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Michael Sipser's textbook Introduction to the Theory of Computation (now 3rd ed.) includes for each major theorem, a demarcated Proof Idea of length a paragraph to more than a page, prior to presenting the formal Proof.

I am seeking examples of textbooks that do something similar, regularly providing proof sketches prior to the proofs. Of course it is not uncommon to sketch the main idea before a proof, but I am seeking systematic use of this pedagogical practice spanning an entire textbook.

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I'm not sure if this is what you're looking for, but "How to Read and Do Proofs: An Introduction to Mathematical Thought Processes" by Solow is an intro-to-proof-writing book that frequently goes very slow and wordily through a proof/argument before giving the concise mathematical version.

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  • $\begingroup$ Great example---Thanks! $\endgroup$
    – Joseph O'Rourke
    May 28 at 12:07
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Two great books that do this are the books on proof writing and real analysis by Jay Cummings.

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