Originally Posted by

**ThePerfectHacker** Often mathematics can be usually broken up into three categories: algebraic, topological, and analytic. If you have a book on Complex Analysis it will first talk about the algebraic properties of the complex numbers, then talk about the topological properties of the complex numbers, and then finally the rest of the book shall be devoted to the analytic properties of the complex numbers. The word 'algebraic' means to be related to algebra, algebra here is not high-school algebra, but something that is sometimes referred to as abstract algebra. All properties of the complex numbers that are based on abstract algebra are therefore referred to as algebraic. While analysis (like calculus) is concerned with studying limits, derivatives, and integration and other properties. Anything that falls under this category is called analytic.