Author: Xerox University MicrofilmsPublisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 856
Book Description
Comprehensive Dissertation Index, 1861-1972: Mathematics and statistics
Author: Xerox University MicrofilmsPublisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 856
Book Description
Comprehensive Dissertation Index
Author: Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 858
Book Description
Bulletin of the American Mathematical Society
Author: American Mathematical SocietyPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1106
Book Description
Acta Arithmetica
Author: Comprehensive Dissertation Index, 1861-1972: Author index
Author: Xerox University MicrofilmsPublisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 1118
Book Description
Perfect Lattices in Euclidean Spaces
Author: Jacques MartinetPublisher: Springer Science & Business Media
ISBN: 3662051672
Category : Mathematics
Languages : en
Pages : 535
Book Description
Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.
Geometry of Continued Fractions
Author: Oleg KarpenkovPublisher: Springer Science & Business Media
ISBN: 3642393683
Category : Mathematics
Languages : en
Pages : 409
Book Description
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.
From Christoffel Words to Markoff Numbers
Author: Christophe ReutenauerPublisher:
ISBN: 0198827547
Category : Mathematics
Languages : en
Pages : 169
Book Description
This book looks to expand on the relationship between Christoffel words and Markoff theory. Part 1 focuses on the classical theory of Markoff, while part II explores the more advanced and recent results around Christoffel words.
The Markoff and Lagrange Spectra
Author: Thomas W. CusickPublisher: American Mathematical Soc.
ISBN: 0821815318
Category : Mathematics
Languages : en
Pages : 109
Book Description
This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.
My Numbers, My Friends
Author: Paulo RibenboimPublisher: Springer Science & Business Media
ISBN: 0387227547
Category : Mathematics
Languages : en
Pages : 384
Book Description
This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as Kummers work on Fermat's last theorem.