A YouTube lecture series on real analysis by Francis Su, based on Rudin's Principles of Mathematical Analysis and mostly following its order. It covers the foundations of calculus and the rigorous treatment of limits, continuity, and sequences and series.

Commenters call Su an amazing teacher and say the lectures made Rudin's ideas understandable when the textbook alone did not.

What commenters said (2)

1. Strongly recommendsedanm2018in “Ask HN: Resources to learn real analysis?”

   I highly recommend Francis Su's Real Analysis Youtube lectures, on Youtube [1]. He is an amazing teacher.

   I first started trying to learn Real Analysis from Baby Rudin, but I couldn't understand the point behind the ideas introduced there. Then I started watching these lectures, which are based on Baby Rudin and mostly follow it, and it helped a lot (together with reading the main text itself - a crucial step).

   The only bad thing is that only half of Rudin is covered - the other half is covered in Real Analysis 2, which is unfortunately not online as far as I can tell.

   [1] https://www.youtube.com/watch?v=sqEyWLGvvdw&list=PL0E754696F...

2. Recommendsryanlbrown2014in “Ask HN: How or where to begin learning mathematics from first principles?”

   I'm trying to do this too right now. I've found this course on real analysis to be very helpful (I suggest watching it sped up though):

   https://youtube.com/playlist?list=PL0E754696F72137EC

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