Algebra And Number Theory

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Algebra and Number Theory

Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Algebra and Number Theory Book PDF

Author : Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Publisher : John Wiley & Sons
Page : 544 pages
File Size : 55,8 Mb
Release : 2011-07-15
Category : Mathematics
ISBN : 0470640537

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Algebra and Number Theory by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin Pdf

Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.

A Brief Guide to Algebraic Number Theory

H. P. F. Swinnerton-Dyer
A Brief Guide to Algebraic Number Theory Book PDF

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 44,5 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Algebraic Number Theory

Edwin Weiss
Algebraic Number Theory Book PDF

Author : Edwin Weiss
Publisher : Courier Corporation
Page : 308 pages
File Size : 48,7 Mb
Release : 2012-01-27
Category : Mathematics
ISBN : 9780486154367

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Algebraic Number Theory by Edwin Weiss Pdf

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.

Lectures on the Theory of Algebraic Numbers

E. T. Hecke
Lectures on the Theory of Algebraic Numbers Book PDF

Author : E. T. Hecke
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 40,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475740929

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Lectures on the Theory of Algebraic Numbers by E. T. Hecke Pdf

. . . 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.

Algebraic Number Theory and Fermat's Last Theorem

Ian Stewart,David Tall
Algebraic Number Theory and Fermat s Last Theorem Book PDF

Author : Ian Stewart,David Tall
Publisher : CRC Press
Page : 334 pages
File Size : 52,8 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9781439864081

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Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart,David Tall Pdf

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

Algebraic Number Theory

Frazer Jarvis
Algebraic Number Theory Book PDF

Author : Frazer Jarvis
Publisher : Springer
Page : 298 pages
File Size : 50,9 Mb
Release : 2014-06-23
Category : Mathematics
ISBN : 9783319075457

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Algebraic Number Theory by Frazer Jarvis Pdf

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.

A Course in Computational Algebraic Number Theory

Henri Cohen
A Course in Computational Algebraic Number Theory Book PDF

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 51,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459

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A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

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.

Algebraic Number Theory

Ian Stewart
Algebraic Number Theory Book PDF

Author : Ian Stewart
Publisher : Springer
Page : 257 pages
File Size : 55,6 Mb
Release : 1979-05-31
Category : Science
ISBN : 0412138409

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Algebraic Number Theory by Ian Stewart Pdf

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.

Problems in Algebraic Number Theory

M. Ram Murty,Jody (Indigo) Esmonde
Problems in Algebraic Number Theory Book PDF

Author : M. Ram Murty,Jody (Indigo) Esmonde
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 51,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387269986

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Problems in Algebraic Number Theory by M. Ram Murty,Jody (Indigo) Esmonde Pdf

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

Geometric Methods in Algebra and Number Theory

Fedor Bogomolov,Yuri Tschinkel
Geometric Methods in Algebra and Number Theory Book PDF

Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 41,5 Mb
Release : 2006-06-22
Category : Mathematics
ISBN : 9780817644178

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Geometric Methods in Algebra and Number Theory by Fedor Bogomolov,Yuri Tschinkel Pdf

* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

Algebraic Number Theory

H. Koch
Algebraic Number Theory Book PDF

Author : H. Koch
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580956

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Algebraic Number Theory by H. Koch Pdf

From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

Algebraic Number Theory

Serge Lang
Algebraic Number Theory Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 53,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461208532

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Algebraic Number Theory by Serge Lang Pdf

This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—-MATHEMATICAL REVIEWS

Computational Algebra and Number Theory

Wieb Bosma,Alf van der Poorten
Computational Algebra and Number Theory Book PDF

Author : Wieb Bosma,Alf van der Poorten
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 49,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401711081

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Computational Algebra and Number Theory by Wieb Bosma,Alf van der Poorten Pdf

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.

A Computational Introduction to Number Theory and Algebra

Victor Shoup
A Computational Introduction to Number Theory and Algebra Book PDF

Author : Victor Shoup
Publisher : Cambridge University Press
Page : 544 pages
File Size : 53,5 Mb
Release : 2005-04-28
Category : Computers
ISBN : 0521851548

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A Computational Introduction to Number Theory and Algebra by Victor Shoup Pdf

This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.

Algebraic Number Theory

Jürgen Neukirch
Algebraic Number Theory Book PDF

Author : Jürgen Neukirch
Publisher : Springer
Page : 0 pages
File Size : 47,8 Mb
Release : 2010-12-15
Category : Mathematics
ISBN : 3642084737

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Algebraic Number Theory by Jürgen Neukirch Pdf

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.