Non-euclidean Geometry in the Theory of Automorphic Functions (History of Mathematics) - Softcover

Hadamard, Jacques

Softcover

ISBN 10: 0821820303 ISBN 13: 9780821820308

Verlag: American Mathematical Society, 1999

Inhaltsangabe

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. The implications of these discoveries continue to be important to this day in numerous different areas of mathematics. Hadamard begins with hyperbolic geometry, which he compares with plane and spherical geometry. He discusses the corresponding isometry groups, introduces the idea of discrete subgroups, and shows that the corresponding quotient spaces are manifolds.In Chapter 2 he presents the appropriate automorphic functions, in particular, Fuchsian functions. He shows how to represent Fuchsian functions as quotients, and how Fuchsian functions invariant under the same group are related, and indicates how these functions can be used to solve differential equations. Chapter 4 is devoted to the outlines of the more complicated Kleinian case. Chapter 5 discusses algebraic functions and linear algebraic differential equations, and the last chapter sketches the theory of Fuchsian groups and geodesics. 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. This volume is one of an informal sequence of works within the ""History of Mathematics"" series. Volumes in this subset, ""Sources"", are classical mathematical works that served as cornerstones for modern mathematical thought.

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Críticas

Jeremy Gray and Abe Shenitzer deserve the gratitude of the entire mathematical community for bringing out this Hadamard volume ... This is an important addition to the literature, of great interest both to mathematical historians and to anyone with even a passing acquaintance with non-Euclidean geometry and automorphic functions ... this book is essential reading. (Mathematical Reviews )

Reseña del editor

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 Poincaré. Poincaré'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. The implications of these discoveries continue to be important to this day in numerous different areas of mathematics. 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. This book is the second in an informal sequence of works called "History of Mathematics, Sources", to be included within the History of Mathematics series, co-published by the AMS and the London Mathematical Society. Volumes to be published within this subset are classical mathematical works that served as cornerstones for modern mathematical thought. (For another historical translation on this topic, see Sources of Hyperbolic Geometry, volume 10 in the History of Mathematics series.) Co-published with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 1999
• Sprache: Englisch
• ISBN 10: 0821820303
• ISBN 13: 9780821820308
• Einband: Tapa blanda
• Anzahl der Seiten: 95
• Herausgeber: Gray Jeremy
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar