This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic
number fields including many topics not usually covered in books at this level. Quadratic
fields offer an introduction to algebraic number theory and some of its central objects: rings
of integers the unit group ideals and the ideal class group. This textbook provides solid
grounding for further study by placing the subject within the greater context of modern
algebraic number theory. Going beyond what is usually covered at this level the book
introduces the notion of modularity in the context of quadratic reciprocity explores the close
links between number theory and geometry via Pell conics and presents applications to
Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves.
Throughout the book contains extensive historical comments numerous exercises (with
solutions) and pointers to further study. Assuming a moderate background in elementary number
theory and abstract algebra Quadratic Number Fields offers an engaging first course in
algebraic number theory suitable for upper undergraduate students.
