Mathematics is the body of knowledge justified by deductive reasoning about abstract structures, starting from axioms and definitions. As a Formal Science, Mathematics is not concerned with the validity of theories based on observations in the real world, but with the properties of formal systems based on definitions and rules. In a broad sense, Mathematics goes beyond the study of numbers, counting and measuring to the study of number patterns, relationships and communicating concepts. The field is classified into Pure/Theoretical Mathematics and Applied Mathematics. Pure Mathematics seeks to identify unexplained issues and resolve them while Applied Mathematics uses theories and techniques to address pertinent questions and solve practical problems. The traditional divisions of Mathematics include: Arithmetic which studies numbers, Algebra which studies structures, Geometry which studies space, Analysis which studies infinite processes (such as Calculus) and Probability Theory & Statistics which study random processes.