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Introduction to Modern Number Theory

BuchGebunden
514 Seiten
Englisch
Springererschienen am23.05.20052nd ed.
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory.mehr
Verfügbare Formate
BuchKartoniert, Paperback
EUR181,89
BuchGebunden
EUR181,89
E-BookPDF1 - PDF WatermarkE-Book
EUR171,19

Produkt

Klappentext"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory.
Zusammenfassung
Covers the most recent results around Fermat's Theorem (Andrew Wiles) and the Langlands Conjecture (Lafforgue)

Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-3-540-20364-3
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2005
Erscheinungsdatum23.05.2005
Auflage2nd ed.
ReiheEncyclopaedia of Mathematical Sciences
Seiten514 Seiten
SpracheEnglisch
Gewicht976 g
IllustrationenXVI, 514 p.
Artikel-Nr.10604638

Inhalt/Kritik

Inhaltsverzeichnis
Problems and Tricks.- Number Theory.- Some Applications of Elementary Number Theory.- Ideas and Theories.- Induction and Recursion.- Arithmetic of algebraic numbers.- Arithmetic of algebraic varieties.- Zeta Functions and Modular Forms.- Fermat´s Last Theorem and Families of Modular Forms.- Analogies and Visions.- Introductory survey to part III: motivations and description.- Arakelov Geometry and Noncommutative Geometry (d´après C. Consani and M. Marcolli, [CM]).mehr
Kritik
From the reviews of the second edition:

"Here is a welcome update to Number theory I. Introduction to number theory by the same authors ... . the book now brings the reader up to date with some of the latest results in the field. ... The book is generally well-written and should be of interest to both the general, non-specialist reader of Number Theory as well as established researchers who are seeking an overview of some of the latest developments in the field."

Philip Maynard, The Mathematical Gazette, Vol. 90 (519), 2006

[...] the first edition was a very good book; this edition is even better.

[...] Embedded in the text are a lot of interesting ideas, insights, and clues to how the authors think about the subject. [...]

Things get more interesting in Part II (by far the largest of the tree parts)[...] This part of the book covers such things as approaches through logic, algebraic number theory, arithmetic of algebraic varieties, zeta functions, and modular forms, followed by an extensive (50+ pages ) account of Wiles' proof of Fermat's Last Theorem. This is a valuable addition, new in this edition, and serves as a vivid example of the power of the "ideas and theories" that dominate this part of the book.

Also new and very interesting is Part III, entitled "Analogies and Visions,"

[...] The best surveys of mathematics are those written by deeply insightful mathematicians who are not afraid to infuse their ideas and insights into their outline of subject. This is what we have here, and the result is an essential book. I only wish the price were lower so that I could encourage my students buy themselves a copy. Maybe I'll do that anyway.

Fernado Q. Gouvêa, on 09/10/2005

"This book is a revised and updated version of the first English translation. ... Overall, the book is very well written, and has an impressive reference list. It is an excellent resource for those who are looking for both deep and wide understanding of number theory." (Alexander A. Borisov, Mathematical Reviews, Issue 2006 j)

"This edition feels altogether different from the earlier one ... . There is much new and more in this edition than in the 1995 edition: namely, one hundred and fifty extra pages. ... For my part, I come to praise this fine volume. This book is a highly instructive read with the usual reminder that there lots of facts one does not know ... . the quality, knowledge, and expertise of the authors shines through. ... The present volume is almost startlingly up-to-date ... ." (Alf van der Poorten, Gazette of the Australian Mathematical Society, Vol. 34 (1), 2007)mehr

Schlagworte