Continued Fractions

Author: Aleksandr I?Akovlevich Khinchin,Herbert Eagle

Publisher: Courier Corporation

ISBN: 9780486696300

Category: Mathematics

Page: 95

View: 9671

Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces.

Geometry of Continued Fractions

Author: Oleg Karpenkov

Publisher: Springer Science & Business Media

ISBN: 3642393683

Category: Mathematics

Page: 405

View: 5269

Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Continued Fractions

Author: Andrew M Rockett,Peter Szüsz

Publisher: World Scientific Publishing Company

ISBN: 9813103418

Category: Mathematics

Page: 196

View: 3526

This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers. Request Inspection Copy

Uniform Distribution of Sequences

Author: L. Kuipers,H. Niederreiter

Publisher: Courier Corporation

ISBN: 0486149994

Category: Mathematics

Page: 416

View: 4843

The theory of uniform distribution began with Weyl's celebrated paper of 1916 and this book summarizes its development through the mid-1970s, with comprehensive coverage of methods and principles. 1974 edition.

Continued Fractions

Author: Doug Hensley

Publisher: World Scientific

ISBN: 9812774688

Category: Mathematics

Page: 245

View: 1580

This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction to the history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context.

Continued Fractions with Applications

Author: Lisa Lorentzen,Haakon Waadeland

Publisher: North Holland


Category: Mathematics

Page: 606

View: 9191

This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.

Elementary Theory of Numbers

Author: William J. LeVeque

Publisher: Courier Corporation

ISBN: 0486150763

Category: Mathematics

Page: 160

View: 7543

Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.

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: 2966

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.

Diophantine Approximations

Author: Ivan Niven

Publisher: Courier Corporation

ISBN: 0486164705

Category: Mathematics

Page: 80

View: 5995

This self-contained treatment covers approximation of irrationals by rationals, product of linear forms, multiples of an irrational number, approximation of complex numbers, and product of complex linear forms. 1963 edition.

Excursions in Number Theory

Author: Charles Stanley Ogilvy,John Timothy Anderson

Publisher: Courier Corporation

ISBN: 9780486257785

Category: Mathematics

Page: 168

View: 7580

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.

Mathematical Methods in the Theory of Queuing

Author: A. Y. Khinchin

Publisher: Courier Corporation

ISBN: 0486316319

Category: Mathematics

Page: 128

View: 9291

Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. Prerequisites include a familiarity with the theory of probability and mathematical analysis. 1960 edition.

Neverending Fractions

An Introduction to Continued Fractions

Author: Jonathan Borwein,Alf van der Poorten,Jeffrey Shallit,Wadim Zudilin

Publisher: Cambridge University Press

ISBN: 0521186498

Category: Mathematics

Page: 224

View: 6103

This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.

Algebraic Theory of Numbers

Author: Pierre Samuel,Allan J. Silberger

Publisher: N.A

ISBN: 9780486466668

Category: Mathematics

Page: 109

View: 6309

Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics — algebraic geometry, in particular. This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Galois theory, Noetherian rings and modules, and rings of fractions. It covers the basics, starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number, and the more elementary theorems of Hilbert ramification theory. Numerous examples, applications, and exercises appear throughout the text.

History of the Theory of Numbers

Author: Leonard Eugene Dickson

Publisher: American Mathematical Soc.

ISBN: 9780821819364

Category: Mathematics

Page: 313

View: 9911

The last volume of Dickson's History is the most modern, covering quadratic and higher forms. The treatment here is more general than in Volume II, which, in a sense, is more concerned with special cases. Indeed, this volume chiefly presents methods of attacking whole classes of problems. Again, Dickson is exhaustive with references and citations.

Practical Conic Sections

The Geometric Properties of Ellipses, Parabolas and Hyperbolas

Author: J. W. Downs

Publisher: Courier Corporation

ISBN: 0486148882

Category: Mathematics

Page: 112

View: 8110

Using examples from everyday life, this text studies ellipses, parabolas, and hyperbolas. Explores their ancient origins and describes the reflective properties and roles of curves in design applications. 1993 edition. Includes 98 figures.