TITLE: Is spending a long time to understand logic very well worth it to learn math better?
QUESTION [7 upvotes]: My goal is to become a computer/electrical/mechanical engineer. To become one i have to read a lot of math based books (physics, operation research, etc). I know some real analysis, linear algebra and more already, but in college we go over topics too fast and i can't grasp everything so well. So I want to start studying math from the beginning on the side. I discovered that there exist a "foundation of mathematics" which is pretty much set theory and logic if I'm correct (plus a few more) and I was wondering how important logic is to understand more complicated topics later on (let's say, multivariable calculus, multilinear algebra, differential geometry etc). Is it worth spending a "long time" studying logic (prepositional and predicate logic), since sometimes definitions can be confusing (vacuous truths for example) or written symbolically, or it would just be a waste of time?

REPLY [4 votes]: If you want an easy overview of the foundational approach, I recommend you have a look at Halmos's classic book "Naive Set Theory". It gives a rigorous, but lightweight account of all the set theory that is needed for the vast majority of mathematics. If this doesn't satisfy your thirst for knowledge about logic and foundations, then I would recommend something like Mendelson's "Introduction to Mathematical Logic", which covers the basics of propositional and predicate logic and their most important applications. I would not recommend reading a heavyweight book like Jech's "Set Theory" unless the intricacies of set theory itself begin to turn you on.