A Classical Introduction to Modern Number Theory
2nd Edition
Published on 1. December 2010
Book
Paperback/Softback
XIV, 394 pages
978-1-4419-3094-1 (ISBN)
Description
This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
Reviews / Votes
From the reviews of the second edition: K. Ireland and M. Rosen A Classical Introduction to Modern Number Theory "Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution." - MATHEMATICAL REVIEWS "This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. ... for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvêa, MathDL, January, 2006)More details
Product info
Previously published in hardcover
Series
Edition
2nd ed. 1990. Corr. 5th printing. Softcover version of original hardcover edition 1990
Language
English
Place of publication
New York, NY
United States
Target group
Graduate
Product notice
Paperback (trade)
Illustrations
biography
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 21 mm
Weight
615 gr
ISBN-13
978-1-4419-3094-1 (9781441930941)
DOI
10.1007/978-1-4757-2103-4
Schweitzer Classification
Other editions
Additional editions
Kenneth Ireland | Michael Rosen
A Classical Introduction to Modern Number Theory
Book
08/1998
2nd Edition
Springer
€75.92
Shipment within 5-7 days
Content
1: Unique Factorization. 2: Applications of Unique Factorization. 3: Congruence. 4: The Structure of U. 5: Quadratic Reciprocity. 6: Quadratic Gauss Sums. 7: Finite Fields. 8: Gauss and Jacobi Sums. 9: Cubic and Biquadratic Reciprocity. 10: Equations over Finite Fields. 11: The Zeta Function. 12: Algebraic Number Theory. 13: Quadratic and Cyclotomic Fields. 14: The Stickelberger Relation and the Eisenstein Reciprocity Law. 15: Bernoulli Numbers. 16: Dirichlet L-functions. 17: Diophantine Equations. 18: Elliptic Curves. 19: The Mordell-Weil Theorem. 20: New Progress in Arithmetic Geometry.