Disquisitiones Arithmeticae

Disquisitiones Arithmeticae
Author :
Publisher : Springer
Total Pages : 491
Release :
ISBN-10 : 9781493975600
ISBN-13 : 1493975609
Rating : 4/5 (00 Downloads)

Book Synopsis Disquisitiones Arithmeticae by : Carl Friedrich Gauss

Download or read book Disquisitiones Arithmeticae written by Carl Friedrich Gauss and published by Springer. This book was released on 2018-02-07 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae
Author :
Publisher : Springer Science & Business Media
Total Pages : 579
Release :
ISBN-10 : 9783540347200
ISBN-13 : 3540347208
Rating : 4/5 (00 Downloads)

Book Synopsis The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae by : Catherine Goldstein

Download or read book The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae written by Catherine Goldstein and published by Springer Science & Business Media. This book was released on 2007-02-03 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Classical Mathematics I

Introduction to Classical Mathematics I
Author :
Publisher : Springer Science & Business Media
Total Pages : 482
Release :
ISBN-10 : 0792312317
ISBN-13 : 9780792312314
Rating : 4/5 (17 Downloads)

Book Synopsis Introduction to Classical Mathematics I by : Helmut Koch

Download or read book Introduction to Classical Mathematics I written by Helmut Koch and published by Springer Science & Business Media. This book was released on 1991-05-31 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Classical Theory of Algebraic Numbers

Classical Theory of Algebraic Numbers
Author :
Publisher : Springer Science & Business Media
Total Pages : 676
Release :
ISBN-10 : 9780387216904
ISBN-13 : 0387216901
Rating : 4/5 (04 Downloads)

Book Synopsis Classical Theory of Algebraic Numbers by : Paulo Ribenboim

Download or read book Classical Theory of Algebraic Numbers written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.

Number Theory Revealed: An Introduction

Number Theory Revealed: An Introduction
Author :
Publisher : American Mathematical Soc.
Total Pages : 290
Release :
ISBN-10 : 9781470441579
ISBN-13 : 1470441578
Rating : 4/5 (79 Downloads)

Book Synopsis Number Theory Revealed: An Introduction by : Andrew Granville

Download or read book Number Theory Revealed: An Introduction written by Andrew Granville and published by American Mathematical Soc.. This book was released on 2019-11-12 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory Revealed: An Introduction acquaints undergraduates with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p p and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an “elective appendix” with additional reading, projects, and references. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach to these core topics and adds additional material in further chapters and appendices, allowing instructors to create an individualized course tailored to their own (and their students') interests.

A History of Abstract Algebra

A History of Abstract Algebra
Author :
Publisher : Springer
Total Pages : 412
Release :
ISBN-10 : 9783319947730
ISBN-13 : 3319947737
Rating : 4/5 (30 Downloads)

Book Synopsis A History of Abstract Algebra by : Jeremy Gray

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.

Introduction to Number Theory

Introduction to Number Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 228
Release :
ISBN-10 : 9781470446949
ISBN-13 : 1470446944
Rating : 4/5 (49 Downloads)

Book Synopsis Introduction to Number Theory by : Daniel E. Flath

Download or read book Introduction to Number Theory written by Daniel E. Flath and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the p−q symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled Δ=b2−4ac. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.