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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!

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Perhaps the book Journey into Mathematics: An Introduction to Proofs by Joseph Rotman could help. Its Table of Contents (see e.g. here) looks quite close to what is requested in the question; see also this review.

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You could try this syllabus of a course, Math 347, "Fundamental Mathematics", at Urbana-Champaign. The course is a bit controversial in the department: while the authors of the book like it, others feel that this course doesn't quite work. The detractors claim that the course lacks focus and fails as a preparation for higher level courses. There is no hard data, as far as I know, that backs either point of view --- just anecdotal evidence.

edit: Browsing in the library I have come across Fundamental mathematics by Eugene P. Northrop, first edition, September 1944, University of Chicago. The subtitle says "prepared for the general course Mathematics I in the college." I guess these kinds of courses have a long history!

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  • $\begingroup$ I taught a bridge course from this book for a few semesters. Depending on the average level of your undergraduates, you may want to "dumb it down" a little bit- the Schroeder-Bernstein theorem is not that interesting for people who don't really know what a set is for. $\endgroup$
    – Richard Rast
    Commented Jul 3, 2014 at 19:53

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