Logic and Set Theory:

the branch of pure mathematics that deals with the nature and relations of sets.

Set theory is important for many areas of mathematics, including analysis, probability, and topology. You have done some set theory when you drew Venn diagrams to prove basic theorems.

Logic is very important in the foundations of computer science -- in complexity theory and in recursive function theory. A recursive function is one which is defined in terms of itself. For example, the factorial function

n! = n 4 (n -1) 4 ... 3 4 2 4 1

may be defined as

n! = n 4 (n - 1)!

Recursive functions are very important in some computer languages such as Pascal.