ISBN: 9789048148769

The Nile on eBay   The Riemann Legacy by Krzysztof Maurin Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in … Meer...

The Nile on eBay   The Riemann Legacy by Krzysztof Maurin Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description The study of the rise and fall of great mathematical ideas is undoubtedly one of the most fascinating branches of the history of science. It enables one to come into contact with and to participate in the world of ideas. Nowhere can we see more concretely the enormous spiritual energy which, initially still lacking clear contours, begs to be moulded and developed by mathematicians, than in Riemann (1826-1866). He perceived mathematics and physics as one discipline and thought of himself as both mathematician and physicist. His ideas as well as their contemporary descendants are the theme of this book. Audience: This volume will be useful to those interested in such diverse fields as the mathematics of physics, algebra and number theory, topology and geometry, analysis, and the history of science. Notes Springer Book Archives Table of Contents I Riemannian Ideas in Mathematics and Physics.- 1 Gauss Inner Curvature of Surfaces.- 2 Sectional Curvature. Spaces of Constant Curvature. Weyl Hypothesis.- 3 Cohomology of Riemann spaces. Theorems of de Rham, Hodge, Kodaira.- 4 Chern—Gauss—Bonnet theorem.- 5 Curvature and Topology or Characteristic Forms of Chern, Pontriagin, and Euler.- 6 Kähler Spaces. Bergman Metrics. Harish-Chandra-Cartan Theorem. Siegel Space (once again!).- II General Structures of Mathematics.- 1 Differentiable Structures. Tangent Spaces. Vector Fields.- 2 Projective (Inverse) Limits of Topological Spaces.- 3 Inductive Limits. Presheaves. Covering Defined by Presheaf.- 4 Algebras. Groups, Tensors, Clifford, Grassmann, and Lie Algebras. Theorems of Bott—Milnor, Wedderburn, and Hurwitz.- 5 Fields and their Extensions.- 6 Galois Theory. Solvable Groups.- 7 Ruler and Compass Constructions. Cyclotomic Fields. Kronecker—Weber Theorem.- 8 Algebraic and Transcendental Elements.- 9 Weyl principle.- 10 Topology of Compact Lie Groups.- 11 Representations of Compact Lie Groups.- 12 Nilpotent, Semimple, and Solvable Lie Algebras.- 13 Reflections, Roots, and Weights. Coxeter and Weyl groups.- 14 Covariant Differentiation. Parallel Transport. Connections.- 15 Remarks on Rich Mathematical Structures of Simple Notions of Physics Based on Example of Analytical Mechanics.- 16 Tangent Bundle TM. Vector, Fiber, Tensor and Tensor Densities, and Associate Bundles.- 17 G-spaces. Group Representations.- 18 Principal and Associated Bundles.- 19 Induced Representations and Associated Bundles.- 20 Vector Bundles and Locally Free Sheaves.- 21 Axiom of Covering Homotopy.- 22 Serre Fibering. General Theory of Connection. Corollaries.- 23 Homology. Cohomology. de Rham Cohomology.- 24 Cohomology of Sheaves. Abstract deRham Theorem.- 25 Homotopy Group ?k(X, x0). Hopf Fibering. Serre Theorem on Exact Sequence of Homotopy Groups of a Fibering.- 26 Various Benefits of Characteristic Classes (Orientability, Spin Structures). Clifford Groups, Spin Group.- 27 Divisors and Line Bundles. Algebraic and Abelian Varieties.- 28 General Abelian Varieties and Theta Function.- 29 Theorems on Algebraic Dependence.- III The Idea of the Riemann Surface.- IV Riemann and Calculus of Variations.- 1 Introduction.- 2 The Plateau Problem.- 3 Teichmüller Theory. Riemann Moduli Problem.- 4 Riemannian Approach to Teichmiiller Theory. Harmonic Maps and Teichmüller Space.- 5 Teichmüller theory and Plateau—Douglas problem.- 6 Rescuing Riemann's Dirichlet Principle. Potential Theory.- 7 The Royal Road to Calculus of Variations (Constantin Carathéodory).- 8 Symplectic and Contact Geometries. Conservation Laws.- 9 Direct Methods in Calculus of Variations for Manifolds with Isometries. Equivariant Sobolev Theorems. Yamabe Problem and its Relation to General Relativity.- V Riemann and Complex Geometry.- 1 Introduction.- 2 On Complex Analysis in Several Variables.- 3 Ellipticity, Runge Property, and Runge Type Theorems.- 4 Hörmander Method in Complex Analysis.- 5 Wirtinger Theorems. Metric Theory of Analytic Sets.- 6 The Problem of Poincaré and the Cousin Problems.- 7 Ringed Spaces and General Complex Spaces.- 8 Construction of Complex Spaces by Gluing and by Taking Quotient.- 9 Differential Geometry of Holomorphic Vector Bundles over Compact Riemann Surfaces and Kähler manifolds. Stable Vector Bundles, Hermite-Einstein Connections, and their Moduli Spaces.- VI Riemann and Number Theory.- 1 Introduction.- 2 The Riemann ? function.- 3 Hecke Theory.- 4 Dedekind ?K function for number field K and Selberg ?function.- Concluding Remarks.- Suggestions for Further Reading. Promotional Springer Book Archives Long Description very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum). Details ISBN9048148766 Author Krzysztof Maurin Publisher Springer Year 2010 ISBN-10 9048148766 ISBN-13 9789048148769 Format Paperback Publication Date 2010-12-06 Imprint Springer Place of Publication Dordrecht Country of Publication Netherlands DEWEY 510 Edition 1st Language English Media Book Series Number 417 Short Title RIEMANN LEGACY SOFTCOVER REPRI Series Mathematics and Its Applications Pages 719 Subtitle Riemannian Ideas in Mathematics and Physics Illustrations 3 Illustrations, black and white; XXII, 719 p. 3 illus. Edition Description Softcover reprint of the original 1st ed. 1997 Alternative 9780792346364 Audience Professional & Vocational Country of Origin NL Product Class Description Mathematics We've got thisAt The Nile, if you're looking for it, we've got it.With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96230524; , von Profianbieter, Neu, Festpreisangebot, [LT: FixedPrice], ISBN-13: 9789048148769, Book Title: The Riemann Legacy<

2010, ISBN: 9789048148769

gewerbliches Angebot, [SC: 0.00], Neuware, [PU: Springer], 744, [GW: 1107g], [ED: Taschenbuch], DE, very small domain (environment) affects through analytic continuation the whole of Riem… Meer...

gewerbliches Angebot, [SC: 0.00], Neuware, [PU: Springer], 744, [GW: 1107g], [ED: Taschenbuch], DE, very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel..., Banküberweisung, PayPal, [CT: Sonstiges / Sonstiges]<

2013, ISBN: 9789048148769

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 1997, 744 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 3 black & white illustra… Meer...

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 1997, 744 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 3 black & white illustrations, biography, 2.26 kg, Algebra & Zahlentheorie, Naturwissenschaft & Mathematik, Fachbücher, Kategorien, Bücher, Geometrie, Naturwissenschaften & Technik, Fremdsprachige Bücher, Featured Categories, Englische Bücher, 7c9a6c79-19ea-4dea-90da-d7d47042d341_2301, 7c9a6c79-19ea-4dea-90da-d7d47042d341_0, Arborist Merchandising Root, acc906d0-2585-4921-a56f-3ff277850936_4901, acc906d0-2585-4921-a56f-3ff277850936_0, Special Features Stores, Taschenbücher, acc906d0-2585-4921-a56f-3ff277850936_4201, Springer, 2013<

2010, ISBN: 9789048148769

Springer, Paperback, Auflage: Softcover reprint of the original 1st ed. 1997, 741 Seiten, Publiziert: 2010-12-06T00:00:01Z, Produktgruppe: Book, Hersteller-Nr.: 3 black & white illustrati… Meer...

Springer, Paperback, Auflage: Softcover reprint of the original 1st ed. 1997, 741 Seiten, Publiziert: 2010-12-06T00:00:01Z, Produktgruppe: Book, Hersteller-Nr.: 3 black & white illustrations, biography, 1.02 kg, Algebra, Mathematics, Science, Nature & Maths, Subjects, Books, Applied Mathematics, Mathematical Analysis, Geometry & Topology, Scientific, Technical & Medical, Calculus & Mathematical Analysis, Springer, 2010<

2013, ISBN: 9789048148769

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 1997, 744 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 3 black & white illustra… Meer...

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 1997, 744 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 3 black & white illustrations, biography, 2.47 kg, Algebra & Zahlentheorie, Naturwissenschaft & Mathematik, Fachbücher, Kategorien, Bücher, Geometrie, Naturwissenschaften & Technik, Springer, 2013<