Primes Of The Form X2 Ny2

Author: David A. Cox
Publisher: Wiley
ISBN: 9781118390184
Size: 50.75 MB
Format: PDF, ePub
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Primes Of The Form X2 Ny2 from the Author: David A. Cox. An exciting approach to the history and mathematics of number theory “. . . the author’s style is totally lucid and very easy to read . . .the result is indeed a wonderful story.” —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat’s work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: • A well-motivated introduction to the classical formulation of class field theory • Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations • An elementary treatment of quadratic forms and genus theory • Simultaneous treatment of elementary and advanced aspects of number theory • New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.

Primes Of The Form X2 Ny2

Author: David A. Cox
Publisher: Wiley-Interscience
ISBN:
Size: 28.72 MB
Format: PDF, ePub, Docs
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Primes Of The Form X2 Ny2 from the Author: David A. Cox. Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.

Basic Atonal Theory

Author: John Rahn
Publisher: MacMillan Publishing Company
ISBN:
Size: 65.73 MB
Format: PDF, Mobi
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Basic Atonal Theory from the Author: John Rahn.

The Structure Of Atonal Music

Author: Allen Forte
Publisher: Yale University Press
ISBN: 9780300021202
Size: 18.43 MB
Format: PDF, ePub
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The Structure Of Atonal Music from the Author: Allen Forte. Describes and cites examples of pitch-class sets and relations in atonal music.

Harmony Book

Author: Elliott Carter
Publisher: Carl Fischer, L.L.C.
ISBN: 9780825845949
Size: 56.96 MB
Format: PDF, Kindle
View: 1806
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Harmony Book from the Author: Elliott Carter. This comprehensive resource features more than 400 projections and colour illustrations augmented by MRI images for added detail to enhance the anatomy and positioning presentations.

Primes Of The Form X2 Ny2

Author: David A. Cox
Publisher: Wiley-Interscience
ISBN:
Size: 54.74 MB
Format: PDF, ePub, Docs
View: 2980
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Primes Of The Form X2 Ny2 from the Author: David A. Cox. Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of class field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.

Tata Lectures On Theta Iii

Author: David Mumford
Publisher: Springer Science & Business Media
ISBN: 0817645705
Size: 39.49 MB
Format: PDF
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Tata Lectures On Theta Iii from the Author: David Mumford. This volume is the third of three in a series surveying the theory of theta functions which play a central role in the fields of complex analysis, algebraic geometry, number theory and most recently particle physics. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III). Researchers and graduate students in mathematics and physics will find these volumes to be valuable additions to their libraries.

Introduction To Post Tonal Theory

Author: Joseph N. Straus
Publisher: W. W. Norton & Company
ISBN: 0393938832
Size: 52.85 MB
Format: PDF, Kindle
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Introduction To Post Tonal Theory from the Author: Joseph N. Straus. Now published by Norton, Introduction to Post-Tonal Theory has been thoroughly updated to reflect the latest developments in the field, with additional coverage of transformational theory and voice leading. The Fourth Edition helps students identify key theoretical points and guides them through the process of analysis, while also offering new recently composed musical examples—all at an exceptional value.

Functional Differential Equations

Author: Constantin Corduneanu
Publisher: John Wiley & Sons
ISBN: 1119189497
Size: 19.36 MB
Format: PDF, Mobi
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Functional Differential Equations from the Author: Constantin Corduneanu. Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.