Algebraic Theory Of Numbers
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Algebraic Theory Of Numbers
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Author : Pierre Samuel
language : en
Publisher: Dover Books on Mathematics
Release Date : 2008
Algebraic Theory Of Numbers written by Pierre Samuel and has been published by Dover Books on Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.
The Theory Of Algebraic Numbers Second Edition
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Author : Harry Pollard
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31
The Theory Of Algebraic Numbers Second Edition written by Harry Pollard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-12-31 with Mathematics categories.
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.
The Theory Of Algebraic Number Fields
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Author : David Hilbert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Theory Of Algebraic Number Fields written by David Hilbert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, "The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory.
Algebraic Theory Of Numbers Am 1 Volume 1
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Author : Hermann Weyl
language : en
Publisher: Princeton University Press
Release Date : 2016-04-21
Algebraic Theory Of Numbers Am 1 Volume 1 written by Hermann Weyl and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-21 with Mathematics categories.
In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.
A Brief Guide To Algebraic Number Theory
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Author : H. P. F. Swinnerton-Dyer
language : en
Publisher: Cambridge University Press
Release Date : 2001-02-22
A Brief Guide To Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-22 with Mathematics categories.
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Algebraic Theory Of Quadratic Numbers
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Author : Mak Trifković
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-14
Algebraic Theory Of Quadratic Numbers written by Mak Trifković and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-14 with Mathematics categories.
By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory.
Classical Theory Of Algebraic Numbers
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Author : Paulo Ribenboim
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03-30
Classical Theory Of Algebraic Numbers written by Paulo Ribenboim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-30 with Mathematics categories.
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.
Algebraic Number Theory And Fermat S Last Theorem
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Author : Ian Stewart
language : en
Publisher: CRC Press
Release Date : 2001-12-12
Algebraic Number Theory And Fermat S Last Theorem written by Ian Stewart and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-12 with Mathematics categories.
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
Problems In Algebraic Number Theory
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Author : M. Ram Murty
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Problems In Algebraic Number Theory written by M. Ram Murty and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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
Lectures On The Theory Of Algebraic Numbers
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Author : E. T. Hecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Lectures On The Theory Of Algebraic Numbers written by E. T. Hecke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.