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Non-Euclidean Geometry in the Theory of Automorphic Functions

Non-Euclidean Geometry in the Theory of Automorphic Functions
Author: Jacques Hadamard
Publisher: American Mathematical Soc.
Total Pages: 109
Release: 1999
Genre: Mathematics
ISBN: 0821820303

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"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.


Non-Euclidean Geometry in the Theory of Automorphic Functions

Non-Euclidean Geometry in the Theory of Automorphic Functions
Author: Jacques Hadamard
Publisher: American Mathematical Soc.
Total Pages: 116
Release: 1999-01-01
Genre: Mathematics
ISBN: 9780821890479

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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.


An Introduction to the Theory of Automorphic Functions

An Introduction to the Theory of Automorphic Functions
Author: Lester R. Ford
Publisher: Createspace Independent Publishing Platform
Total Pages: 104
Release: 2016-01-31
Genre:
ISBN: 9781523796991

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This is an excellent tract on what is now an extensive subject. The main points are very clearly put; room has even been found for an outline of non-Euclidean geometry, and the expression of co-ordinates of points on an algebraic curve as one-valued functions. There is a bibliography which seems to include most of the books and papers of really first-rate importance; and there is a sufficient number of diagrams. English-speaking students ought now, at any rate, to appreciate Poincaré's wonderful discoveries in this field. -Nature, Vol. 96


A Simple Non-Euclidean Geometry and Its Physical Basis

A Simple Non-Euclidean Geometry and Its Physical Basis
Author: I.M. Yaglom
Publisher: Springer Science & Business Media
Total Pages: 326
Release: 2012-12-06
Genre: Mathematics
ISBN: 146126135X

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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.


A Short Course in Automorphic Functions

A Short Course in Automorphic Functions
Author: Joseph Lehner
Publisher: Courier Corporation
Total Pages: 162
Release: 2015-01-21
Genre: Mathematics
ISBN: 0486789748

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Concise treatment covers basics of Fuchsian groups, development of Poincaré series and automorphic forms, and the connection between theory of Riemann surfaces with theories of automorphic forms and discontinuous groups. 1966 edition.


Spectral Theory of Automorphic Functions

Spectral Theory of Automorphic Functions
Author: A. B. Venkov
Publisher: American Mathematical Soc.
Total Pages: 196
Release: 1983
Genre: Mathematics
ISBN: 9780821830789

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Pearls from a Lost City

Pearls from a Lost City
Author: Roman Duda
Publisher: American Mathematical Society
Total Pages: 247
Release: 2014-08-07
Genre: Biography & Autobiography
ISBN: 1470410761

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The fame of the Polish school at Lvov rests with the diverse and fundamental contributions of Polish mathematicians working there during the interwar years. In particular, despite material hardship and without a notable mathematical tradition, the school made major contributions to what is now called functional analysis. The results and names of Banach, Kac, Kuratowski, Mazur, Nikodym, Orlicz, Schauder, Sierpiński, Steinhaus, and Ulam, among others, now appear in all the standard textbooks. The vibrant joie de vivre and singular ambience of Lvov's once scintillating social scene are evocatively recaptured in personal recollections. The heyday of the famous Scottish Café--unquestionably the most mathematically productive cafeteria of all time--and its precious Scottish Book of highly influential problems are described in detail, revealing the special synergy of scholarship and camaraderie that permanently elevated Polish mathematics from utter obscurity to global prominence. This chronicle of the Lvov school--its legacy and the tumultuous historical events which defined its lifespan--will appeal equally to mathematicians, historians, or general readers seeking a cultural and institutional overview of key aspects of twentieth-century Polish mathematics not described anywhere else in the extant English-language literature.


The War of Guns and Mathematics

The War of Guns and Mathematics
Author: David Aubin
Publisher: American Mathematical Society
Total Pages: 414
Release: 2014-10-07
Genre: Mathematics
ISBN: 1470414694

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For a long time, World War I has been shortchanged by the historiography of science. Until recently, World War II was usually considered as the defining event for the formation of the modern relationship between science and society. In this context, the effects of the First World War, by contrast, were often limited to the massive deaths of promising young scientists. By focusing on a few key places (Paris, Cambridge, Rome, Chicago, and others), the present book gathers studies representing a broad spectrum of positions adopted by mathematicians about the conflict, from militant pacifism to military, scientific, or ideological mobilization. The use of mathematics for war is thoroughly examined. This book suggests a new vision of the long-term influence of World War I on mathematics and mathematicians. Continuities and discontinuities in the structure and organization of the mathematical sciences are discussed, as well as their images in various milieux. Topics of research and the values with which they were defended are scrutinized. This book, in particular, proposes a more in-depth evaluation of the issue of modernity and modernization in mathematics. The issue of scientific international relations after the war is revisited by a close look at the situation in a few Allied countries (France, Britain, Italy, and the USA). The historiography has emphasized the place of Germany as the leading mathematical country before WWI and the absurdity of its postwar ostracism by the Allies. The studies presented here help explain how dramatically different prewar situations, prolonged interaction during the war, and new international postwar organizations led to attempts at redrafting models for mathematical developments.