I'm learning analysis from the book Principles of Mathematical Analysis by Walter Rudin, third edition.

This book, popularly known as Baby Rudin, is being used for analysis courses at such elite places as the MIT, Harvard, Stanford, UC Berkeley, Yale, and Princeton. Am I right?

Now is there any video lecture analysis course based on Baby Rudin available on the Internet from any of the above-mentioned institutions?

Which other text(s) treat the same material as Baby Rudin and so can be used in combination with it?

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    $\begingroup$ This is not entirely on topic so I'm putting it in a comment. While I think Baby Rudin is a great book and I really loved using it myself, I think the later chapters, despite being rigorous, is not easily comprehensible. Limiting yourself to this book is not a good idea and don't get discouraged if you can't understand some part of it. Some proofs in this book, while short, are not quite "clean" in my opinion. $\endgroup$ – BigbearZzz Apr 26 '16 at 5:31
  • $\begingroup$ @BigbearZzz perhaps you're right, but Rudin's compact presentation is also one of its merits. He establishes in the first 200 pages of his book results which are spread out in three to four books by an Indian or Pakistani writer. $\endgroup$ – Saaqib Mahmood Apr 26 '16 at 5:37

I would not limit yourself just to those universities if you want good analysis lectures. I would highly recommend looking into Francis Su's lectures from Harvey Mudd College. His is a one-semester course and he ends roughly when they get into single-variable differentiation. A first glance at MIT's Open Courseware doesn't show any video lectures in analysis, though you may possibly find other materials (possibly written lectures) on their site.

  • $\begingroup$ thank you for the suggestion, but the problem with those video lectures is they cover very little of Rudin. They fail to cover integration (Chapter 6 ) and uniform convergence (Chapter 7). On the other hand, the MIT 18.100 B and C courses cover even part of Chapter 8 of Rudin as well! $\endgroup$ – Saaqib Mahmood Apr 26 '16 at 5:33

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