The Theory of Algebraic Numbers: Second Edition PDF Download

Author: Harry Pollard
Publisher: American Mathematical Soc.
ISBN: 1614440093
Category : Algebraic number theory
Languages : en
Pages : 162

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Book Description
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: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
ISBN: 9780521004237
Category : Mathematics
Languages : en
Pages : 164

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

Author: Jürgen Neukirch
Publisher: Springer
ISBN: 9783642084737
Category : Mathematics
Languages : en
Pages : 0

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Book Description
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.

Author: Edwin Weiss
Publisher: Courier Corporation
ISBN: 048615436X
Category : Mathematics
Languages : en
Pages : 308

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Book Description
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: Hermann Weyl
Publisher: Princeton University Press
ISBN: 9780691059174
Category : Mathematics
Languages : en
Pages : 244

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Book Description
This work explores the fundamental concepts in arithmetic. It begins with the definitions and properties of algebraic fields. The theory of divisibility is then discussed. There follows an introduction to p-adic numbers and then culminates with an extensive examination of algebraic number fields.

Author: M. Ram Murty
Publisher: Springer Science & Business Media
ISBN: 0387269983
Category : Mathematics
Languages : en
Pages : 352

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Book Description
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: CRC Press
ISBN: 143986408X
Category : Mathematics
Languages : en
Pages : 334

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Book Description
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

Author: Paul Pollack
Publisher: American Mathematical Soc.
ISBN: 1470436531
Category : Algebraic number theory
Languages : en
Pages : 312

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Book Description
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: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486477541
Category : Mathematics
Languages : en
Pages : 130

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Book Description
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: Ian Stewart
Publisher: Springer
ISBN: 9780412138409
Category : Science
Languages : en
Pages : 257

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Book Description
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.