The Topology of Fibre Bundles. (PMS-14)

Author: Norman Steenrod

Publisher: Princeton University Press

ISBN: 1400883873

Category: Mathematics

Page: 224

View: 6427

Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
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The Topology of Fibre Bundles

Author: Norman Earl Steenrod

Publisher: Princeton University Press

ISBN: 9780691005485

Category: Mathematics

Page: 229

View: 1037

Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
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Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)

Author: Kari Astala,Tadeusz Iwaniec,Gaven Martin

Publisher: Princeton University Press

ISBN: 9780691137773

Category: Mathematics

Page: 677

View: 3686

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
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Spin Geometry (PMS-38)

Author: H. Blaine Lawson,Marie-Louise Michelsohn

Publisher: Princeton University Press

ISBN: 1400883911

Category: Mathematics

Page: 440

View: 589

This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
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Introduction to Fourier Analysis on Euclidean Spaces (PMS-32)

Author: Elias M. Stein,Guido Weiss

Publisher: Princeton University Press

ISBN: 140088389X

Category: Mathematics

Page: 312

View: 1537

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
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Singular Integrals and Differentiability Properties of Functions (PMS-30)

Author: Elias M. Stein

Publisher: Princeton University Press

ISBN: 1400883881

Category: Mathematics

Page: 304

View: 9977

Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself. Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance. Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.
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Topologie

Author: K. Jänich

Publisher: Springer-Verlag

ISBN: 3662225549

Category: Mathematics

Page: 215

View: 3925

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Die Gene sind es nicht ...

Biologie, Ideologie und menschliche Natur

Author: Richard C. Lewontin,Leon J. Kamin,Steven P. R. Rose

Publisher: N.A

ISBN: 9783621270366

Category:

Page: 264

View: 2199

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Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit

Author: Edward Frenkel

Publisher: Springer-Verlag

ISBN: 3662434210

Category: Mathematics

Page: 317

View: 7374

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Lineare Algebra

Author: Werner Greub

Publisher: Springer-Verlag

ISBN: 3642663850

Category: Mathematics

Page: 222

View: 1715

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Mathematik und Technologie

Author: Christiane Rousseau,Yvan Saint-Aubin

Publisher: Springer-Verlag

ISBN: 3642300928

Category: Mathematics

Page: 609

View: 3670

Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.
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Differentialgleichungen und ihre Anwendungen

Author: Martin Braun

Publisher: Springer-Verlag

ISBN: 3642973418

Category: Mathematics

Page: 596

View: 7133

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#
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Vor dem Anfang

Eine Geschichte des Universums

Author: Martin Rees

Publisher: S. Fischer Verlag

ISBN: 3105608508

Category: Science

Page: 352

View: 2924

Gibt es neben unserem noch andere Universen? Wie und wann sind sie entstanden? Welche physikalischen Gesetze herrschen dort? – Die Grundfragen der Kosmologie, beantwortet von Martin Rees, einem der renommiertesten Astronomen der Welt. (Dieser Text bezieht sich auf eine frühere Ausgabe.)
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Deckname Dora

Author: Sándor Radó

Publisher: N.A

ISBN: N.A

Category: World War, 1939-1945

Page: 441

View: 6327

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TensorFlow für Dummies

Author: Matthew Scarpino

Publisher: John Wiley & Sons

ISBN: 3527818960

Category: Computers

Page: 324

View: 1295

TensorFlow ist Googles herausragendes Werkzeug für das maschinelle Lernen, und dieses Buch macht es zugänglich, selbst wenn Sie bisher wenig über neuronale Netze und Deep Learning wissen. Sie erfahren, auf welchen Prinzipien TensorFlow basiert und wie Sie mit TensorFlow Anwendungen schreiben. Gleichzeitig lernen Sie die Konzepte des maschinellen Lernens kennen. Wenn Sie Softwareentwickler sind und TensorFlow in Zukunft einsetzen möchten, dann ist dieses Buch der richtige Einstieg für Sie. Greifen Sie auch zu, wenn Sie einfach mehr über das maschinelle Lernen erfahren wollen.
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