• Mathematics

Disquisitiones Arithmeticae


Author: Carl Friedrich Gauss,William C. Waterhouse
Publisher: Springer
ISBN: 1493975609
Category: Mathematics
Page: 472
View: 653
Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .

    • Mathematics

Disquisitiones Arithmeticae


Author: Carl F. Gauss
Publisher: Springer
ISBN: 0387962549
Category: Mathematics
Page: 472
View: 9776

    • Mathematics

Disquisitiones Arithmeticae


Author: Carl Friedrich Gauss
Publisher: New Haven : Yale University Press
ISBN: 9780300094732
Category: Mathematics
Page: 472
View: 8500
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 the greatest mathematical treatises of all fields and periods. . . . The appearance of an English version of this classic is most welcome."--Asger Aaboe.

    • Mathematics

The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae


Author: Catherine Goldstein,Norbert Schappacher,Joachim Schwermer
Publisher: Springer Science & Business Media
ISBN: 3540347208
Category: Mathematics
Page: 578
View: 1869
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.

    • Number theory

Disquisitiones arithmeticae


Author: Carl Friedrich Gauss
Publisher: N.A
ISBN: N.A
Category: Number theory
Page: 668
View: 3547

    • Mathematics

Lectures on Number Theory


Author: Peter Gustav Lejeune Dirichlet,Richard Dedekind
Publisher: American Mathematical Soc.
ISBN: 0821820176
Category: Mathematics
Page: 275
View: 4532
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.)

    • Mathematics

Introduction to Classical Mathematics I

From the quadratic reciprocity law to the uniformization theorem. 1
Author: Helmut Koch
Publisher: Springer Science & Business Media
ISBN: 9780792312314
Category: Mathematics
Page: 453
View: 5087
6Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the human mce. It has put common sense back je n'y serais point alle.' Jules Verne where it belongs, on the topmost shelf nCllt to the dusty canister labelled 'discarded non­ sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com­ puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

    • Language Arts & Disciplines

Gauss

A Biographical Study
Author: W. K. Bühler
Publisher: Springer Science & Business Media
ISBN: 364249207X
Category: Language Arts & Disciplines
Page: 208
View: 4329
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.

    • Mathematics

Basic Number Theory.


Author: Andre Weil
Publisher: Springer Science & Business Media
ISBN: 3662059789
Category: Mathematics
Page: 315
View: 5590

    • Fiction

Measuring the World

A Novel
Author: Daniel Kehlmann
Publisher: Vintage
ISBN: 9780307496751
Category: Fiction
Page: 272
View: 9948
Measuring the World marks the debut of a glorious new talent on the international scene. Young Austrian writer Daniel Kehlmann’s brilliant comic novel revolves around the meeting of two colossal geniuses of the Enlightenment. Late in the eighteenth century, two young Germans set out to measure the world. One of them, the aristocratic naturalist Alexander von Humboldt, negotiates jungles, voyages down the Orinoco River, tastes poisons, climbs the highest mountain known to man, counts head lice, and explores and measures every cave and hill he comes across. The other, the reclusive and barely socialized mathematician Carl Friedrich Gauss, can prove that space is curved without leaving his home. Terrifyingly famous and wildly eccentric, these two polar opposites finally meet in Berlin in 1828, and are immediately embroiled in the turmoil of the post-Napolean world. From the Trade Paperback edition.

    • Mathematics

Reciprocity Laws

From Euler to Eisenstein
Author: Franz Lemmermeyer
Publisher: Springer Science & Business Media
ISBN: 3662128934
Category: Mathematics
Page: 492
View: 4451
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.

    • Mathematics

Galois Theory

Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,
Author: Emil Artin
Publisher: Courier Corporation
ISBN: 048615825X
Category: Mathematics
Page: 86
View: 3639
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.

Disquisitiones Arithmeticae


Author: Carolo Friderico Gauss
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 1958



    • Mathematics

Number Theory

An approach through history From Hammurapi to Legendre
Author: André Weil
Publisher: Springer Science & Business Media
ISBN: 0817645713
Category: Mathematics
Page: 377
View: 2122
This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number theory: Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work.


    • Mathematics

Beautiful, Simple, Exact, Crazy

Mathematics in the Real World
Author: Apoorva Khare,Anna Lachowska
Publisher: Yale University Press
ISBN: 0300190891
Category: Mathematics
Page: 480
View: 8125
In this vibrant work, which is ideal for both teaching and learning, Apoorva Khare and Anna Lachowska explain the mathematics essential for understanding and appreciating our quantitative world. They show with examples that mathematics is a key tool in the creation and appreciation of art, music, and literature, not just science and technology. The book covers basic mathematical topics from logarithms to statistics, but the authors eschew mundane finance and probability problems. Instead, they explain how modular arithmetic helps keep our online transactions safe, how logarithms justify the twelve-tone scale commonly used in music, and how transmissions by deep space probes are similar to knights serving as messengers for their traveling prince. Ideal for coursework in introductory mathematics and requiring no knowledge of calculus, Khare and Lachowska s enlightening mathematics tour will appeal to a wide audience."

    • Mathematics

Higher Arithmetic

An Algorithmic Introduction to Number Theory
Author: Harold M. Edwards
Publisher: American Mathematical Soc.
ISBN: 9780821844397
Category: Mathematics
Page: 210
View: 8072
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.