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.
Answer
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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