I posted this question in the math stackexchange https://math.stackexchange.com/questions/4681694/comparison-of-textbooks-on-how-to-write-proofs and one person suggested that I cross-post it here. I'd be most apprecicative for your inputs. Here is the original post, slightly edited.
Next fall I will teach a class on "How to write proofs". Prerequisite is first-year calculus. The three textbooks I am considering are
Hammack, Book of Proof (3rd ed)
Sundstrom, Mathematical Reasoning: Writing and Proof (3rd ed)
Cummings, Proofs: A long-form mathematics textbook.
This will be my first time teaching such a course, and I'd be most appreciative for feedbacks and comments from those who have taught such a class using these books -- why do you pick one over the others? feedback from students? advice on how to teach such a class/use these books? To give you an idea the issues I'm considering (incorrectly, perhaps!), here are my first impressions of the three books, based on a quick reading:
Sundstrom and Hammack provide free downloads and Cummings is inexpensive, so cost is not an issue.
Sundstrom is the only the one that provides instructor solution manual. I can obviously solve all the problems, but having solutions available does have me in picking problems for homework (e.g. length of solution, complications/tricky spots etc) and lecture preparation (e.g. be sure to go over certain examples before I assign a particular problem).
Sundstrom is (relatively speaking) the most 'old-fashion' of the three. There is not a lot of motivation of the materials, and the "beginning activities" at the start of each section, while helpful for lecture planning, in a way "dilute" the materials, and I worry that it might discourage students from reading the text. I also wish that (very basic) set theory were presented in chap 1, and I find it a bit strange that congruence is covered before equivalence relations (please remember that these are my first impressions).
Cummings is the opposite of Sundstrom: Very fresh and lively, and the presentation/examples are interesting. At the same time the exposition seems too chatty, and the jokes etc get tired after a short while. The problems also seem a bit more challenging that Sundstrom.
Hammack is in a way half way between the two. It does not get to proofs until page 113, which seems a bit late --- speaking as someone who has not taught a "proof class" before. Again congruence is introduced before equivalence relations. I really wish there is a solution manual.
Again, for those who have used these books: Why did you pick one over the others? Feedback from students? Advice on how to teach such a use/use the book? Order of topics? (e.g. congruences before/after equivalence relations)
Note: I am aware of prior posts such as https://math.stackexchange.com/questions/3316114/book-recommendation-for-proof and Book request: teaching proving and reasoning at an American university The posts there are either lists of books and/or recommendation for a specific book. What I am looking for are comments and comparison about the three specific ones listed above. THANKS!