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Author: Peter Gustav Lejeune Dirichlet
Publisher: Cambridge University Press
ISBN: 1108050395
Category : Mathematics
Languages : en
Pages : 651
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Book Description
The third edition (1879) of Dirichlet's posthumously published 1856-7 lectures on number theory includes several famous proofs.
Author: Peter Gustav Lejeune Dirichlet
Publisher: Cambridge University Press
ISBN: 1108050395
Category : Mathematics
Languages : en
Pages : 651
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Book Description
The third edition (1879) of Dirichlet's posthumously published 1856-7 lectures on number theory includes several famous proofs.
Author: Franz Lemmermeyer
Publisher: Springer Science & Business Media
ISBN: 3662128934
Category : Mathematics
Languages : en
Pages : 503
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Book Description
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.
Author: E. T. Hecke
Publisher: Springer Science & Business Media
ISBN: 1475740921
Category : Mathematics
Languages : en
Pages : 251
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Book Description
. . . 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.
Author: John HENRY WILKINSON
Publisher: Springer
ISBN: 3662397781
Category : Mathematics
Languages : en
Pages : 450
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Book Description
Author: William J. LeVeque
Publisher: Courier Corporation
ISBN: 0486152081
Category : Mathematics
Languages : en
Pages : 496
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Book Description
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.
Author: Ralf Krömer
Publisher: Springer Nature
ISBN: 3031597974
Category : Electronic books
Languages : en
Pages : 962
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Book Description
This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.
Author: Catherine Goldstein
Publisher: Springer Science & Business Media
ISBN: 3540347208
Category : Mathematics
Languages : en
Pages : 579
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Book Description
Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.
Author: Sir Norman Lockyer
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 1166
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Book Description
Author: Maria Luisa Dalla Chiara
Publisher: Springer Science & Business Media
ISBN: 9400989377
Category : Science
Languages : en
Pages : 523
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Book Description
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.
Author: L. Rédei
Publisher: Elsevier
ISBN: 1483222640
Category : Mathematics
Languages : en
Pages : 843
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Book Description
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
