ABSTRACT ALGEBRA
Abstract algebra Main articles: Abstract algebra and Algebraic structure Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts. Here are the listed fundamental concepts in abstract algebra. Sets : Rather than just considering the different types of numbers , abstract algebra deals with the more general concept of sets : collections of objects called elements . All collections of the familiar types of numbers are sets. Other examples of sets include the set of all two-by-two matrices , the set of all second-degree polynomials ( ax 2 + bx + c ), the set of all two dimensional vectors of a plane, and the various finite groups such as the cyclic groups , which are the groups of integers modulo n . Set theory is a branch of logic and not technically a bra...