Number Theory: An Introduction to Algebra

This book introduces the elements of abstract algebra (groups, rings and fields) motivated by the purpose of using it to describe the properties of integers and to prove theorems about them. Thus two purposes are fulfilled: giving good introductions to both number theory and abstract algebra. Abstract algebra is a tricky area for many students, but the use of it to explain the properties of integers makes it more accessible and prepares the student for more advanced texts. The book is an excellent guide for self-study. Everything is well motivated and presented in a very readable manner. The problems are challenging but not impossibly difficult. No answers are provided but hints are given for the more difficult ones. Although intended for undergraduates, I could see a high school course for advanced students being built around this book.