A Course In Algebraic Number Theory
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Author | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 556 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662029456 |
Download A Course in Computational Algebraic Number Theory Book in PDF, Epub and Kindle
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Author | : Edwin Weiss |
Publisher | : Courier Corporation |
Total Pages | : 308 |
Release | : 2012-01-27 |
Genre | : Mathematics |
ISBN | : 048615436X |
Download Algebraic Number Theory Book in PDF, Epub and Kindle
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 | : Robert B. Ash |
Publisher | : Courier Corporation |
Total Pages | : 130 |
Release | : 2010-01-01 |
Genre | : Mathematics |
ISBN | : 0486477541 |
Download A Course in Algebraic Number Theory Book in PDF, Epub and Kindle
This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.
Author | : Harry Pollard |
Publisher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 1975-12-31 |
Genre | : Algebraic number theory |
ISBN | : 1614440093 |
Download The Theory of Algebraic Numbers: Second Edition Book in PDF, Epub and Kindle
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 | : M. Ram Murty |
Publisher | : Springer Science & Business Media |
Total Pages | : 354 |
Release | : 2005-09-28 |
Genre | : Mathematics |
ISBN | : 0387269983 |
Download Problems in Algebraic Number Theory Book in PDF, Epub and Kindle
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 | : Paul Pollack |
Publisher | : American Mathematical Soc. |
Total Pages | : 329 |
Release | : 2017-08-01 |
Genre | : Mathematics |
ISBN | : 1470436531 |
Download A Conversational Introduction to Algebraic Number Theory Book in PDF, Epub and Kindle
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 | : Paulo Ribenboim |
Publisher | : Springer Science & Business Media |
Total Pages | : 676 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 0387216901 |
Download Classical Theory of Algebraic Numbers Book in PDF, Epub and Kindle
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 | : H. E. Rose |
Publisher | : Oxford University Press |
Total Pages | : 420 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9780198523765 |
Download A Course in Number Theory Book in PDF, Epub and Kindle
This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.
Author | : H. P. F. Swinnerton-Dyer |
Publisher | : Cambridge University Press |
Total Pages | : 164 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 9780521004237 |
Download A Brief Guide to Algebraic Number Theory Book in PDF, Epub and Kindle
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author | : Pierre Samuel |
Publisher | : Dover Books on Mathematics |
Total Pages | : 0 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780486466668 |
Download Algebraic Theory of Numbers Book in PDF, Epub and Kindle
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.