Lectures On The Theory Of Algebraic Numbers
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Lectures on the Theory of Algebraic Numbers
Author | : E. T. Hecke |
Publsiher | : Springer Science & Business Media |
Total Pages | : 251 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9781475740929 |
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. . . 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.
Lectures on the Theory of Algebraic Numbers
Author | : E. T. Hecke |
Publsiher | : Springer Science & Business Media |
Total Pages | : 266 |
Release | : 1981-12-04 |
Genre | : Mathematics |
ISBN | : 0387905952 |
Download Lectures on the Theory of Algebraic Numbers Book in PDF, Epub and Kindle
. . . 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.
Lectures on the Theory of the Algebraic Numbers
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Author | : Erich Hecke |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 1925 |
Genre | : Algebraic number theory |
ISBN | : OCLC:803623336 |
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Classical Theory of Algebraic Numbers
Author | : Paulo Ribenboim |
Publsiher | : Springer Science & Business Media |
Total Pages | : 676 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 9780387216904 |
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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.
Lectures on the Theory of the Algebraic Numbers
![Lectures on the Theory of the Algebraic Numbers](https://youbookinc.com/wp-content/themes/mts_schema/cover.jpg)
Author | : Erich Hecke,Earl L. Thompson |
Publsiher | : Unknown |
Total Pages | : 135 |
Release | : 1925 |
Genre | : Algebraic number theory |
ISBN | : OCLC:803623336 |
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My Numbers My Friends
Author | : Paulo Ribenboim |
Publsiher | : Springer Science & Business Media |
Total Pages | : 384 |
Release | : 2006-05-10 |
Genre | : Mathematics |
ISBN | : 9780387227542 |
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This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as Kummers work on Fermat's last theorem.
Computational Algebraic Number Theory
Author | : M.E. Pohst |
Publsiher | : Birkhäuser |
Total Pages | : 99 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9783034885898 |
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Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction • Topics from finite fields • Arithmetic and polynomials • Factorization of polynomials • Topics from the geometry of numbers • Hermite normal form • Lattices • Reduction • Enumeration of lattice points • Algebraic number fields • Introduction • Basic Arithmetic • Computation of an integral basis • Integral closure • Round-Two-Method • Round-Four-Method • Computation of the unit group • Dirichlet's unit theorem and a regulator bound • Two methods for computing r independent units • Fundamental unit computation • Computation of the class group • Ideals and class number • A method for computing the class group • Appendix • The number field sieve • KANT • References • Index
Algebraic Number Theory and Fermat s Last Theorem
Author | : Ian Stewart,David Tall |
Publsiher | : CRC Press |
Total Pages | : 334 |
Release | : 2001-12-12 |
Genre | : Mathematics |
ISBN | : 9781439864081 |
Download Algebraic Number Theory and Fermat s Last Theorem Book in PDF, Epub and Kindle
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