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Author: Jacques Hadamard Publisher: American Mathematical Soc. ISBN: 0821820303 Category : Automorphic functions Languages : en Pages : 109
Book Description
"This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts."--Jacket.
Author: Jacques Hadamard Publisher: American Mathematical Soc. ISBN: 0821820303 Category : Automorphic functions Languages : en Pages : 109
Book Description
"This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts."--Jacket.
Author: Jacques Hadamard Publisher: American Mathematical Soc. ISBN: 9780821890479 Category : Mathematics Languages : en Pages : 116
Book Description
This is the English translation of a volume originally published only in Russian and now out of print. The book was written by Jacques Hadamard on the work of Poincare. Poincare's creation of a theory of automorphic functions in the early 1880s was one of the most significant mathematical achievements of the nineteenth century. It directly inspired the uniformization theorem, led to a class of functions adequate to solve all linear ordinary differential equations, and focused attention on a large new class of discrete groups. It was the first significant application of non-Euclidean geometry. This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts.
Author: I.M. Yaglom Publisher: Springer Science & Business Media ISBN: 146126135X Category : Mathematics Languages : en Pages : 326
Book Description
There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.
Author: Joseph Lehner Publisher: American Mathematical Soc. ISBN: 0821815083 Category : Automorphic functions Languages : en Pages : 425
Book Description
Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. The purpose of this book is to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation. The emphasis in this book is on the fundamental parts of the subject. The book is directed to three classes of readers: graduate students approaching the subject for the first time, mature mathematicians who wish to gain some knowledge and understanding of automorphic function theory, and experts.
Author: Werner Fenchel Publisher: Walter de Gruyter ISBN: 3110891352 Category : Mathematics Languages : en Pages : 389
Book Description
This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups). The current book is based on what became known as the famous Fenchel-Nielsen manuscript. Jakob Nielsen (1890-1959) started this project well before World War II, and his interest arose through his deep investigations on the topology of Riemann surfaces and from the fact that the fundamental group of a surface of genus greater than one is represented by such a discontinuous group. Werner Fenchel (1905-1988) joined the project later and overtook much of the preparation of the manuscript. The present book is special because of its very complete treatment of groups containing reversions and because it avoids the use of matrices to represent Moebius maps. This text is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups.
Author: Jacques Hadamard
Author: Jacques Hadamard
Author: Jacques Hadamard
Author: Jacques Hadamard
Author: Lester R. Ford
Author: I.M. Yaglom
Author: Lester R. Ford
Author: A. B. Venkov
Author: Joseph Lehner
Author: Joseph Lehner
Author: Werner Fenchel