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Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 43,7 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author : J. S. Chahal
Publisher : Unknown
Page : 150 pages
File Size : 44,9 Mb
Release : 2003
Category : Mathematics
ISBN : CORNELL:31924104903194
Author : Harry Pollard,Harold G. Diamond
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 51,8 Mb
Release : 1975-12-31
Category : Algebraic number theory
ISBN : 9781614440093
This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Author : Paul Pollack
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 51,5 Mb
Release : 2017-08-01
Category : Algebraic number theory
ISBN : 9781470436537
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Author : Edwin Weiss
Publisher : Courier Corporation
Page : 308 pages
File Size : 50,7 Mb
Release : 2012-01-27
Category : Mathematics
ISBN : 9780486154367
Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
Author : Şaban Alaca
Publisher : Unknown
Page : 428 pages
File Size : 40,5 Mb
Release : 2004
Category : Algebraic number theory
ISBN : 1107148855
An introduction to algebraic number theory for senior undergraduates and beginning graduate students in mathematics. It includes numerous examples, and references to further reading and to biographies of mathematicians who have contributed to the development of the subject. Includes over 320 exercises, and an extensive index.
Author : Ian Stewart,David Tall
Publisher : CRC Press
Page : 334 pages
File Size : 45,6 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9781439864081
First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it
Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 40,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9780387216904
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
Author : Frazer Jarvis
Publisher : Springer
Page : 298 pages
File Size : 45,6 Mb
Release : 2014-06-23
Category : Mathematics
ISBN : 9783319075457
This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.
Author : J.S. Chahal
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 43,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489904393
This book reproduces, with minor changes, the notes prepared for a course given at Brigham Young University during the academic year 1984-1985. It is intended to be an introduction to the theory of numbers. The audience consisted largely of undergraduate students with no more background than high school mathematics. The presentation was thus kept as elementary and self-contained as possible. However, because the discussion was, generally, carried far enough to introduce the audience to some areas of current research, the book should also be useful to graduate students. The only prerequisite to reading the book is an interest in and aptitude for mathe matics. Though the topics may seem unrelated, the study of diophantine equations has been our main goal. I am indebted to several mathematicians whose published as well as unpublished work has been freely used throughout this book. In particular, the Phillips Lectures at Haverford College given by Professor John T. Tate have been an important source of material for the book. Some parts of Chapter 5 on algebraic curves are, for example, based on these lectures.
Author : M. Ram Murty,Jody (Indigo) Esmonde
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 49,8 Mb
Release : 2005-09-28
Category : Mathematics
ISBN : 9780387269986
The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
Author : Jürgen Neukirch
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 46,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662039830
This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.
Author : M. Pohst,H. Zassenhaus
Publisher : Cambridge University Press
Page : 520 pages
File Size : 41,6 Mb
Release : 1997-09-25
Category : Mathematics
ISBN : 0521596696
Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
Author : Richard A. Mollin
Publisher : CRC Press
Page : 424 pages
File Size : 50,7 Mb
Release : 2011-01-05
Category : Computers
ISBN : 9781439845998
Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.
Author : L.-K. Hua
Publisher : Springer Science & Business Media
Page : 591 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642681301
To Number Theory Translated from the Chinese by Peter Shiu With 14 Figures Springer-Verlag Berlin Heidelberg New York 1982 HuaLooKeng Institute of Mathematics Academia Sinica Beijing The People's Republic of China PeterShlu Department of Mathematics University of Technology Loughborough Leicestershire LE 11 3 TU United Kingdom ISBN -13 : 978-3-642-68132-5 e-ISBN -13 : 978-3-642-68130-1 DOl: 10.1007/978-3-642-68130-1 Library of Congress Cataloging in Publication Data. Hua, Loo-Keng, 1910 -. Introduc tion to number theory. Translation of: Shu lun tao yin. Bibliography: p. Includes index. 1. Numbers, Theory of. I. Title. QA241.H7513.5 12'.7.82-645. ISBN-13:978-3-642-68132-5 (U.S.). AACR2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustra tions, broadcasting, reproductiOli by photocopying machine or similar means, and storage in data banks. Under {sect} 54 of the German Copyright Law where copies are made for other than private use a fee is payable to "VerwertungsgeselIschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1982 Softcover reprint of the hardcover 1st edition 1982 Typesetting: Buchdruckerei Dipl.-Ing. Schwarz' Erben KG, Zwettl. 214113140-5432 I 0 Preface to the English Edition The reasons for writing this book have already been given in the preface to the original edition and it suffices to append a few more points