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 Proofs (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 like to get inputs and comments from those who have used/are familiar with these specific books.
Note: I am aware of prior posts such as Book recommendation for proof? and https://matheducators.stackexchange.com/questions/13034/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, especially from those who have taught such classes using these specific books. THANKS!
EDIT: I was asked to clarify what information I am looking for, so here it is: Based on quick peeks at the three books, here are my first impressions:
Sundstrom and Hammack provide free downloads and Cummings is in-expensive, 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.
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 sections, while helpful for lecture planning, in a way "dilute" the materials, and I worry that it might makes it harders for students to pick out information they need. I also wish that (very basic) set theory were presented in chap 1, and I find it a bit strange that congruence got covered before equivalence relations. (please remember that these are my first impressions)
Cummings is the opposite of that: Very fresh and lively, and the presentation/examples are interesting. At the same time the exposition seem 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.
These are my first impressions, not criticisms. 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?
Thanks!
