Algebra and Number Theory (PDF)

Explore the main algebraic structures and number systems that
play a central role across the field of mathematics

Algebra and number theory are two powerful branches of modern
mathematics at the forefront of current mathematical research, and
each plays an increasingly significant role in different branches
of mathematics, from geometry and topology to computing and
communications. Based on the authors' extensive experience within
the field, Algebra and Number Theory has an innovative
approach that integrates three disciplines--linear algebra,
abstract algebra, and number theory--into one comprehensive
and fluid presentation, facilitating a deeper understanding of the
topic and improving readers' retention of the main concepts.

The book begins with an introduction to the elements of set
theory. Next, the authors discuss matrices, determinants, and
elements of field theory, including preliminary information related
to integers and complex numbers. Subsequent chapters explore key
ideas relating to linear algebra such as vector spaces, linear
mapping, and bilinear forms. The book explores the development of
the main ideas of algebraic structures and concludes with
applications of algebraic ideas to number theory.

Interesting applications are provided throughout to demonstrate
the relevance of the discussed concepts. In addition, chapter
exercises allow readers to test their comprehension of the
presented material.

Algebra and Number Theory is an excellent book for
courses on linear algebra, abstract algebra, and number theory at
the upper-undergraduate level. It is also a valuable reference for
researchers working in different fields of mathematics, computer
science, and engineering as well as for individuals preparing for a
career in mathematics education.