Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic (Dolciani Mathematical Expositions) (Dolciani Mathematical Expositions, 52) - Hardcover

J. L. Lehman

Hardcover

ISBN 10: 1470447371 ISBN 13: 9781470447373

Publisher: American Mathematical Society, 2019

Synopsis

Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured the author's notation makes these computations particularly illuminating. Quadratic Number Theory, with its exceptionally clear prose, hundreds of exercises, and historical motivation, would make an excellent textbook for a second undergraduate course in number theory. The clarity of the exposition would also make it a terrific choice for independent reading. It will be exceptionally useful as a fruitful launching pad for undergraduate research projects in algebraic number theory.

About this title

About the Author

J. L. Lehman: University of Mary Washington, Fredericksburg, VA

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470447371
• ISBN 13: 9781470447373
• Binding: Hardcover
• Number of pages: 394