How Do Transition to Proof Textbooks Relate Logic, Proof Techniques, and Sets?

Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks connect three topics ubiquitous to such courses: logic, proof techniques, and sets. In particular, we were motivated by recent research showing that focusing on sets is propitious to novice students' ability to reason about logic and construct valid arguments. Our objectives were to (1) analyze examples of how these connections were made in relation to what is known about student thinking and learning in TTP courses and also to (2) identify situations in these texts in which there are opportunities for such connections to be made that could benefit students' learning. We focus on how logic was used to explain ideas related to sets and proof techniques, and how sets were used to explain ideas in the other domains. In addition to providing examples from our textbook sample illustrating instances in which connections were (or potentially could be made), we suggest several key recommendations TTP instructors can leverage in their unit(s) on sets.