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Algebraic Theory Of Numbers Am 1 Volume 1
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Book Synopsis Algebraic Theory of Numbers. (AM-1), Volume 1 by : Hermann Weyl
Download or read book Algebraic Theory of Numbers. (AM-1), Volume 1 written by Hermann Weyl and published by . This book was released on 2016 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.
Book Synopsis Algebraic Theory of Numbers. (AM-1), Volume 1 by : Hermann Weyl
Download or read book Algebraic Theory of Numbers. (AM-1), Volume 1 written by Hermann Weyl and published by Princeton University Press. This book was released on 2016-04-21 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.
Book Synopsis Algebraic Theory of Numbers by : Hermann Weyl
Download or read book Algebraic Theory of Numbers written by Hermann Weyl and published by Princeton University Press. This book was released on 1998 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Number Theory by : A. Fröhlich
Download or read book Algebraic Number Theory written by A. Fröhlich and published by Cambridge University Press. This book was released on 1991 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical number-theoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithmetic content. It will be indispensable for all practising and would-be algebraic number theorists.
Book Synopsis Classical Theory of Algebraic Numbers by : Paulo Ribenboim
Download or read book Classical Theory of Algebraic Numbers written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Brief Guide to Algebraic Number Theory by : H. P. F. Swinnerton-Dyer
Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Book Synopsis Mathematics across the Iron Curtain by : Christopher Hollings
Download or read book Mathematics across the Iron Curtain written by Christopher Hollings and published by American Mathematical Society. This book was released on 2014-07-16 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.
Download or read book Basic Number Theory written by Andre Weil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "L.R. Shafarevich showed me the first edition [...] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH
Book Synopsis Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57 by : Richard S. Palais
Download or read book Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57 written by Richard S. Palais and published by Princeton University Press. This book was released on 2016-03-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57, will be forthcoming.
Book Synopsis Biographical Memoirs by : National Academy of Sciences
Download or read book Biographical Memoirs written by National Academy of Sciences and published by National Academies Press. This book was released on 1994-02-01 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biographic Memoirs: Volume 63 contains the biographies of deceased members of the National Academy of Sciences and bibliographies of their published works. Each biographical essay was written by a member of the Academy familiar with the professional career of the deceased. For historical and bibliographical purposes, these volumes are worth returning to time and again.
Book Synopsis Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic by : J. L. Lehman
Download or read book Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic written by J. L. Lehman and published by American Mathematical Soc.. This book was released on 2019-02-13 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured—the author's notation makes these computations particularly illuminating. Quadratic Number Theory, with its exceptionally clear prose, hundreds of exercises, and historical motivation, would make an excellent textbook for a second undergraduate course in number theory. The clarity of the exposition would also make it a terrific choice for independent reading. It will be exceptionally useful as a fruitful launching pad for undergraduate research projects in algebraic number theory.
Book Synopsis Rational Number Theory in the 20th Century by : Władysław Narkiewicz
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Book Synopsis Number Theory and Its History by : Oystein Ore
Download or read book Number Theory and Its History written by Oystein Ore and published by Courier Corporation. This book was released on 2012-07-06 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Book Synopsis Algebraic Number Theory by : Richard A. Mollin
Download or read book Algebraic Number Theory written by Richard A. Mollin and published by CRC Press. This book was released on 2011-01-05 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.
Book Synopsis Algebraic Number Theory by : Richard A. Mollin
Download or read book Algebraic Number Theory written by Richard A. Mollin and published by CRC Press. This book was released on 1999-03-16 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin's popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory. In this way Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written for upper-level undergraduate and graduate courses in algebraic number theory, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality. It easily serves as the basis for a range of courses, from bare-bones algebraic number theory, to a course rich with cryptography applications, to a course using the basic theory to prove Fermat's Last Theorem for regular primes. Its offering of over 430 exercises with odd-numbered solutions provided in the back of the book and, even-numbered solutions available a separate manual makes this the ideal text for both students and instructors.
Book Synopsis Algebraic Theory of Numbers by : Hermann Weyl
Download or read book Algebraic Theory of Numbers written by Hermann Weyl and published by . This book was released on 1959 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introductory Algebraic Number Theory by : Şaban Alaca
Download or read book Introductory Algebraic Number Theory written by Şaban Alaca and published by . This book was released on 2004 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to algebraic number theory for senior undergraduates and beginning graduate students in mathematics. It includes numerous examples, and references to further reading and to biographies of mathematicians who have contributed to the development of the subject. Includes over 320 exercises, and an extensive index.
