Rudin’s Principles of Mathematical Analysis or Apostol’s Mathematical Analysis?

I am in high school and have no access to a professor or anyone. I previously used Calculus Volume I by Tom Apostol and Spivak’s Calculus (for the differential calculus bit).

I can choose between Mathematical Analysis by Tom Apostol and Principles of Mathematical Analysis by Walter Rudin, as I was gifted Rudin by a friend and ended up buying Apostol as well. I will be indebted if someone told me which one is the tougher one and which one is better for the self-learner. I have no issues about how tough the book is, but I would like the book that enables me to understand the subject better without being too compressed or too verbose and guides me better.

Answer

The best advice I can give you is to do what I did when learning real analysis: Use them both. Apostol has a far better exposition, but his exercises are not really challenging. Rudin is the converse — superb exercises, but dry and sometimes uninformative exposition. The 2 books really complement each other very well — especially if you’re self-learning.

Attribution
Source : Link , Question Author : Eisen , Answer Author : Rudy the Reindeer

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