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Disquisitiones Arithmeticae

Author: Carl Friedrich Gauss
Publisher: Springer
ISBN: 1493975609
Size: 73.34 MB
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Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .

The Shaping Of Arithmetic After C F Gauss S Disquisitiones Arithmeticae

Author: Catherine Goldstein
Publisher: Springer Science & Business Media
ISBN: 3540347208
Size: 39.71 MB
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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.

Disquisitiones Arithmeticae

ISBN: 9780300194258
Size: 26.43 MB
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The first translation into English of the standard work on the theory of numbers by one of the greatest masters of modern mathematical analysis, this classic was first published in 1801 in Latin. It has continued to be important to mathematicians as the source of the ideas from which number theory was developed and to students of the history of the electrical, astronomical, and engineering sciences, which were furthered by Gauss’ application of his mathematical principles to these fields. Father Clarke has achieved a sympathetic and faithful translation of this monumental work. The book is complete and unabridged, and a bibliography of the references cited by Gauss has been added by the translator."Whatever set of values is adopted,Gauss's Disquistiones Arithmeticae surely belongs among thegreatest mathematical treatises of all fields and periods. . . . The appearance of an English version of this classic is most welcome."—Asger Aaboe.

Lectures On Number Theory

Author: Peter Gustav Lejeune Dirichlet
Publisher: American Mathematical Soc.
ISBN: 0821820176
Size: 64.56 MB
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This volume is a translation of Dirichlet's Vorlesungen uber Zahlentheorie which includes nine supplements by Dedekind and an introduction by John Stillwell, who translated the volume. Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions. The book is suitable as a textbook, yet it also offers a fascinating historical perspective that links Gauss with modern number theory. The legendary story is told how Dirichlet kept a copy of Gauss's Disquisitiones Arithmeticae with him at all times and how Dirichlet strove to clarify and simplify Gauss's results. Dedekind's footnotes document what material Dirichlet took from Gauss, allowing insight into how Dirichlet transformed the ideas into essentially modern form. Also shown is how Gauss built on a long tradition in number theory--going back to Diophantus--and how it set the agenda for Dirichlet's work. This important book combines historical perspective with transcendent mathematical insight. The material is still fresh and presented in a very readable fashion. This volume is one of an informal sequence of works within the History of Mathematics series. Volumes in this subset, ``Sources'', are classical mathematical works that served as cornerstones for modern mathematical thought. (For another historical translation by Professor Stillwell, see Sources of Hyperbolic Geometry, Volume 10 in the History of Mathematics series.)

Higher Arithmetic

Author: Harold M. Edwards
Publisher: American Mathematical Soc.
ISBN: 9780821844397
Size: 34.57 MB
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Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.


Author: W. K. Bühler
Publisher: Springer Science & Business Media
ISBN: 364249207X
Size: 65.98 MB
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Procreare iucundum, sed parturire molestum. (Gauss, sec. Eisenstein) The plan of this book was first conceived eight years ago. The manuscript developed slowly through several versions until it attained its present form in 1979. It would be inappropriate to list the names of all the friends and advisors with whom I discussed my various drafts but I should like to mention the name of Mr. Gary Cornell who, besides discussing with me numerous details of the manuscript, revised it stylistically. There is much interest among mathematicians to know more about Gauss's life, and the generous help I received has certainly more to do with this than with any individual, positive or negative, aspect of my manuscript. Any mistakes, errors of judgement, or other inadequacies are, of course, the author's responsi bility. The most incisive and, in a way, easiest decisions I had to make were those of personal taste in the choice and treatment of topics. Much had to be omitted or could only be discussed in a cursory way.

Galois Theory

Author: Emil Artin
Publisher: Courier Corporation
ISBN: 048615825X
Size: 55.26 MB
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Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

Reciprocity Laws

Author: Franz Lemmermeyer
Publisher: Springer Science & Business Media
ISBN: 3662128934
Size: 60.66 MB
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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.