Reciprocity Laws
Reciprocity Laws

Author: Franz Lemmermeyer

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 503

ISBN-13: 3662128934

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This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

Lectures on the Theory of Algebraic Numbers
Lectures on the Theory of Algebraic Numbers

Author: E. T. Hecke

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 251

ISBN-13: 1475740921

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. . . 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.

Advanced Number Theory
Advanced Number Theory

Author: Harvey Cohn

Publisher: Courier Corporation

Published: 2012-05-04

Total Pages: 289

ISBN-13: 0486149242

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Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.

History and Philosophy of Modern Mathematics
History and Philosophy of Modern Mathematics

Author: William Aspray

Publisher: U of Minnesota Press

Published: 1988

Total Pages: 396

ISBN-13: 0816615675

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History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

Italian Studies in the Philosophy of Science
Italian Studies in the Philosophy of Science

Author: Maria Luisa Dalla Chiara

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 523

ISBN-13: 9400989377

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The impressive record of Italian philosophical research since the end of Fascism thirty-two years ago is shown in many fields: esthetics, social and" personal ethics, history and sociology of philosophy, and magnificently, perhaps above all, in logic, foundations of mathematics and the philosophY, methodology, and intellectual history ofthe empirical sciences. To our pleasure, Maria Luisa Dalla Chiara of the University of Florence gladly agreed to assemble a 'sampler' of recent Italian logical and analytical work on the philosophical foundations of mathematics and physics, along with a number of historical studies of epistemological and mathematical concepts. The twenty-five essays that form this volume will, we expect, encourage English-reading philosophers and scientists to seek further works by these authors and by their teachers, colleagues, and students; and, we hope, to look for those other Italian currents of thought in the philosophy of science for which points of departure are not wholly analytic, and which also deserve study and recognition in the world wide philosophical community. Of course, Italy has long been related to that world community in scien titlc matters.

Topics in Number Theory, Volumes I and II
Topics in Number Theory, Volumes I and II

Author: William J. LeVeque

Publisher: Courier Corporation

Published: 2012-06-22

Total Pages: 496

ISBN-13: 0486152081

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Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 edition.

Algebra
Algebra

Author: L. Rédei

Publisher: Elsevier

Published: 2014-07-21

Total Pages: 843

ISBN-13: 1483222640

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Compared with the original German edition this volume contains the results of more recent research which have to some extent originated from problems raised in the previous German edition. Moreover, many minor and some important modifications have been carried out. For example paragraphs 2 — 5 were amended and their order changed. On the advice of G. Pickert, paragraph 7 has been thoroughly revised. Many improvements originate from H. J. Weinert who, by enlisting the services of a working team of the Teachers' Training College of Potsdam, has subjected large parts of this book to an exact and constructive review. This applies particularly to paragraphs 9, 50, 51, 60, 63, 66, 79, 92, 94, 97 and 100 and to the exercises. In this connection paragraphs 64 and 79 have had to be partly rewritten in consequence of the correction

Elementary and Analytic Theory of Algebraic Numbers
Elementary and Analytic Theory of Algebraic Numbers

Author: Wladyslaw Narkiewicz

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 712

ISBN-13: 3662070014

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This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.