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Author : Legh Wilber Reid
Publisher :
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.F/5 ( download)
Download or read book The Elements of the Theory of Algebraic Numbers written by Legh Wilber Reid and published by . This book was released on 1910 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Helmut Koch
Publisher : American Mathematical Soc.
ISBN 13 : 9780821820544
Total Pages : 390 pages
Book Rating : 4.8/5 (25 download)
Download or read book Number Theory written by Helmut Koch and published by American Mathematical Soc.. This book was released on 2000 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.
Author : David Hilbert
Publisher : Springer Science & Business Media
ISBN 13 : 3662035456
Total Pages : 360 pages
Book Rating : 4.6/5 (62 download)
Download or read book The Theory of Algebraic Number Fields written by David Hilbert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Author : George Abram Miller
Publisher :
ISBN 13 :
Total Pages : 330 pages
Book Rating : 4.A/5 ( download)
Download or read book Historical Introduction to Mathematical Literature written by George Abram Miller and published by . This book was released on 1916 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pratt Institute. Free Library
Publisher :
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.:/5 (31 download)
Download or read book Bulletin of the Pratt Institute Free Library written by Pratt Institute. Free Library and published by . This book was released on 1910 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Legh W. Reid
Publisher :
ISBN 13 :
Total Pages : 454 pages
Book Rating : 4.:/5 (633 download)
Download or read book The elements of the theory of algebraic numbers written by Legh W. Reid and published by . This book was released on 1946 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 720 pages
Book Rating : 4.:/5 (319 download)
Download or read book The American Mathematical Monthly written by and published by . This book was released on 1908 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 592 pages
Book Rating : 4.0/5 ( download)
Download or read book Bulletin (new Series) of the American Mathematical Society written by and published by . This book was released on 1911 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 622 pages
Book Rating : 4.A/5 ( download)
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1911 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 668 pages
Book Rating : 4.:/5 (334 download)
Download or read book Bulletin ... written by and published by . This book was released on 1914 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joan Roselló
Publisher : Cambridge Scholars Publishing
ISBN 13 : 152752762X
Total Pages : 295 pages
Book Rating : 4.5/5 (275 download)
Download or read book Hilbert, Göttingen and the Development of Modern Mathematics written by Joan Roselló and published by Cambridge Scholars Publishing. This book was released on 2019-02-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. In doing so, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program. The book also discusses the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics. In addition, it considers the famous list of Mathematical Problems presented in Paris in 1900, the mathematical tradition of the University of Göttingen, the great debate on the foundations of mathematics in the twenties between formalists and intuitionists, and, finally, Hilbert’s work on the theory of relativity and the foundations of quantum mechanics. The book will primarily appeal to an academic audience, although it will also be of interest to general-interest science readers.
Author : Jeremy Gray
Publisher : Springer
ISBN 13 : 3319947737
Total Pages : 412 pages
Book Rating : 4.3/5 (199 download)
Download or read book A History of Abstract Algebra written by Jeremy Gray and published by Springer. This book was released on 2018-08-07 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
Author : University of Aberdeen. Library
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.A/5 ( download)
Download or read book Bulletin written by University of Aberdeen. Library and published by . This book was released on 1917 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : University of St. Andrews. Library
Publisher :
ISBN 13 :
Total Pages : 646 pages
Book Rating : 4.:/5 (31 download)
Download or read book Bulletin ... written by University of St. Andrews. Library and published by . This book was released on 1914 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : University of St. Andrews
Publisher :
ISBN 13 :
Total Pages : 642 pages
Book Rating : 4.:/5 (891 download)
Download or read book Library Bulletin of the University of St. Andrews written by University of St. Andrews and published by . This book was released on 1914 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3662029456
Total Pages : 556 pages
Book Rating : 4.6/5 (62 download)
Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : University of St. Andrews. Library
Publisher :
ISBN 13 :
Total Pages : 664 pages
Book Rating : 4.:/5 (3 download)
Download or read book Library Bulletin of the University of Saint Andrews written by University of St. Andrews. Library and published by . This book was released on 1914 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:
