I wish people talked about the relationship between logic and math in high school. No one told me that math is really an extension of logic until I got to college (or if they did I ignored them.) Once you realize that you realize how unimportant the application actually is and the whole subject starts to make sense (at least to me.)
This. I can't express this enough. And other thing I can't express enough is how logic is an extension of common sense. Just go and read the wikipedia articles about the Three Laws of Thought: the Law of identity, the Law of noncontradiction, the Law of the excluded middle and the Principle of Reason.
