Author: Aleksandr I?Akovlevich Khinchin,Herbert Eagle

Publisher: Courier Corporation

ISBN: 9780486696300

Category: Mathematics

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### Continued Fractions

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

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

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

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

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

### Continued Fractions with Applications

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.

### A Brief Introduction to Theta Functions

Originally published: New York: Rinehart and Winston, 1961.

### Elementary Theory of Numbers

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

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

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

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.

### The Real Number System in an Algebraic Setting

Proceeding from a review of the natural numbers to the positive rational numbers, this text advances to the nonnegative real numbers and the set of all real numbers. 1962 edition.

### Mathematical Methods in the Theory of Queuing

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.

### Fibonacci and Lucas Numbers, and the Golden Section

This survey of the use of Fibonacci and Lucas numbers and the ancient principle of the Golden Section covers areas relevant to operational research, statistics, and computational mathematics. 1989 edition.

### Neverending Fractions

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

### Algebraic Theory of Numbers

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

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.

### The gamma function

### Practical Conic Sections

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.

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Author: Aleksandr I?Akovlevich Khinchin,Herbert Eagle

Publisher: Courier Corporation

ISBN: 9780486696300

Category: Mathematics

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*Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,*

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ISBN: 0486462765

Category: Mathematics

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*An Introduction to Continued Fractions*

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Publisher: N.A

ISBN: N.A

Category: Functions, Gamma

Page: 39

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*The Geometric Properties of Ellipses, Parabolas and Hyperbolas*

Author: J. W. Downs

Publisher: Courier Corporation

ISBN: 0486148882

Category: Mathematics

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