Algebra: The Basics of Mathematics

Algebra is one of the major areas of study in mathematics, along with geometry, number theory and analysis. Algebra studies mathematical symbols as well as the regulations which govern their manipulation. It is also considered as the unifying thread of almost the entirety of mathematics. In terms of complexity, algebra is divided into two parts, elementary algebra and abstract algebra. Elementary algebra, which is considered to be integral to the study of mathematics, deals with the basic aspects of algebra. Polynomials and polynomial expressions are examples of subjects which are studied under elementary algebra. The abstract parts of algebra fall under abstract algebra, which is also known as modern algebra. Sets, identity elements, inverse elements and associativity are some concepts studied within abstract algebra. The objective of this book is to give a general view of the different areas of algebra. It consists of contributions made by international experts. This book will serve as a reference to a broad spectrum of readers.