A Course In Algebraic Number Theory PDF Download
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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 | : 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 | : 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 | : Ian Stewart |
Publisher | : Springer |
Total Pages | : 257 |
Release | : 1979-05-31 |
Genre | : Science |
ISBN | : 9780412138409 |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
The title of this book may be read in two ways. One is 'algebraic number-theory', that is, the theory of numbers viewed algebraically; the other, 'algebraic-number theory', the study of algebraic numbers. Both readings are compatible with our aims, and both are perhaps misleading. Misleading, because a proper coverage of either topic would require more space than is available, and demand more of the reader than we wish to; compatible, because our aim is to illustrate how some of the basic notions of the theory of algebraic numbers may be applied to problems in number theory. Algebra is an easy subject to compartmentalize, with topics such as 'groups', 'rings' or 'modules' being taught in comparative isolation. Many students view it this way. While it would be easy to exaggerate this tendency, it is not an especially desirable one. The leading mathematicians of the nineteenth and early twentieth centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, without ever defining an abstract vector space: nor is there anything to suggest that they suf fered thereby. This historical fact may indicate that abstrac tion is not always as necessary as one commonly imagines; on the other hand the axiomatization of mathematics has led to enormous organizational and conceptual gains.
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 | : 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.