Rings and Fields

This book aims to provide an accessible introduction to rings and fields that will give the reader an appreciation of the power of algebraic techniques to handle diverse and difficult problems. A review of the prerequisite mathematics is given at the start of the book. Rather than presenting theory in abstract terms, chapters begin by introducing a problem and then go on to develop the necessary algebraic techniques for its solution, using concrete mathematical and non-mathematical examples. Although prior knowledge of group theory is unnecessary to understand the rest of the book, for those interested there is a chapter which states the axiom for a group and proves the group theoretic results needed in Galois theory.