has an introduction to proof, logic, and topics like sets and groups. Books
can prepare you for rigorous calculus texts like Spivak and Apostol.
Question 1. I've been looking at the books by Gelfand (Algebra, Trigonometry, Functions and Graphs, The Method of Coordinates). I'm not sure if they cover all of the precalculus curriculum, though.
Question 2. What would be some good calculus books other than Spivak and Apostol?