Introduction to Differential Geometry

Author: Luther Pfahler Eisenhart

Publisher: Princeton University Press

ISBN: 1400877865

Category: Mathematics

Page: 316

View: 8813

Book 3 in the Princeton Mathematical Series. Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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Differentialgeometrie

Kurven - Flächen - Mannigfaltigkeiten

Author: Wolfgang Kühnel

Publisher: Springer-Verlag

ISBN: 332292808X

Category: Mathematics

Page: 256

View: 1534

Eine Einführung in die Differentialgeometrie. Es wird großer Wert auf Anschaulichkeit gelegt, was auch durch zahlreiche Abbildungen unterstützt wird. Für die 2. Auflage wurden alle Kapitel gründlich überarbeitet. Hinzu kamen einige neue Übungsaufgaben und zusätzliche Abbildungen.
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From Riemann to Differential Geometry and Relativity

Author: Lizhen Ji,Athanase Papadopoulos,Sumio Yamada

Publisher: Springer

ISBN: 3319600397

Category: Mathematics

Page: 647

View: 6479

This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
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Notes on Crystalline Cohomology. (MN-21)

Author: Pierre Berthelot,Arthur Ogus

Publisher: Princeton University Press

ISBN: 1400867312

Category: Mathematics

Page: 256

View: 2914

Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry. Specifically, it provides the basic tools used in the study of crystalline cohomology of algebraic varieties in positive characteristic. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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D-Modules and Spherical Representations. (MN-39)

Author: Frédéric V. Bien

Publisher: Princeton University Press

ISBN: 1400862078

Category: Mathematics

Page: 142

View: 1772

The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to attach geometric invariants, like the support and the characteristic variety, to representations of Lie groups. By considering D-modules on flag varieties, one obtains a simple classification of all irreducible admissible representations of reductive Lie groups. On the other hand, it is natural to study the representations realized by functions on pseudo-Riemannian symmetric spaces, i.e., spherical representations. The problem is then to describe the spherical representations among all irreducible ones, and to compute their multiplicities. This is the goal of this work, achieved fairly completely at least for the discrete series representations of reductive symmetric spaces. The book provides a general introduction to the theory of D-modules on flag varieties, and it describes spherical D-modules in terms of a cohomological formula. Using microlocalization of representations, the author derives a criterion for irreducibility. The relation between multiplicities and singularities is also discussed at length. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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Lectures on Riemann Surfaces

Jacobi Varieties

Author: Robert C. Gunning

Publisher: Princeton University Press

ISBN: 1400872693

Category: Mathematics

Page: 198

View: 2160

A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well. The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic cross-sections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic cross-sections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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GAMMA

Eulers Konstante, Primzahlstrände und die Riemannsche Vermutung

Author: Julian Havil

Publisher: Springer-Verlag

ISBN: 3540484965

Category: Mathematics

Page: 302

View: 8032

Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.
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Encyclopedia of mathematical physics

Author: Sheung Tsun Tsou

Publisher: Academic Pr

ISBN: 9780125126601

Category: Science

Page: 3500

View: 568

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.
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The Pythagorean Theorem

A 4,000-year History

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 9780691125268

Category: Mathematics

Page: 259

View: 8928

Brings to life many of the characters who played a role in the development of the Pythagorean theorem--from the ancient Babylonians and Pythagoras to Albert Einstein and modern-day mathematicians--in a history that provides a fascinating backdrop to an enduring mathematical legacy.
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Professor Stewarts mathematische Schätze

Author: Ian Stewart

Publisher: Rowohlt Verlag GmbH

ISBN: 3644017115

Category: Mathematics

Page: 432

View: 3757

Was war noch mal die Catalan’sche Vermutung? Und woher kommt eigentlich das Wurzelsymbol? Was hat die Zahl Pi mit dem Sternenhimmel zu tun? Wer erfand das Gleichheitszeichen? Der britische Matheguru Ian Stewart breitet in diesem Band Schätze aus, die er in Jahrzehnten gesammelt hat: über 180 interessante Matherätsel, Lösungen, Spiele, Tricks, Geschichten, Anekdoten und Logeleien. Zudem ist Stewarts Schatztruhe mit interessanten historischen Exkursen angereichert, zum Beispiel einer kurzen Einführung in das Rechnen der Maya und der alten Ägypter und auch in die Vergangenheit unseres eigenen Rechnens: Wer erfand das Gleichheitszeichen – und warum? Ein Buch zum Blättern und Stöbern, zum Spaßhaben und Dazulernen, für Laien und für Fortgeschrittene.
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Einführung in die computerorientierte Mathematik mit Sage

Author: Thorsten Theobald,Sadik Iliman

Publisher: Springer-Verlag

ISBN: 3658104538

Category: Computers

Page: 195

View: 6757

Das an Studienanfänger der Mathematik gerichtete Lehrbuch bietet eine breit angelegte Einführung in verschiedene Facetten der computerorientierten Mathematik. Es ermöglicht eine frühzeitige und wertvolle Auseinandersetzung mit computerorientierten Methoden, Denkweisen und Arbeitstechniken innerhalb der Mathematik. Hierzu werden grundlegende mathematische Teilgebiete behandelt, die eine enge Beziehung zu computerorientierten Aspekten haben: Graphen, mathematische Algorithmen, Rekursionsgleichungen, computerorientierte lineare Algebra, Zahlen, Polynome und ihre Nullstellen. Anhand des mathematischen Kernstrangs werden Einblicke in die Modellierung, Analyse und algorithmische Aufbereitung fundamentaler mathematischer Sachverhalte gegeben. Eine Besonderheit des Buches ist die Verwendung des sich immer stärker in Forschung und Lehre verbreitenden, frei verfügbaren Software-Systems Sage. Das Buch eignet sich besonders gut zur Komplementierung der klassischen Grundvorlesungen in Analysis und linearer Algebra.
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Forthcoming Books

Author: Rose Arny

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 1605

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Lineare Algebra

Author: Werner Greub

Publisher: Springer-Verlag

ISBN: 3642663850

Category: Mathematics

Page: 222

View: 6094

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Series

AAAS to Intro Handbks

Author: N.A

Publisher: N.A

ISBN: 9780835221061

Category:

Page: 1444

View: 5083

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