Search Results: on-riemann-s-theory-of-algebraic-functions-and-their-integrals-a-supplement-to-the-usual-treatises

On Riemann's Theory of Algebraic Functions and Their Integrals

A Supplement to the Usual Treatises

Author: Felix Klein

Publisher: Cosimo, Inc.

ISBN: 1602063273

Category: Mathematics

Page: 92

View: 4579

German mathematician FELIX KLEIN (1849-1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. In his scholarly supplement to Riemann's complex mathematical theory, rather than offer proofs in support of the theorem, Klein chose to offer this exposition and annotation, first published in 1893, in an effort to broaden and deepen understanding. This approach makes Klein's commentary an essential element of any mathematics scholar's library.

Enzyklopädie Philosophie und Wissenschaftstheorie

Bd. 4: Ins–Loc

Author: Jürgen Mittelstraß

Publisher: Springer-Verlag

ISBN: 3476001369

Category: Philosophy

Page: 595

View: 9421

Das ganze Wissen der Philosophie und Wissenschaftstheorie. Lückenlos belegt das größte allgemeine Lexikon zur Philosophie in deutscher Sprache den heutigen Kenntnisstand. Erweitert auf acht Bände dokumentiert die 2. Auflage insbesondere die jüngsten Entwicklungen in Logik, Erkenntnis- und Wissenschaftstheorie sowie Sprachphilosophie. Jetzt liegt der vierte Band in Neuauflage vor mit über 100 zusätzlichen Einträgen, u. a. zu Intelligenz, Interdisziplinarität, Isotropie, Kognitionswissenschaft, Komplexitätstheorie, Konvention, Lebenswissenschaften und einer Vielzahl neuer Personenartikel.

A Course in Complex Analysis and Riemann Surfaces

Author: Wilhelm Schlag

Publisher: American Mathematical Society

ISBN: 0821898477

Category: Mathematics

Page: 384

View: 2785

Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.

Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A

Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 1470411008

Category: Mathematical analysis

Page: 641

View: 9268

A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces

Author: Milagros Izquierdo, S. Allen Broughton, Antonio F. Costa,Rubí E. Rodríguez

Publisher: American Mathematical Soc.

ISBN: 1470410931

Category: Mathematics

Page: 348

View: 7495

This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24-28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.

Doing Mathematics

Convention, Subject, Calculation, Analogy

Author: Martin H Krieger

Publisher: World Scientific

ISBN: 9814571865

Category: Mathematics

Page: 492

View: 2433

Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands' program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see "an identity in a manifold presentation of profiles," as the phenomenologists would say. This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an "ugly" first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude. Contents:IntroductionConvention: How Means and Variances are Entrenched as StatisticsSubject: The Fields of TopologyAppendix: The Two-Dimensional Ising Model of a FerromagnetCalculation: Strategy, Structure, and Tactics in Applying Classical AnalysisAnalogy: A Syzygy Between a Research Program in Mathematics and a Research Program in PhysicsIn Concreto: The City of MathematicsAppendices:The Spontaneous Magnetization of a Two-Dimensional Ising Model (C N Yang)On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom (C Fefferman and L A Seco)Sur la Forme des Espaces Topologiques et sur les Points Fixes des Représentations (J Leray)Une Lettre à Simone Weil (A Weil) Readership: Mathematicians, physicists, philosophers and historians of science. Keywords:Means and Variances;Topology;SyzygyReviews: Reviews of the First Edition: "The book Doing Mathematics, by Martin Krieger is truly a masterpiece. He has not only explained ways of doing mathematical work to aspiring mathematicians and the intelligent laymen, but has also shown how various pieces of research work are related to each other. Even experts may not have realized such inter-relations. The cases studied include, especially, the stability of matter and the Ising model, two topics of great depth. Such clear explanations cannot be found anywhere else. Furthermore, his style of writing makes the book exceptionally enjoyable to read." T T Wu Gordon McKay Professor of Applied Physics Professor of Physics, Harvard University, USA "This is the first time I have seen a mathematician deal substantively with the issue of mathematics as culturally based, and he does it superbly and mathematically … Although this book is no easy read, it is well worth the effort, and I am sure it will stimulate and inform, perhaps even surprise, the most sophisticated of mathematical readers. It is refreshing to find such a book being published." Mathematical Reviews "Both challenging and provocative reading, Doing Mathematics sheds bright light on some of the main characteristics of the mathematical quest." Library of Science "Krieger has made some effort to accommodate different levels of readers; for example, structuring his text so that lay readers are alerted to sections that can be safely skipped and paragraphs that provide nontechnical summaries." Mathematical Association of America

The Academy and Literature

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Publisher: N.A

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The Academy

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Category: Art

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Bulletin of the American Mathematical Society

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Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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Mathematica Scandinavica

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

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Nature

Author: Sir Norman Lockyer

Publisher: N.A

ISBN: N.A

Category: Electronic journals

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View: 4971

Bulletin

Author: Mechanics' Institute (San Francisco, Calif.). Library

Publisher: N.A

ISBN: N.A

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View: 4835

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A Classified Cumulation : Volumes 1-10, March 1964--February 1974

Author: Richard K. Gardner,Phyllis Grumm

Publisher: N.A

ISBN: N.A

Category: Best books

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A History of Mathematics

Author: Florian Cajori

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 422

View: 7677

The Publishers' Trade List Annual

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Publisher: N.A

ISBN: N.A

Category: American literature

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Monthly Record of Scientific Literature

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Publisher: N.A

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Shinshū yōsho sōgō mokuroku

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Catalogs, Union

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The Annual American Catalogue

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Publisher: N.A

ISBN: N.A

Category: American literature

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Scientific and Technical Books in Print

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Category: Engineering

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Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert

Author: Felix Klein

Publisher: Springer-Verlag

ISBN: 3642672302

Category: Mathematics

Page: 594

View: 3217

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