Algebra and Number Theory: An Integrated Approach

This book successfully blends algebra and number theory as an integrated discipline and consists of seven parts: Part 1 discusses the elements of set theory; Parts 2 and 3 address number systems; Parts 4 and 5 cover the main topics of linear algebra; Part 6 develops the main ideas of algebraic structures; and Part 7 demonstrates the applications of algebraic ideas to number theory. Based on the experience of the authors, this book was developed for one course that integrates three disciplines - linear algebra, abstract algebra, and number theory - in an effort to use time more efficiently. Many theorems in number theory have very simple proofs using algebraic tools, and most importantly, the book’s integrated approach helps to build a deeper understanding of the subject for readers as well as improve their retention of knowledge. Applications are provided at the end of each chapter to further explain the results found in the book, and exercises are also ample throughout. While the book is mathematically self-contained, readers should be comfortable with mathematical formalism and have some experience in reading and writing mathematical proofs.