Reddit reviews Doing Mathematics: An Introduction to Proofs and Problem-Solving
We found 2 Reddit comments about Doing Mathematics: An Introduction to Proofs and Problem-Solving. Here are the top ones, ranked by their Reddit score.
Can I ask what topics it will cover? That would help in seeing what you would need to do. Set arithmetic sounds like it would be in there, along with concepts like mapping and functions. What I would suggest is is just getting a cheap intro to mathematical proofs book. You can usually find them online for cheap (or free, although my administration would never condone pirating). This is the one we used. It has a little calculus in there, but not enough to make you miss any topics that you would need to know. For this, I would suggest focusing on definitions and learning how to prove. If there is some lacking of knowledge of arithmetic that is hindering your progress, you can always use khan academy to learn it. Also, Russle's introduction to mathematical logic is very readable, and from what i remember, it did not seem to expect the reader to know much prior to reading that book.
High school performance has very, very little to do with how prepared you are for MAT157. In fact you could probably argue that no high school preparation is even needed since the course starts everything from scratch: you'll start with the basic properties of numbers, formally construct the Real Numbers, and work your way up to infinite series - the whole course is very self-contained.
SAT/AP math is gonna be different by a long shot because MAT157 is a course emphasizing proofs - there's hardly any "number crunching" anymore. If you do not have any experience with proofs (perhaps through math contests and stuff like that) then I strongly recommend taking MAT138 (if Prof. Alfonso Gracia-Saz is teaching, this will be a really great class). While you can certainly pull off a good MAT157 performance without MAT138 (I only took MAT138 in the Winter), it's going to be a steep learning curve, and trust me, you want to be very comfortable with proofs involving sets before tackling Dedekind cuts.
(Edit: As an alternative to MAT138, you could work through Galovich's An introduction to proofs and problem-solving during the summer. It's the MAT138 textbook.)