My department is in the very early stages of developing a "bridge course" or "introduction to proofs" course, motivated by our lower-level courses not currently doing a good job of preparing our majors to go on to more advanced topics, which in this case means primarily abstract algebra and real analysis. The various service needs of those lower courses precludes making them more mathematically rigorous, so we feel the need to add something else. I know that other universities have instituted such courses, but it's not so easy to find information about them through brute force web searches. Therefore, I'm hoping to gather some information more directly. Ideally, I'd love to get some links to course syllabi and some suggestions for textbook choices, but I'd also very much welcome any other general resources concerning such courses, including any input concerning what's worked well (or what hasn't) at other universities.

I think that right now the faculty preference for such a course would be for it to focus more on getting the students practice with actual advanced material than on simply being a litany of propositional logic and proof techniques, but, again, any information about what's worked elsewhere would be a big help to us.

Thanks!

historyof these bridge courses might be of interest; I left a response here: mathoverflow.net/a/151910/22971 $\endgroup$ – Benjamin Dickman May 13 '14 at 0:46