When I was an undergraduate, we had an entire class dedicated to making the transition from calculus-type mathematics to abstract upperclass-level mathematics. We learned basic logic and set notation and manipulation, proof structures, and induction, proving simple number theory results that didn’t require additional new concepts beyond induction. I got to teach such a course once, at the University of Florida. At Dartmouth, I taught two courses that had that as a secondary goal: linear algebra, for math majors, and discrete math for computer science, for CS majors. In the latter class there was a lot more space to fit that conceptual material in. Linear algebra, however, is packed with, well, linear algebra, and in fact I think I only discussed induction in one of the iterations I taught. I did need to teach induction to my computability theory students, however, so my handout on that topic continued to see use.

Here are those handouts for your potential use:

• Proof-writing tips and notes on mathematical definitions, aimed at my linear algebra students but not subject-specific.
• An explanation, with examples and exercises, of mathematical induction.