In class on Wednesday I mentioned the following book
It is a short, well written presentation of SOME of the topics we are considering in this course. I highly recommend it if you feel like you need some extra reading material.
A few years ago I wrote up some notes on logic and set theory for my analysis course. Those notes develop the topics we have discussed so far in a somewhat more formal fashion. They may be useful to you or they may not be. Use them if they are useful!
If you are interested in delving much deeper into the mathematical theory of logic and mathematical argument, I recommend the text
It is not a book to help you with this course! Instead it is something for you to look at it in case you are interested in seeing where all this can go.