Self-teaching mathematics, with questionning about category theory I understand that this is a question which has been asked probably hundreds of times. I'm asking it again because I have a specific set of circumstances which could use a slightly more specific response.
Sorry if it breaks the rules or something, this is just something that would help me I think.
Basically the last math class I really took was Calculus back in High School. That was 10 years ago. I've looked at the following topics and find them interesting, but sometimes feel like I can't really get into any of them because I always feel like I'm somehow missing knowledge from another field, or something. My specific interests are the following:
-Category Theory
-abstract algebra
-Probability
-analysis 
-Chaos
-the book Concrete mathematics
I've picked up some of this stuff and find myself basically able to grasp set theory and look at the problems, however OFTEN there are concepts that come up with weird names where I feel completely lost.
Is it even possible to learn category theory without doing analysis first or having a broad knowledge of other fields of math? I just don't get how to draw this path for myself.
 A: Category theory is an abstract language involving "objects" and "arrows". There are many examples of categories, but since sets are very basic objects of mathematics, and since you have written that you have learned some set theory for yourself, I might as well mention the category of sets: Here the "objects" are sets and the "arrows" are functions between sets. So I believe it would do much good to be very familiar and more importantly very comfortable with notation such as
$f:X \rightarrow Y$
You also mentioned analysis in your question. I would like to point out that analysis might be thought of as an advanced form of calculus, and might not fit in with the rest of your interests in logic and programming. Nevertheless, if these are your interests, I would like to recommend the book Topology by Munkres. The first chapter teaches set theory and then takes you to point-set topology, which forms the foundation of analysis. I also find that it is useful for getting used to the level of abstraction used in higher level mathematics. When you are comfortable with this, a good book on category theory is Conceptual Mathematics by Lawvere. Note that point-set topology in itself is not required to start learning category theory, but the important thing is to get used to the level of abstraction. If you want you may want to try Conceptual Mathematics first and then backtrack if you find yourself having difficulty.
