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One of the most annoying gaps in my math education is Real analysis.

I tried hard, but all I could find are either Harvey Mudd College lectures or MathDoctorBob. The latter are too short and the former are in horrendous format, I can barely make out what is written on the blackboard.

Ideally I'd like the lectures to cover topics such as proofs of continuity, differentiation, some main inequalities, $\limsup$ and $\liminf$, uniform/pointwise convergence and continuity, dominated and monotone convergence and maybe a bit more.

So if anyone knows if this material is available online, I'd be quite grateful.

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    $\begingroup$ If you speak portuguese, try these: video.impa.br/… They are from Elon Lages Lima, a well known brazilian Mathematician. Those lectures are from the world-wide known IMPA, from 2011. I don't know if there are subtitles... $\endgroup$ – Marra Feb 24 '13 at 1:29
  • $\begingroup$ No, sorry, I don't speak Portuguese. I'd prefer English. $\endgroup$ – Alex Feb 24 '13 at 1:30
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    $\begingroup$ I have a (very smart) friend who is fond of the ICTP TV lectures. A quick glance at the offerings shows that they have a collection of undergraduate lectures in analysis (real and complex). Downside: the video and sound quality may not be to your liking. $\endgroup$ – Chris Feb 24 '13 at 1:35
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    $\begingroup$ At the risk of making worse the fact that I left what may not be an appropriate answer to your question: may I ask why you are specifically interested in video lectures rather than written lecture notes? To my mind, the big advantage of a lecture is that you can ask questions of the lecturer. This is not possible when watching a pre-taped video lecture. It can be easier and quicker to learn the tiniest bit of subject X from a video lecture than from written notes, but it sounds like you want to learn things thoroughly. For this I really think the written word is superior. $\endgroup$ – Pete L. Clark Feb 24 '13 at 3:59
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    $\begingroup$ @PeteL.Clark I suppose that there are things which are easier done when speaking than when typing lecture notes - like handwaving, drawing pictures, getting big picture across... (I am not saying that they are impossible in written notes; but they seem to be communicated in spoken word more easily.) So maybe this might be an advantage of videos. Another possibility - when someone is teaching, they are limited by the time. In written notes, there is no limit, so it is possible to digress, go in detail. That might be another reason why some people would prefer a video from actual lecture. $\endgroup$ – Martin Sleziak Jul 3 '14 at 17:05

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You can try: http://www.uccs.edu/math/student-resources/video-course-archive.html

They have a Real Analysis course listed, Math 533 Real Analysis I - Fall 2007. They are good, though not that challenging.

You may need to create a [free] account to view the videos.

If you really don't want to make an account the videos start with:

http://cmes.uccs.edu/Fall2007/Math533/pages/video3.html

and go up to /video24.html. There is, for some reason, no video 1 or 2.

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Video Lectures in Mathematics , This site contains links to math videos, withch includes a lot of mathematical topics for example Topology, Algebra, Complex and real analysis and anything that you think.

Specifically, the site has 38 videos in real analysis: Analysis, Real.

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Check out these YouTube video lectures by S K Ray on real analysis.

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Roughly the lower level half of what you're asking for is covered in these lecture notes of mine on honors calculus. (To me, honors calculus is a flavor of undergraduate real analysis, and not the least ambitious possible flavor.)

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  • $\begingroup$ Of course these are not video lectures. I'm assuming you might in principle be interested in a more conventional format... $\endgroup$ – Pete L. Clark Feb 24 '13 at 3:31
  • $\begingroup$ Thanks I'll check out your lectures, I'm sure they are cool. The thing is, I tend to understand things better if they are explained by a person. Unfortunately, I missed most of the real analysis and beyond in my uni study. So now, when I have a job, I need to catch up somehow and video lectures are the best choice. $\endgroup$ – Alex Feb 25 '13 at 3:52
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This was basically already posted by Alex - but Joel Feistein has his 2nd year undergrad introductory course to real analysis (complete with camcasts/videos, notes, exercises and solutions) posted here http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c6c045f6-286d-6b9f-b96c-36a998632fc3 and his 4th year undergrad course on functional analysis here http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c9eec1dc-8c27-9949-dc16-2728edf6c994.

They are both quite good (the first one introduced me, at the time an engineering undergrad, to rigorous mathematics and how to do proofs and I cannot be happier of having watched it).

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  • $\begingroup$ True, although I found them kind hard) $\endgroup$ – Alex Mar 10 '13 at 0:06
  • $\begingroup$ Did you try doing the exercises as you went along? Doing them made all the difference for me. $\endgroup$ – jkn Mar 12 '13 at 13:56
  • $\begingroup$ Yes I'm. The part on uniform vs pointwise convergence in quite helpful $\endgroup$ – Alex Mar 13 '13 at 16:02
  • $\begingroup$ pages not found $\endgroup$ – baxx Apr 7 '17 at 21:29
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In fact I ended up using Nottingham Uni's lectures on Youtube, like this one:

http://www.youtube.com/watch?v=mB4Yny0T3HA

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Francis Su 's YouTube Lectures on Real Analysis

this web page contain the links: http://analysisyawp.blogspot.com/

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  • $\begingroup$ very low resolution - op stated these in their original post $\endgroup$ – baxx Apr 7 '17 at 21:31
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3 https://www.youtube.com/playlist?list=PLil-R4o6jmGhUqtKbZf0LIFKd-xN__g_M real analysis 1 of NTU ( more advanced version of 1)

4 https://www.youtube.com/playlist?list=PLil-R4o6jmGhkuZPmKL_A5Y7N4HOsa1nX real analysis 2 (continuation of 3)

these lectures are in Chinese, but he writes in english and his handwritting should be clear enough for you to read. I really enjoyed it and plan to go through all of them.

There isnt a lot of good RA lectures on YT, so hope this will help

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Here is a friendly list of lecture recordings of real analysis. From lecture 4 quality of lectures is good but first three are also understandable.

https://www.youtube.com/playlist?list=PL4fpys7KOcYhcH3jWB2dBGUSMpXGMOVDc

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1 http://ocw.aca.ntu.edu.tw/ntu-ocw/index.php/ocw/cou/104S115 real analysis 1 at National Taiwan University ( Called Calculus for math majors 1)

2 http://ocw.aca.ntu.edu.tw/ntu-ocw/index.php/ocw/cou/104S210 real analysis 2 at National Taiwan University ( Called Calculus for math majors 2)

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