Modern Algebra

Modern AlgebraModern algebra provides important foundational applications to other branches of mathematics such as analysis and number theory. This book, based upon nearly a decade of independent study outside the classroom, is a detailed and thorough introduction to the subject. The work begins with a review of preliminary definitions and facts of sets, relations and maps, and then leads the reader through group theory, ring theory, linear algebra and field

Modern algebra provides important foundational applications to other branches of mathematics such as analysis and number theory. This book, based upon nearly a decade of independent study outside the classroom, is a detailed and thorough introduction to the subject. The work begins with a review of preliminary definitions and facts of sets, relations and maps, and then leads the reader through group theory, ring theory, linear algebra and field theory. Throughout this development, the topics are presented with an emphasis on theory over application. The reader is assumed to have no previous knowledge of modern algebra. Some experience with logic as used in mathematical proofs such as induction and contraposition will be helpful. The book is not intended as a textbook and is suitable for someone pursuing mathematics as a hobby outside the classroom.