Logic is the ability to use reason and personal understanding to solve a problem. I'm not sure how it could be mixed with math, but by definition, it could be considered a branch of any type of knowledge. I think it's psychology more then anything...but that's just me.

Pure logic sort of straddles philosophy and math: its mathematical in being symbol-manipulation and functional, but its philosophical in being intertwined with wisdom. I've seen it show up in both sides of the course catalog at universities. (But I still have coffee yet! So it must be time for a long-winded ramble on whatever thought just hit my head...) In common usage, logic is often confused with common sense. The Intelligent Design view is an example: e.g. "life is very complex, complex things have designers, therefore life has a designer". This seems like logic, and in a very simplistic way, it is. But its really much more in the common-sense domain, in that its a conclusion drawn from aggregated experience at "human scale" activities. Common sense is a very efficient -- but not very precise -- kind of knowledge that allows us to operate effectively in everyday life, but it breaks down severely when we try to extrapolate from that to areas in which we have no experience. This is why we can't "get" relativity or quantum mechanics easily: we have no experience on those scales for common sense to work with. Logic has a similar shortcoming: its really only valid within a "local context" which specifies the rules -- e.g. if A is B, then B is A, A is always A and never not-A, etc. These rules are hard-and fast distinctions drawn in pure abstraction, and thus don't map to anything in the real world very well. They draw sharp boundaries where in reality all is interdependent, interconnected, and impermanent. Smart people sense -- at some level -- the shortcomings of both logic and common sense, and this makes us nervous. On what can we base knowledge? How can we absolutely know anything if these two pillars of knowledge are shaky outside of their local contexts? This craving for absolute, unshakeable knowledge is what turns our minds around in circles repeatedly, producing philosophical and religious schools that battle it out for dominance. It turns out that the only way to resolve this anxiety is to back away from reliance on ideas and concepts, and reconnect with the most basic, irrefutable, and immediate knowledge we have: direct, in-the-moment experience. This is one of the reasons meditation works: by reconnecting with Reality in its most direct and accessible form, we begin to resolve the psychological "addiction" to conceptual certainty. As the mind loosens its grip on these crutches, it begins to become more free, and more able to integrate its various sources of knowledge into a coherent whole which is undistorted by ego needs. Now there's a speech you didn't ask for today! :-)