Quadratic Number Fields
Description
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.
Reviews / Votes
"The book is very nicely written and the original style and choices of the topics make it agreeable reading, and might well complement and motivate the study of other classical introductions to the theory of more general number fields." (Alessandro Cobbe, zbMATH 1498.11003, 2022)"The book is very nicely written and the original style and choices of the topics make it agreeable reading, and might well complement and motivate the study of other classical introductions to the theory of more general number fields." (Alessandro Cobbe, zbMATH 1498.11003, 2022)
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Franz Lemmermeyer has worked in algebraic number theory and has published several books on the history of number theory, in particular on reciprocity laws.