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Question:

I'm looking for writers and their books that are written in similar fashion to the book of Munkres Analsis on Manifolds. In other words, books with the properties (or at least with a subset of them);

  • not-terse proofs,
  • readable
  • short list of exercises (if possible; optional)
  • pedagogically written
  • states motivations explicitly
  • Rigorous
  • Non introductory text

Note that, I'm not looking for such books in a specific subject; the book can be on any subject.

Also note that, most of the time, texts for undergraduates has the smell of an "introduction" text, which I do not want to spend time because I'm just bored, so I would appreciate if you just constraint yourself to the graduate text / texts with serious analysis of its subject.

Edit:

There are already lots of posts on subjects that are looking for "best" book on various subjects, and this post does not asks which book that you are thinking is the best book on the subject x. Because of that reason, please do not post any book that is "good" unless you really think that it satisfies the above properties (if it satisfies only a subset of those properties, then please specify)

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I am a fan of George Simmons' Introduction to Topology and Modern Analysis, and it seems to cover all your criteria.

The proofs are not terse, it is eminently readable and contains lots of motivation for the topics it covers. Each section ends with a short list of exercises, and it has remarkably few typos. If you are not interested in the introductory part then you can skip directly to the second chapter and later. Simmons covers a wide range of topics in this book.


Another recommendation of mine would be Tristan Needham's Visual Complex Analysis. If you have been introduced to complex analysis already, then this is a great book to polish your insights. Don't be deceived by the casual tone of the author; this book is a gold mine of geometric insights.

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    $\begingroup$ Needham is not rigorous. This appears to be a strength of the book, though, rather than a weakness, at least if you already know some complex analysis. $\endgroup$ – Theoretical Economist Aug 6 '18 at 14:02
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    $\begingroup$ I agree. I should have mentioned that Needham isn't rigorous. He does tick all the other boxes, in my opinion :) $\endgroup$ – Brahadeesh Aug 6 '18 at 14:05

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