The second course doesn't seem to be available on their site. For clarification, it is aimed at well-prepared students who have not done a multivariable calc course yet (many Harvard freshmen seem to be taking the course, so it doesn't really fall into our "upper-level" classification).

It is an interesting mix. By introducing linear algebra at the same time as multivariable calculus, it is able to treat a lot of things in much more generality. Bamberg mixes applications and proofs in the course, but his choice of material often seems strange to me. A lot of it seemed shoe-horned in just for the "shiny" factor rather than it actually being a useful time to learn the topic (finite fields, finite topologies, etc.).

I am not sure I would have liked learning this way. There isn't enough time to devote to the linear algebra. Really, I would do LA first and then build a course like Hubbards just assuming the LA material as background. Then you wouldn't be trying to do everything at once.
 
  • #32
sponsoredwalk
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http://nptel.iitm.ac.in/courses/111101005/ [Broken] by I.K. Rana, author of the best book in existence...
 
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  • #33
Sankaku
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http://nptel.iitm.ac.in/courses/111101005/ [Broken] by I.K. Rana, author of the best book in existence...

Looks great. Thanks for the link.
 
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  • #34
sponsoredwalk
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F... F... http://nptel.iitm.ac.in/courses/111105037/ [Broken]
 
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  • #35
Sankaku
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F... F... http://nptel.iitm.ac.in/courses/111105037/ [Broken]

It looks like they are finally putting the upper-level mathematics courses online. I look forward to seeing what they come up with over the next year. It is too bad the Algebraic Topology course doesn't have any videos, though...
 
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