Daniel A. Marcus: Number Fields | Taschenbuch

Cover: 9783319902326 | Number Fields | Daniel A. Marcus | Taschenbuch | Universitext | 2018

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Sprache: Englisch

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Beschreibung

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra.

Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject.

From the reviews:

¿A thoroughly delightful introduction to algebraic number theory¿ ¿ Ezra Brown in the Mathematical Reviews

¿An excellent basis for an introductory graduate course in algebraic number theory¿ ¿ Harold Edwards in the Bulletin of the American Mathematical Society

Über den Autor

Daniel A. Marcus received his PhD from Harvard University in 1972. He was a J. Willard Gibbs Instructor at Yale University from 1972 to 1974 and Professor of Mathematics at California State Polytechnic University, Pomona, from 1979 to 2004. He published research papers in the areas of graph theory, number theory and combinatorics. The present book grew out of a lecture course given by the author at Yale University.

Zusammenfassung

Contains over 300 exercises

Assumes only basic abstract algebra

Covers topics leading up to class field theory

Inhaltsverzeichnis

1: A Special Case of Fermat's Conjecture.- 2: Number Fields and Number Rings.- 3: Prime Decomposition in Number Rings.- 4: Galois Theory Applied to Prime Decomposition.- 5: The Ideal Class Group and the Unit Group.- 6: The Distribution of Ideals in a Number Ring.- 7: The Dedekind Zeta Function and the Class Number Formula.- 8: The Distribution of Primes and an Introduction to Class Field Theory.- Appendix A: Commutative Rings and Ideals.- Appendix B: Galois Theory for Subfields of C.- Appendix C: Finite Fields and Rings.- Appendix D: Two Pages of Primes.- Further Reading.- Index of Theorems.- List of Symbols.

Details

Erscheinungsjahr:	2018
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xviii 203 S.
ISBN-13:	9783319902326
ISBN-10:	3319902326
Sprache:	Englisch
Herstellernummer:	978-3-319-90232-6
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Marcus, Daniel A.
Auflage:	2nd ed. 2018
Hersteller:	Springer International Publishing Springer International Publishing AG Universitext
Maße:	235 x 155 x 13 mm
Von/Mit:	Daniel A. Marcus
Erscheinungsdatum:	23.07.2018
Gewicht:	0,347 kg

Artikel-ID: 112813872