I am having a heck of a time Googling for this. But I want to learn the same kind of formal logic you might learn when studying for a computer science or math degree. Problem is I don't even know what I should be looking for. Prepositional logic? Boolean logic? Predicate logic? First order logic? Second order logic? Discrete mathematics? Something else?
I am just looking to get an all-around understanding of logic so I can be more literate in that area since it underlies so much else.
Are there any good resources for learning all of these things that doesn't require spending a ton of money or reading thousands of pages? Decent PDFs would be ideal if they exist.
Thank you very much in advance.
To help you decide what you want, you might try this Teach Yourself Logic Study Guide (i.e. heavily annotated reading list). Only the first few chapters will be relevant -- ignore the more advanced stuff.
An update: one of the top-recommended books, the Friendly Guide to Mathematical Logic, is now freely available as a PDF. A number of other recommendations are also freely (and officially!) available too