Abstract mathematics

From Freepedia

Abstract mathematics, sometimes called pure mathematics, refers to mathematics qua mathematics, as contrasted to applied mathematics. The three primary branches of abstract mathematics are the study of shape, called geometry at the undergraduate level, extended to topology at the graduate level (if not sooner); the study of number, called algebra at the beginning undergraduate level, extended to abstract algebra at a more advanced level; and the study of functions, called calculus at the Freshman level and analysis at a more advanced level. Each of these branches of abstract mathematics have many sub-specialties, and there are many connections between pure mathematics and applied mathematics.