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Call number: | 9783319463100:ONLINE Show nearby items on shelf |
Title: | Mathematics Across Contemporary Sciences AUS-ICMS, Sharjah, UAE, April 2015 |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (X, 259 p. 22 illus., 5 illus. in color p.) |
Contents: | 1 Samirah Alsulami, Hellen Colman and Frank Neumann: The Lusternik-Schnirelmann Category for a Differentiable Stack -- 2 Richard A. Brualdi and Shi-Mei Ma: Centrosymmetric, Symmetric and Hankel-Symmetric Matrices -- 3 Costanza |
Catalano and Alberto Gandolfi: Partially Independent Random Variables -- 4 Dmitry Efimov and Hana Sulieman: Sobol Sensitivity for Machine Learning -- 5 Jon Pierre Fortney: Basis Independence of Implicitly Defined Hamiltonian Circuit | |
Dynamics -- 6 Hichem Hajaeij: On a New Class of Variational Problems -- 7 A. Samad Hedayat: A Scientific Tour on Orthogonal Arrays -- 8 Hadi Kharaghani and Sho Suda: Hoffman’s Coclique Bound for Normal Regular Diagraphs and | |
Nonsymmetric Association Schemes -- 9 Salim A. Messaoudi and Soh Edwin Mukiawa: A Suspension Bridge Problem: Existence and Stability -- 10 Greg Orosi: An Interpolation-Based Approach to American Put Option Pricing -- 11 Inès Saihi: | |
Stable Homotopy Groups of Moore Spaces -- 12 Minjia Shi, Yiping Zhang and Patrick Solé: Notes on Quasi-Cyclic Codes with Cyclic Constituent Codes -- 13 Linda Smail and Zineb Azouz: Factorization of Computations in Bayesian Networks: | |
Interpretation of Factors -- 14 Abessamad Tridane, Mohamed Ali Hajji and Eduardo Mojica-Nava: Optimal Drug Treatment in a Simple Pandemic Switched System -- 15 Thomas Wunderli: On Carathéodory quasilinear functionals for BV functions | |
and their time flows for a dual H^1 penalty model for image restoration | |
ISBN: | 9783319463100 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Matrix theory , Algebra , Mathematical analysis , Analysis (Mathematics) , Mathematical physics , Mathematics , Mathematical Applications in the Physical Sciences , Linear and Multilinear Algebras, Matrix Theory , Analysis |
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Call number: | 9783319419176:ONLINE Show nearby items on shelf |
Title: | An Introduction to the Language of Category Theory |
Author(s): |
Steven Roman |
Date: | 2017 |
Size: | 1 online resource (XII, 169 p. 176 illus., 5 illus. in color p.) |
Contents: | Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index |
ISBN: | 9783319419176 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Algebra , Ordered algebraic structures , Mathematics , Category Theory, Homological Algebra , Order, Lattices, Ordered Algebraic Structures , General Algebraic Systems |
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Call number: | 9780465051694:ONLINE Show nearby items on shelf |
Title: | How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics |
Author(s): |
Eugenia Cheng |
Date: | 2015 |
Publisher: | New York, NY: Basic Books |
Size: | 1 online resource (288 p) |
Contents: | Math. What is math?, Abstraction, Principles, Process, Generalization, Internal vs. external, Axiomatization, What mathematics is -- Category theory. What is category theory?, Context, Relationships, Structure, Sameness, Universal properties, What category theory is. |
ISBN: | 9780465051717 |
Series: | eBooks |
Series: | EBL eBook |
Keywords: | Mathematics. |
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Location: | NEW |
Call number: | SPRINGER-2016-9784431560562:ONLINE Show nearby items on shelf |
Title: | Structural Analysis of Metallic Glasses with Computational Homology |
Author(s): |
Akihiko Hirata |
Date: | 2016 |
Size: | 1 online resource (7 p.) |
Note: | 10.1007/978-4-431-56056-2 |
Contents: | 1. Introduction -- 2. Metallic glasses -- 2.1. What is glass? -- 2-2. Structure and properties of metallic glasses -- 2-3. Structure determination and its difficulty -- 3. Homology and computational homology -- 3.1. Cubical complex -- 3.2. Cubical homology -- 3.3. Computing homology groups -- 4. Structure analysis of metallic glasses -- 4.1. Advantage of computational homology -- 4.2. Preparation of input data for metallic glasses -- 4.3. Computing procedure for metallic glasses -- 4.4. Interpretat ion of results obtained by computational homology -- 5. Appendix |
ISBN: | 9784431560562 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | SpringerBriefs in the Mathematics of Materials: 2 |
Keywords: | Mathematics , Chemometrics , Category theory (Mathematics) , Homological algebra , Mathematical physics , Mathematics , Mathematical Applications in the Physical Sciences , Category Theory, Homological Algebra , Math. Applications in Chemistry |
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Call number: | SPRINGER-2016-9783662493618:ONLINE Show nearby items on shelf |
Title: | Topologie algébrique Chapitres 1 à 4 |
Author(s): |
N Bourbaki |
Date: | 2016 |
Size: | 1 online resource (498 p.) |
Note: | 10.1007/978-3-662-49361-8 |
Contents: | Mode d'Emploi -- Introduction -- Chapitre I. Revêtements -- 1. Produits fibrés et carrés cartésiens -- 2. Applications étales -- 3. Faisceaux -- 4. Revêtements -- 5. Revêtements principaux -- 6. Espaces simplement connexes -- Exercices -- Ch apitre II. Groupoïdes -- 1. Carquois -- 2. Graphes -- 3. Groupoïdes -- 4. Homotopies -- 5. Coégalisateur -- Exercices -- Chapitre III. Homotopie et Groupoïdes de Poincaré -- 1. Homotopies, homéotopies -- 2. Homotopie et chemins -- 3. Groupoïde de P oincaré -- 4. Homotopie et revêtements -- 5. Homotopie et revêtements (cas des espaces localement connexes par arcs) -- Exercices -- Chapitre IV. Espaces Delaçables -- 1. Espaces délaçables -- 2. Groupes de Poincaré des espaces délaçables -- 3. G roupes de Poincaré des groupes topologiques -- 4. Théorie de la descente -- 5. Théorème de van Kampen -- 6. Espaces classifiants -- Exercices -- Index des notations -- Index terminologique |
ISBN: | 9783662493618 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Group theory , Algebraic topology , Manifolds (Mathematics) , Complex manifolds , Mathematics , Algebraic Topology , Category Theory, Homological Algebra , Manifolds and Cell Complexes (incl. Diff.Topology) , Group Theory and Generalizations |
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Call number: | SPRINGER-2016-9783658106331:ONLINE Show nearby items on shelf |
Title: | Manifolds, Sheaves, and Cohomology |
Author(s): |
Torsten Wedhorn |
Date: | 2016 |
Size: | 1 online resource (354 p.) |
Note: | 10.1007/978-3-658-10633-1 |
Contents: | Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis |
ISBN: | 9783658106331 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319311593:ONLINE Show nearby items on shelf |
Title: | Continuity Theory |
Author(s): |
Louis Nel |
Date: | 2016 |
Size: | 1 online resource (460 p.) |
Note: | 10.1007/978-3-319-31159-3 |
Contents: | Overview -- General Preparation -- Continuity Enabling Structures -- Construction of New Spaces -- Various Kinds of Spaces -- Fundamentals of Linear Continuity -- Basic Categorical Concepts -- The Category C -- Reflective Categories of C -- Enriche d Dualities -- The Category CV -- Reflective Subcategories of CV -- Linear Continuous Representations -- Smooth Continuity -- Supplementary Reading. |
ISBN: | 9783319311593 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Topology , Mathematics , Functional Analysis , Topology |
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Call number: | SPRINGER-2016-9783319264370:ONLINE Show nearby items on shelf |
Title: | Minimal Free Resolutions over Complete Intersections |
Author(s): |
David Eisenbud |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (107 p.) |
Note: | 10.1007/978-3-319-26437-0 |
ISBN: | 9783319264370 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2152 |
Keywords: | Mathematics , Algebraic geometry , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Physics , Mathematics , Commutative Rings and Algebras , Algebraic Geometry , Category Theory, Homological Algebra , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-2016-9783319247564:ONLINE Show nearby items on shelf |
Title: | Modern Logic 1850-1950, East and West |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (4 p.) |
Note: | 10.1007/978-3-319-24756-4 |
Contents: | Contributors -- Introduction -- Irving H. Anellis: Preface and Prospectus -- Irving H. Anellis and Francine F. Abeles: The Historical Sources of Tree Graphs and the Tree Method in the Work of Peirce and Gentzen -- Jean Paul Van Bendegem: Logic and A rgumentation in Belgium: The Role of Leo Apostel -- Philippe de Rouilhan: Tarski’s Recantation: Reading the Postscript to “Wahrheitsbegriff” -- Jan Woleński: The Paradox of Analyticity and Related Issues -- David DeVidi and Herbert Korté: Naturali zing Natural Deduction -- Alberto Peruzzi: Category Theory and the Search for Universals: A Very Short Guide for Philosophers -- Roman Murawski: On the Way to Modern Logic – The Case of Polish Logic -- Valentin A. Bazhanov: Russian Origins of Non-Classi cal Logics -- Vladik Kreinovich: Constructive Mathematics in St. Petersburg, Russia: A (Somewhat Subjective) View from Within -- Jonathan P. Seldin: On Normalizing Disjunctive Intermediate Logic -- R.E. Hodel: A Natural Axiom System for Boolean |
Algebras with Applications. | |
ISBN: | 9783319247564 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Logic , History , Mathematical logic , Mathematics , Mathematical Logic and Foundations , Logic , History of Mathematical Sciences |
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Call number: | SPRINGER-2016-9783319234885:ONLINE Show nearby items on shelf |
Title: | Homotopical Topology |
Author(s): |
Anatoly Fomenko |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (627 p.) |
Note: | 10.1007/978-3-319-23488-5 |
Contents: | Introduction -- Homotopy -- Homology -- Spectral Sequences of Fibrations -- Cohomology Operations -- The Adams Spectral Sequence -- K-Theory and Other Extraordinary Cohomology Theories |
ISBN: | 9783319234885 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 273 |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , K-theory , Algebraic topology , Mathematics , Category Theory, Homological Algebra , K-Theory , Algebraic Topology |
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Call number: | SPRINGER-2014-9788132215998:ONLINE Show nearby items on shelf |
Title: | Basic Modern Algebra with Applications [electronic resource] |
Author(s): |
Mahima Ranjan Adhikari Avishek Adhikari |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource |
Contents: | Prerequisites: Basics of Set Theory and Integers |
Groups: Introductory Concepts | |
Actions of Groups, Topological Groups and semigroups | |
Rings: Introductory Concepts | |
Ideals of Rings: Introductory concepts | |
Factorization in Integral Domains and in Polynomial Rings | |
Rings with Chain Conditions | |
Vector Spaces | |
Modules | |
Algebraic Aspects of Number Theory | |
Algebraic Numbers | |
Introduction to Mathematical Cryptography | |
Appendix A: Some Aspects of Semirings | |
Appendix B: Category Theory | |
Appendix C: A Brief Historical Note | |
ISBN: | 9788132215998 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Number theory |
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Call number: | SPRINGER-2014-9783642393839:ONLINE Show nearby items on shelf |
Title: | Conformal Field Theories and Tensor Categories [electronic resource] : Proceedings of a Workshop Held at Beijing International Center for Mathematical Research |
Author(s): |
Chengming Bai Jrgen Fuchs Yi-Zhi Huang Liang Kong Ingo Runkel Christoph Schweigert |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | The present volume is a collection of seven papers that are either based on the talks presented at the workshop Conformal field theories and tensor categories held June 13 to June 17, 2011 at the Beijing International Centerfor Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories andnew applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gappedsystems, logarithmic conformal field theories and the corresponding no n-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductorymaterial that is helpful for graduate students and researchers looking for an introduction to th ese research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categoriesand their applications and will be extremely useful for researchers working in these areas |
Contents: | From Hopf algebras to tensor categories |
Pattern | |
of | |
zeros approach to Fractional quantum Hall states and a classification of symmetric polynomial of infinite variables | |
Virasoro central changes for Nichols algebras | |
Logarithmic bulk and boundary conformal field theory and the full centre construction | |
Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules | |
C2 | |
cofinite w | |
algebras and their logarithmic representations | |
C1 | |
co_niteness and fusion products of vertex operator al | |
ISBN: | 9783642393839 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematical Lectures from Peking University, 2197-4209 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2014-9783319029528:ONLINE Show nearby items on shelf |
Title: | Advances in Lie Superalgebras [electronic resource] |
Author(s): |
Maria Gorelik Paolo Papi |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The volume is the outcome of the conference Lie superalgebras, which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held providedcomprehensive insights into the n ewest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field andprovides a complete account of the newest trends in r esearch on Lie Superalgebras |
Contents: | 1 A. Alldridge, Z. Shaikh: Superbosonisation, Riesz superdistributions, and highest weight modules |
2 K. Coulembier: Homological algebra for osp(1|2n) | |
3 A. DAndrea: Finiteness and orbifold vertex operator algebras | |
4 A. De Sole: On classical finite and affine W | |
algebras | |
5 M. Gorelik, D. Grantcharov: Q | |
type Lie superalgebras | |
6 C. Hoyt: Weight modules for the Lie superalgebra D(2,1,a) | |
7 R. Fioresi, S. Kwok: On SUSY curves | |
8 V. G. Kac, P. Moseneder Frajria, P. Papi: Dirac operators and the Very Strange Formula for Lie superalgebras | |
9 V. Mazorchuk: Parabolic category O fo | |
ISBN: | 9783319029528 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v7 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topology |
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Call number: | SPRINGER-2014-9781461495338:ONLINE Show nearby items on shelf |
Title: | Genericity in Nonlinear Analysis [electronic resource] |
Author(s): |
Simeon Reich Alexander J Zaslavski |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This book presents an extensive collection of state-of-the-art results and references in nonlinear functional analysis demonstrating how the generic approach proves to be very useful in solving many interesting and importantproblems. Nonlinear analys is plays an ever-increasing role in theoretical and applied mathematics, as well as in many other areas of science such as engineering, statistics, computer science, economics, finance, and medicine. The textmay be used as supplementary material for gradu ate courses in nonlinear functional analysis, optimization theory and approximation theory, and is a treasure trove for instructors, researchers, and practitioners in mathematics and inthe mathematical sciences. Each chapter is self-contained proofs are solid and carefully communicated. Genericity in Nonlinear Analysis is the first book to systematically present the generic approach to nonlinear analysis. Topicspresented include convergence analysis of powers and infinite products via the Baire Category Theorem, fixed point theory of both single- and set-valued mappings, best approximation problems, discrete and continuous descent methods forminimization in a general Banach space, and the structure of minimal energy configurations with rational numbers i n the AubryMather theory |
Contents: | Preface |
1. Introduction | |
2. Fixed Point Results and Convergence of Powers of Operators | |
3. Contractive Mappings | |
4. Dynamical Systems with Convex Lyapunov Functions | |
5. Relatively Nonexpansive Operators with Respect to Bregman Distances | |
6. Infinite Products | |
7.Best Approximation | |
8. Descent Methods | |
9. Set | |
Valued Mappings | |
References | |
Index | |
ISBN: | 9781461495338 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Developments in Mathematics, 1389-2177 : v34 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory , Mathematical optimization |
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Call number: | SPRINGER-2013-9783642394850:ONLINE Show nearby items on shelf |
Title: | Algebras, Quivers and Representations [electronic resource] : The Abel Symposium 2011 |
Author(s): |
Aslak Bakke Buan Idun Reiten yvind Solberg |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas ofmathematics like commutati ve algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systemsand triangulated categories. In addition, it in cludes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students inalgebra, representation theory and triangulated categories |
Note: | Springer eBooks |
Contents: | C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions |
L. Avramov: (Contravariant) Koszul duality for DG algebras | |
R. Buchweitz: The fundamental group of a morphism in a triangulated category | |
K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras | |
D. Happel: Algebras of finite global dimension | |
K. Igusa (with G. Todorov): Continuous Frobenius categories | |
D.A. Jorgensen: Triangle functors from generic hypersurfaces | |
Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian | |
H. Krause: Mo | |
ISBN: | 9783642394850 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Abel Symposia, 2193-2808 : v8 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9783642307096:ONLINE Show nearby items on shelf |
Title: | Variational, Topological, and Partial Order Methods with Their Applications [electronic resource] |
Author(s): |
Zhitao Zhang |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry,measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been usedextensively to solve existence of solutions for ellipt ic equations, wave equations, Schrdinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This bookis useful for researchers and graduate students in the field of nonlinear fu nctional analysis. Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, andmixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the auth or uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with aclass of MongeAmpre equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications i s studied. Chapter 7 is devoted to the DancerFucik spectrum. In Chapter 8, some results on sign-changingsolutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, thefocus is on free boundary problems, Schrdinger systems from BoseEinstein condensate and competing systems with many species |
Note: | Springer eBooks |
Contents: | 1 Preliminaries |
Sobolev spaces and embedding theorems | |
Critical point | |
Cone and partial order | |
Brouwer Degree | |
Compact map and Leray | |
Schauder Degree | |
Fredholm operators | |
Fixed point index | |
Banach's Contract Theorem, Implicit Functions Theorem | |
Krein | |
Rutman theorem | |
Bifurcation theory | |
Rearrangements of sets and functions | |
Genus and Category | |
Maximum principles and symmetry of solution | |
Comparison theorems | |
2 Cone and Partial Order Methods | |
Increasing operators | |
Decreasing operators | |
Mixed monotone operators | |
Applications of mixed monotone operators | |
Fur | |
ISBN: | 9783642307096 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, 1389-2177 : v29 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2013-9783034805858:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators, Generalized Functions and Asymptotics [electronic resource] |
Author(s): |
Shahla Molahajloo Stevan Pilipovi Joachim Toft M. W Wong |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume consists of twenty peer-reviewed papers from the special sessions on pseudodifferential operators and on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples FriendshipUniversity of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifoldswith edges, heat kernels and Green functions of sub-Lapla cians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, L^p-boundedness of pseudo-differential operators on thetorus, and pseudo-differential operators related to time-frequency analysis. The s econd group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlineardifferential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differ ential equations. This second group of papers is related to the third collection of papers via the setting ofColombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volumecontains the synergi es of the three areas treatedand is a useful complement toitspredecessorspublished in the same series |
Note: | Springer eBooks |
Contents: | Preface |
Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds | |
The Singular Functions of Branching Edge Asymptotics | |
The Heat Kernel and Green Function of the Sub | |
Laplacian on the Heisenberg Group | |
Metaplectic Equivalence of the Hierarchical Twisted Laplacian | |
The Heat Kernel and Green Function of a Sub | |
Laplacian on the Hierarchical Heisenberg Group | |
Lp | |
Bounds for Pseudo | |
Differential Operators on the Torus | |
Multiplication Properties in Gelfand | |
Shilov Pseudo | |
Differential Calculus | |
Operator Invariance | |
Initial Value Problems in the Time | |
Frequency Do | |
ISBN: | 9783034805858 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v231 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034804783:ONLINE Show nearby items on shelf |
Title: | Functional Analysis in Asymmetric Normed Spaces [electronic resource] |
Author(s): |
tefan Cobza |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the normimplies that the mult iplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, ismerely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplaybetween the asymmetric norm p and its conjugate. Among the positi ve results one can mention: HahnBanach type theorems and separation results for convex sets, KreinMilman type theorems, analogs of the fundamental principles open mapping, closed graph and uniform boundedness theorems an analog of the Schauders theorem o n the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, oneconsiders normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since t he basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of thebook contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in function al analysis completeness, compactness and Baire category which drasticallydiffer from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analys is, so it may be used for an introduction to thesubject.Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference |
Note: | Springer eBooks |
Contents: | Introduction |
1. Quasi | |
metric and Quasi | |
uniform Spaces. 1.1. Topological properties of quasi | |
metric and quasi | |
uniform spaces | |
1.2. Completeness and compactness in quasi | |
metric and quasi | |
uniform spaces | |
2. Asymmetric Functional Analysis | |
2.1. Continuous linear operators between asymmetric normed spaces | |
2.2. Hahn | |
Banach type theorems and the separation of convex sets | |
2.3. The fundamental principles | |
2.4. Weak topologies | |
2.5. Applications to best approximation | |
2.6. Spaces of semi | |
Lipschitz functions | |
Bibliography | |
Index | |
ISBN: | 9783034804783 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory , Topology |
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Call number: | SPRINGER-2013-9781461462712:ONLINE Show nearby items on shelf |
Title: | Elementary Analysis [electronic resource] : The Theory of Calculus |
Author(s): |
Kenneth A Ross |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very usefulfor mathematics major s who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and thelarge number of well-chosen examples and exerc ises range from routine to challenging. The second edition preserves the books clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics includematerial on the irrationality of pi, the Baire category theorem, Newton' s method and the secant method, and continuous nowhere-differentiable functions. Review from the first edition: This book is intended for the student who has agood, but nave, understanding of elementary calculus and now wishes to gain a thorough understan ding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation andmethods of proof, and ... has succeeded admirably. MATHEMATICAL REVIEWS |
Note: | Springer eBooks |
Contents: | Preface |
1 Introduction | |
2 Sequences | |
3 Continuity | |
4 Sequences and Series of Functions | |
5 Differentiation | |
6 Integration | |
7 Capstone | |
Appendix on Set Notation | |
Selected Hints and Answers | |
References | |
Index | |
ISBN: | 9781461462712 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2013-9781447148630:ONLINE Show nearby items on shelf |
Title: | Symmetries, Integrable Systems and Representations [electronic resource] |
Author(s): |
Kenji Iohara Sophie Morier-Genoud Bertrand Rmy |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is the result of two international workshops Infinite Analysis 11 Frontier of Integrability held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems andRepresentations held at Universit Claude Be rnard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some reviewarticles. The subjects discussed range across diverse areas such as algeb raic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through thesetopics, the readerwill find some recent developments in the field of mathematical physics and thei r interactions with several other domains |
Note: | Springer eBooks |
Contents: | A presentation of the deformed W1+1 algebra |
Generating series of the Poincar polynomials of quasihomogeneous Hilbert schemes | |
PBW filtration over Z and compatible bases for VZ(_) in type An and Cn | |
On the subgeneric restricted blocks of affine category O at the critical level | |
Slavnov determinants, Yang | |
Mills structure constants, and discrete KP | |
Monodromy of partial KZ functors for rational Cherednik algebras | |
Category of finite dimensional modules over an orthosymplectic Lie superalgebra: small rank examples | |
Monoidal categorifications of cluster algebras of type A and D | |
ISBN: | 9781447148630 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v40 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Functions, special , Combinatorics , Mathematical physics |
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Call number: | SPRINGER-2013-9781447148326:ONLINE Show nearby items on shelf |
Title: | Modular Representation Theory of Finite Groups [electronic resource] |
Author(s): |
Peter Schneider |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for exampleover the fieldof complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory of finitegroups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as wellas Green's direct analysis of indecomposable representations. Ther e is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's workthen establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple acategory a block is by the size and structure of its so-called 'defect group'. All these concepts are made explic it for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentationis strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the read er the group theoretic approach. In particular, in the case of defect groups a detailed proof of theequivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with thesemisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwis |
Note: | Springer eBooks |
Contents: | Prerequisites in module theory |
The Cartan{Brauer triangle | |
The Brauer character | |
Green's theory of indecomposable modules | |
Blocks | |
ISBN: | 9781447148326 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2012-9783642295140:ONLINE Show nearby items on shelf |
Title: | A1-Algebraic Topology over a Field [electronic resource] |
Author(s): |
Fabien Morel |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This text deals with A^{1}-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It isa natural sequel to the foundational paper on A^{1}-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to theproperties and computations of A^{1-homotopy sheaves, A1-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties} |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Unramified sheaves and strongly A1 | |
invariant sheaves | |
3 Unramified Milnor | |
Witt K | |
theories | |
4 Geometric versus canonical transfers | |
5 The Rost | |
Schmid complex of a strongly A1 | |
invariant sheaf | |
6 A1 | |
homotopy sheaves and A1 | |
homology sheaves | |
7 A1 | |
coverings | |
8 A1 | |
homotopy and algebraic vector bundles | |
9 The affine B.G. property for the linear groups and the Grassmanian | |
ISBN: | 9783642295140 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2052 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , K-theory , Algebraic topology |
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Call number: | SPRINGER-2012-9783642192258:ONLINE Show nearby items on shelf |
Title: | A Royal Road to Algebraic Geometry [electronic resource] |
Author(s): |
Audun Holme |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to readall of his work Eleme nts. Euclid is said to have answered: There is no royal road to geometry! The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royalroad to algebraic geometry. From a point of depart ure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendiecks theory of schemes. Contemporary homological tools areexplained. The reader will follow a directed path leading up to the main elem ents of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to awonderful field of research. The greatest scientific experience of a lifetime! |
Note: | Springer eBooks |
Contents: | Part I Curves: 1 Affine and Projective Space |
2 Curves in A2 k and in P2 | |
3 Higher Geometry in the Projective Plane | |
4 Plane Curves and Algebra | |
5 Projective Varieties in PNk | |
Part II Introduction to Grothendiecks Theory of Schemes: 6 Categories and Functors | |
7 Constructions and Representable Functors | |
8 Abelian Categories | |
9 The Concept of Spec(A) | |
10 The Category of Schemes | |
11 Properties of Morphisms of Schemes | |
12 Modules, Algebras and Bundles on a Scheme | |
13 More Properties of Morphisms, Scheme Theoretic Image and the Sorite | |
14 Projective Schemes and Bu | |
ISBN: | 9783642192258 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Geometry , Algebraic topology |
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Call number: | SPRINGER-2012-9783034804059:ONLINE Show nearby items on shelf |
Title: | Associahedra, Tamari Lattices and Related Structures [electronic resource] : Tamari Memorial Festschrift |
Author(s): |
Folkert Mller-Hoissen Jean Marcel Pallo Jim Stasheff |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. Thiswas the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematicalwork. Tamari lattices ca n be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure andapplied mathematics, such as algebra, combinator ics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari'scentennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers inmathematics and mathematical physics and are accompanied by high quality illustrations |
Note: | Springer eBooks |
ISBN: | 9783034804059 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v299 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Discrete groups , Number theory , Algebraic topology |
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Call number: | SPRINGER-2012-9783034802604:ONLINE Show nearby items on shelf |
Title: | Representations of Finite Groups: Local Cohomology and Support [electronic resource] |
Author(s): |
David J Benson Srikanth Iyengar Henning Krause |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas fromcommutative algebra, co homology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been DanielQuillens description of the algebraic variety co rresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods ofalgebraic geometry to obtain representation theoretic information. Thei r work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutativeHopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins classification ofthick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localiz ing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approachto address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with rin g of operators. The book serves as an introduction to this circle of ideas |
Note: | Springer eBooks |
Contents: | Preface |
1 Monday | |
1.1 Overview | |
1.2 Modules over group algebras | |
1.3 Triangulated categories | |
1.4 Exercises | |
2 Tuesday | |
2.1 Perfect complexes over commutative rings | |
2.2 Brown representability and localization | |
2.3 The stable module category of a finite group | |
2.4 Exercises | |
3 Wednesday | |
3.1 | |
3.2 Koszul objects and support | |
3.3 The homotopy category of injectives | |
3.4 Exercises | |
4 Thursday | |
4.1 Stratifying triangulated categories | |
4.2 Consequences of stratification | |
4.3 The Klein four group | |
4.4 Exercises | |
5 Friday | |
5.1 Localising subcategories of D | |
ISBN: | 9783034802604 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Oberwolfach Seminars : v43 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2012-9783034801546:ONLINE Show nearby items on shelf |
Title: | Frames and Locales [electronic resource] : Topology without points |
Author(s): |
Jorge Picado Ale Pultr |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the 1920s offered an expression of the geometric intuition of arealistic place (spot, gr ain) of non-trivial extent. Imitating the behaviour of open sets and their relationsled to a new approach to topology flourishing since the end of the 1950s. It has proved to be beneficial in manyrespects. Neglecting points, only little information was lo st, while deeper insights have been gained moreover, many results previously dependent onchoice principles became constructive. The result is often a smoother, rather than amore entangled, theory. No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book formfor the first time or is presented from new points of view. Two appendices provide an introduction to s ome requisite concepts from order and category theories |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
I. Spaces and lattices of open sets | |
II. Frames and locales. Spectra | |
III. Sublocales | |
IV. Structure of localic morphisms. The categories Loc and Frm | |
V. Separation axioms | |
VI. More on sublocales | |
VII. Compactness and local compactness | |
VIII. (Symmetric) uniformity and nearness | |
IX. Paracompactness | |
X. More about completion | |
XI. Metric frames | |
XII. Entourages, non | |
symmetric uniformity | |
XIII. Connectedness | |
XIV. The frame of reals and real functions | |
XV. Localic groups | |
Appendix I: Posets | |
Appendix II: Categories | |
Bibliography | |
Index | |
ISBN: | 9783034801546 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topology |
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Call number: | SPRINGER-2012-9781447122944:ONLINE Show nearby items on shelf |
Title: | Syzygies and Homotopy Theory [electronic resource] |
Author(s): |
F.E.A Johnson |
Date: | 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivialfundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematicrehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. Theinnovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation these are confronted in the second, practical, part of the book. Inparticular, the second part of the book considers how the theory works out in detail for the specific e xamples Fn F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms ofthe more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potentialapplications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of inte rest to researchers and also to graduate students with a background in algebra andalgebraic topology |
Note: | Springer eBooks |
Contents: | Preliminaries |
The restricted linear group | |
The calculus of corners and squares | |
Extensions of modules | |
The derived module category | |
Finiteness conditions | |
The Swan mapping | |
Classification of algebraic complexes | |
Rings with stably free cancellation | |
Group rings of cyclic groups | |
Group rings of dihedral groups | |
Group rings of quaternionic groups | |
Parametrizing W1 (Z) : generic case | |
Parametrizing W1 (Z) : singular case | |
Generalized Swan modules | |
Parametrizing W1 (Z) : G = C F | |
Conclusion | |
ISBN: | 9781447122944 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications, 1572-5553 : v17 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2011-9783642217746:ONLINE Show nearby items on shelf |
Title: | From Objects to Diagrams for Ranges of Functors [electronic resource] |
Author(s): |
Pierre Gillibert Friedrich Wehrung |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
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Note: | This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). Thebasic idea is: if a fu nctor lifts many objects, then it also lifts many (poset-indexed) diagrams |
Note: | Springer eBooks |
Contents: | 1 Background |
2 Boolean Algebras Scaled with Respect to a Poset | |
3 The Condensate Lifting Lemma (CLL) | |
4 Larders from First | |
order Structures | |
5 Congruence | |
Preserving Extensions | |
6 Larders from von Neumann Regular Rings | |
7 Discussion | |
ISBN: | 9783642217746 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2029 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , K-theory , Logic, Symbolic and mathematical |
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Call number: | SPRINGER-2011-9783642109799:ONLINE Show nearby items on shelf |
Title: | Categories and Commutative Algebra [electronic resource] |
Author(s): |
P Salmon |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | L. Badescu: Sur certaines singularits des varits algbriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algbriques.- B.A. Mitchell:Introduction to category theory and homolog ical algebra.- R. Rivet: Anneaux de sries formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria allalgebra commutativa.- M. Tierney: Axiomatic sheaf theory: someconstructions and applications.- C.B. Winters: An elementary lecture on alg ebraic spaces |
Note: | Springer eBooks |
Contents: | L. Badescu: Sur certaines singularits des varits algbriques |
D.A. Buchsbaum: Homological and commutative algebra | |
S. Greco: Anelli Henseliani | |
C. Lair: Morphismes et structures algbriques | |
B.A. Mitchell: Introduction to category theory and homological algebra | |
R. Rivet: Anneaux de sries formelles et anneaux henseliens | |
P. Salmon: Applicazioni della K | |
teoria allalgebra commutativa | |
M. Tierney: Axiomatic sheaf theory: some constructions and applications | |
C.B. Winters: An elementary lecture on algebraic spaces | |
ISBN: | 9783642109799 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v58 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2011-9783034800068:ONLINE Show nearby items on shelf |
Title: | The Structure of the Real Line [electronic resource] |
Author(s): |
Lev Bukovsk |
Date: | 2011 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The rapid development of set theory in the last fifty years, mainly in obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the realline and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of settheory, topology, measure theory, descriptive set theory are revisited with the purpose to eliminate superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statementspertaining to properties of the real line are shown to be undecidable in s et theory. The metamathematics behind it is shortly explained in the appendix. Each section contains a series of exercises with additional results |
Note: | Springer eBooks |
Contents: | Preface |
1 Introduction | |
2 The Real Line | |
3 Topology of Euclidean Spaces | |
4 Measure Theory | |
5 Useful Tools and Technologies | |
6 Descriptive Set Theory | |
7 Decline and Fall of the Duality | |
8 Special Sets of Reals | |
9 Additional Axioms | |
10 Undecidable Statements | |
11 Appendix | |
Bibliography | |
Index of Notation | |
Index | |
ISBN: | 9783034800068 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne : v71 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2011-9783034604055:ONLINE Show nearby items on shelf |
Title: | From Past to Future: Gramann's Work in Context [electronic resource] : Gramann Bicentennial Conference, September 2009 |
Author(s): |
Hans-Joachim Petsche Albert C Lewis Jrg Liesen Steve Russ |
Date: | 2011 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | On the occasion of the 200th anniversary of the birth of Hermann Gramann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Gramann's hometown Szczecin, Poland. The idea of the conference was topresent a multi-faceted p icture of Gramann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Gramann's work forphilosophical as well as for scientific and methodological questions, for com parative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least,mathematics. In addition, the book contains numerous illustrations and English translations of orig inal sources, which are published here for the first time. These include life histories of Gramann (written by his son Justus) and ofhis brother Robert (written by Robert himself), as well as the paper On the concept and extent of pure theory of number'' by Justus Gramann (the father). In November 2010 the capital of the federal state of Brandenburg (Germany)chose the Gramann Conference as the first-time winner of the Potsdam Conference-Award in the category Innovative and/or exceptional events |
Note: | Springer eBooks |
ISBN: | 9783034604055 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematics_$xHistory |
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Call number: | SPRINGER-2010-9783034800525:ONLINE Show nearby items on shelf |
Title: | Simplicial Methods for Operads and Algebraic Geometry [electronic resource] |
Author(s): |
Ieke Moerdijk Bertrand Ton |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijks lectures offer a detailed introduction to dendroidal sets, which wereintroduced by himself and Weiss a s a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it alsoreveals new phenomena. For example, dendroidal sets ad mit a closed symmetric monoidal structure related to the BoardmanVogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with asuitable model structure on the category of dendroidal sets. Important concepts ar e illustrated with pictures and examples. The lecture series by Ton presents derived algebraic geometry. While classical algebraic geometry studiesfunctors from the category of commutative rings to the category of sets, derived algebraic geometry is conce rned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derivedquotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent conditi on. These lectures provide a concise and focused introduction to this vast subject, glossing over manyof the technicalities that make the subjects research literature so overwhelming. Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Tons lectures, some background in algebraicgeometry is also necessary |
Note: | Springer eBooks |
ISBN: | 9783034800525 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Advanced Courses in Mathematics - CRM Barcelona |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Algebraic topology |
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Call number: | SPRINGER-2010-9783034604369:ONLINE Show nearby items on shelf |
Title: | Homological Algebra of Semimodules and Semicontramodules [electronic resource] : Semi-infinite Homological Algebra of Associative Algebraic Structures |
Author(s): |
Leonid Positselski |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on thesemi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary centralcharges, and relative non-homogeneous Koszul du ality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras,contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish- Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules,introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featur ed prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra andthe theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theo ry. In particular, it will be a valuable addition to the algebraic literature available to mathematicalphysicists |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
0 Preliminaries and Summary | |
1 Semialgebras and Semitensor Product | |
2 Derived Functor SemiTor | |
3 Semicontramodules and Semihomomorphisms | |
4 Derived Functor SemiExt | |
5 Comodule | |
Contramodule Correspondence | |
6 Semimodule | |
Semicontramodule Correspondence | |
7 Functoriality in the Coring | |
8 Functoriality in the Semialgebra | |
9 Closed Model Category Structures | |
10 A Construction of Semialgebras | |
11 Relative Nonhomogeneous Koszul Duality | |
Appendix A Contramodules over Coalgebras over Fields | |
Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Se | |
ISBN: | 9783034604369 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry |
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Call number: | SPRINGER-2010-9781849962513:ONLINE Show nearby items on shelf |
Title: | Mathematica: A Problem-Centered Approach [electronic resource] |
Author(s): |
Roozbeh Hazrat |
Date: | 2010 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Mathematica: A Problem-Centered Approach introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked- out problems. Each section startswith a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate theuse of new commands in Mathematica whilst solvi ng each problem presented - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations and - the third presents morechallenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students ofmathematics, science, engineering and finance, the book also includes chapters on calculus and sol ving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problemsolving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computationaltool. Mathematica: A Problem-Centered Approach comes with a free 30 day trial of the Wolfram Mathematica(R) software |
Note: | Springer eBooks |
Contents: | 1. Introduction |
1.1 Mathematica as a calculator | |
1.2 Numbers | |
1.3 Algebraic computations | |
1.4 Trigonometric computations | |
1.5 Variables | |
1.6 Equalities =, :=, == | |
1.7 Dynamic variables | |
2. Defining functions | |
2.1 Formulas as functions | |
2.2 Anonymous functions | |
3. Lists | |
3.1 Functions producing lists | |
3.2 Listable functions | |
3.3 Selecting from a list | |
4. Changing heads! | |
5. A bit of logic and set theory | |
5.1 Being logical | |
5.2 Handling sets | |
5.3 Decision making, If and Which | |
6. Sums and products | |
6.1 Sum | |
6.2 Product | |
7. Loops and repetitions | |
7 | |
ISBN: | 9781849962513 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 : v53 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Algebra Data processing , Computer software |
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Call number: | SPRINGER-2010-9781441917218:ONLINE Show nearby items on shelf |
Title: | Lattice-ordered Rings and Modules [electronic resource] |
Author(s): |
Stuart A Steinberg |
Date: | 2010 |
Edition: | First |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the workself-contained and ac cessible to a variety of readers is included. Steinberg includes in his presentation of the material 800+ extensive exercises of varying levels of difficulty at the end of each of the sections. The first twochapters of the book provide a thorough introduc tion to the material, while the following four chapters delve into more specific topics. Key topics include: *lattice-ordered groups, rings, and fields *archimedean $l$-groups *f-ringsand larger varieties of $l$-rings *the category of f-modules *various c ommutativity results. Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students andresearchers studying lattice-ordered rings and lattice-ordered modules |
Note: | Springer eBooks |
Contents: | Partially Ordered Sets and Lattices |
Lattice | |
ordered Groups | |
Lattice | |
ordered Rings | |
The Category of | |
Modules | |
Lattice | |
ordered Fields | |
Additional Topics | |
ISBN: | 9781441917218 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2010-9781441915245:ONLINE Show nearby items on shelf |
Title: | Towards Higher Categories [electronic resource] |
Author(s): |
John C Baez J. Peter May |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman whichexplores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are thentwo survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theoryexists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives athorough, but informal, guide to this theory. A paper by Larry Breen on the theory of ge rbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australianschool of category theory, and an historical paper by Ross Street describes its development |
Note: | Springer eBooks |
Contents: | Foreword |
Preface | |
Lectures on n | |
categories and cohomology | |
A survey of (1, 1) | |
categories | |
Internal categorical structures in homotopical algebra | |
A 2 | |
categories companion | |
Notes on 1 | |
and 2 | |
gerbes | |
An Australian conspectus of higher categories | |
IMA summer program participants | |
ISBN: | 9781441915245 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | The IMA Volumes in Mathematics and its Applications, 0940-6573 : v152 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topology , Algebraic topology |
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Call number: | SPRINGER-2009-9783764399986:ONLINE Show nearby items on shelf |
Title: | Frobenius Categories versus Brauer Blocks [electronic resource] : The Grothendieck Group of the Frobenius Category of a Brauer Block |
Author(s): |
Llus Puig |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book contributes to important questions in the representation theory of finite groups over fields of positive characteristic an area of research initiated by Richard Brauer sixty years ago with the introduction of theblocks of characters. On th e one hand, it introduces and develops the abstract setting of the Frobenius categories also called the Saturated fusion systems in the literature created by the author fifteen years ago for a betterunderstanding of what was loosely called the local the ory of a finite group around a prime number p or, later, around a Brauer block, and for the purpose of an eventual classification a reasonable concept of simple Frobeniuscategory arises. On the other hand, the book develops this abstract setting in paral lel with its application to the Brauer blocks, giving the detailed translation of any abstract concept in the particular context of the blocks. One ofthe new features in this direction is a framework for a deeper understanding of one of the central open p roblems in modular representation theory, known as Alperins Weight Conjecture (AWC). Actually, this new framework suggests amore general form of AWC, and a significant result of the book is a reduction theorem of this form of AWC to quasi-simple groups. A lthough this book is a research monograph, all the arguments are widely developed to make it accessibleto the interested graduate students and, at the same time, to put them on the verge of the research on this new subject: the third part of the book on t he localities associated to a Frobenius category gives some insight on the openquestion about the existence and the uniquenes of a perfect locality also called centric linking system in the literature. We have developed a long introduction to explain our purpose and to provide a guideline for the readerthroughout the twenty four sections. A systematic appendix on the cohomology of categories completes the book |
Note: | Springer eBooks |
ISBN: | 9783764399986 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v274 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Algebraic topology |
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Call number: | SPRINGER-2009-9783764399900:ONLINE Show nearby items on shelf |
Title: | Regularity and Substructures of Hom [electronic resource] |
Author(s): |
Friedrich Kasch Adolf Mader |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book generalizes the well-known regularity of ring elements to regularity of homomorphisms in module categories, and further to regularity of morphisms in any category. Regular homomorphisms are characterized in terms ofdecompositions of domain a nd codomain, and numerous other results are presented. While the theory is well developed in module categories many questions remain about generalizations and extensions to other categories. The book onlyrequires the knowledge of a basic course in modern algebra. It is written clearly, with great detail, and is accessible to students and researchers alike |
Note: | Springer eBooks |
ISBN: | 9783764399900 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2009-9783764387365:ONLINE Show nearby items on shelf |
Title: | Quantum Field Theory [electronic resource] : Competitive Models |
Author(s): |
Bertfried Fauser Jrgen Tolksdorf Eberhard Zeidler |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. Thepresent book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including generalconsiderations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT.The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions arecommitted to the idea of this workshop series: 'To bring together outstanding experts worki ng in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics' |
Note: | Springer eBooks |
Contents: | Constructive Use of Holographic Projections |
Topos Theory and Neo | |
Realist Quantum Theory | |
A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications | |
A Comment on the Infra | |
Red Problem in the AdS/CFT Correspondence | |
Some Steps Towards Noncommutative Mirror Symmetry on the Torus | |
Wittens Volume Formula, Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions | |
Noncommutative Field Theories from a Deformation Point of View | |
Renormalization of Gauge Fields using Hopf Algebras | |
Not so Non | |
Renormali | |
ISBN: | 9783764387365 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2009-9783642001482:ONLINE Show nearby items on shelf |
Title: | The Rubato Composer Music Software [electronic resource] Component-Based Implementation of a Functorial Concept Architecture |
Author(s): |
Grard Milmeister |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Both modern mathematical music theory and computer science are strongly influenced by the theory of categories and functors. One outcome of this research is the data format of denotators, which is based on set-valued presheavesover the category of mo dules and diaffine homomorphisms. The functorial approach of denotators deals with generalized points in the form of arrows and allows the construction of a universal concept architecture. This architecture isideal for handling all aspects of music, espec ially for the analysis and composition of highly abstract musical works. This book presents an introduction to the theory of module categories and the theory of denotators, as well as thedesign of a software system, called Rubato Composer, which is an imp lementation of the category-theoretic concept framework. The application is written in portable Java and relies on plug-in components, so-called rubettes, which may becombined in data flow networks for the generation and manipulation of denotators. The Ru bato Composer system is open to arbitrary extension and is freely available under the GPL license. It allows the developer to build specializedrubettes for tasks that are of interest to composers, who in turn combine them to create music. It equally serve s music theorists, who use them to extract information from and manipulate musical structures. They may even develop newtheories by experimenting with the many parameters that are at their disposal thanks to the increased flexibility of the functorial con cept architecture. Two contributed chapters by Guerino Mazzola and Florian Thalmann illustrate theapplication of the theory as well as the software in the development of compositional tools and the creation of a musical work with the help of the Rubato fr amework |
Note: | Springer eBooks |
Contents: | Concepts and Theory |
Overview of Music Theories | |
The Representation of Music | |
Architecture of Concepts I: Principles | |
The Category of Modules | |
Architecture of Concepts II: Forms and Denotators | |
Software Components for Computational Theories | |
Historical Overview | |
The Implementation | |
Overview | |
Architecture | |
Modules and Morphisms | |
Forms and Denotators | |
Tools and Utilities | |
Rubato Composer GUI | |
Rubato Composer in Practice | |
Overview | |
A Tutorial | |
First Applications in Rubette Construction | |
The BigBang Rubette | |
Creative Analysis of Boulezs | |
Conclusion and | |
ISBN: | 9783642001482 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Computational Music Science, 1868-0305 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Information systems , Computer science , Algebra , Music |
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Call number: | SPRINGER-2009-9783540890560:ONLINE Show nearby items on shelf |
Title: | Modules over Operads and Functors [electronic resource] |
Author(s): |
Benoit Fresse |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structureof iterated loop spac es. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modulesover operads as a new device to model functor s between categories of algebras as effectively as operads model categories of algebras |
Note: | Springer eBooks |
Contents: | Categorical and operadic background |
Symmetric monoidal categories for operads | |
Symmetric objects and functors | |
Operads and algebras in symmetric monoidal categories | |
Miscellaneous structures associated to algebras over operads | |
The category of right modules over operads and functors | |
Definitions and basic constructions | |
Tensor products | |
Universal constructions on right modules over operads | |
Adjunction and embedding properties | |
Algebras in right modules over operads | |
Miscellaneous examples | |
Homotopical background | |
Symmetric monoidal model categories for operads | |
The | |
ISBN: | 9783540890560 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1967 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Algebraic topology |
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Call number: | SPRINGER-2009-9783034601894:ONLINE Show nearby items on shelf |
Title: | Simplicial Homotopy Theory [electronic resource] |
Author(s): |
Paul G Goerss John F Jardine |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed modelcategory and, in particula r, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, includingalgebraic K-theory. This book supplies a modern e xposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups,Postnikov towers, and bisimplicial sets. The more advanced material in cludes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence.Interspersed throughout are many results and ideas well-known to experts, but uncollected in the lit erature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory.An extensive background in topology is not assumed. Reviews: a book filling an obvious gap in the literature and the au thors have done an excellent job on it. No monograph or expository paper has been published on this topic inthe last twenty-eight years. - Analele Universitatii din Timisoara is clearly presented and a brief summary preceding every chapter is useful to t he reader. The book should prove enlightening to a broad range of readersincluding prospective students and researchers who want to apply simplicial techniques for whatever reason. - Zentralblatt MATH they succeed. The book is an excellent account of sim plicial homotopy theory from a modern point ofview [] The book is well written. [] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques |
Note: | Springer eBooks |
ISBN: | 9783034601894 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2009-9780817646639:ONLINE Show nearby items on shelf |
Title: | Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics [electronic resource] |
Author(s): |
Claudio Bartocci Ugo Bruzzo Daniel Hernndez Ruiprez |
Date: | 2009 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry,category theory, gauge theory , and string theory has been closely related to generalizations of integral transforms of a more geometric character. FourierMukai and Nahm Transforms in Geometry and Mathematical Physics examines thealgebro-geometric approach (FourierMukai functors) as w ell as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organizedinto a monograph. Key features: * Basic constructions and definitions are presen ted in preliminary background chapters * Presentation explores applications and suggests several open questions * Extensive bibliography and index Thisself-contained monograph provides an introduction to current research in geometry and mathematical physi cs and is intended for graduate students and researchers just entering this field |
Note: | Springer eBooks |
Contents: | Integral functors |
Fourier | |
Mukai functors | |
Fourier | |
Mukai on Abelian varieties | |
Fourier | |
Mukai on K3 surfaces | |
Nahm transforms | |
Relative Fourier | |
Mukai functors | |
Fourier | |
Mukai partners and birational geometry | |
Derived and triangulated categories | |
Lattices | |
Miscellaneous results | |
Stability conditions for derived categories | |
ISBN: | 9780817646639 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v276 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial , Global differential geometry , Mathematical physics |
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Call number: | SPRINGER-2008-9783764387426:ONLINE Show nearby items on shelf |
Title: | Modules and Comodules [electronic resource] |
Author(s): |
Tomasz Brzeziski Jos Luis Gmez Pardo Ivan Shestakov Patrick F Smith |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and dedicated to Robert Wisbauer on the occasion of his 65th birthday. Thesearticles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory, some of which have a long tradition whereas others have emerged in recent years. They include topics in the formaltheory of modules bordering on category theory, in ring theory, in Hopf algebras and quantum groups, and in corings and comodules |
Note: | Springer eBooks |
Contents: | Injective Morita Contexts (Revisited) |
A Categorical Proof of a Useful Result | |
On Nichols Algebras with Generic Braiding | |
Dual Algebras of Some Semisimple Finite | |
dimensional Hopf Algebras | |
Balanced Bilinear Forms for Corings | |
Ring Hulls of Semiprime Homomorphic Images | |
Notes on Formal Smoothness | |
Certain Chain Conditions in Modules over Dedekind Domains and Related Rings | |
? | |
Injective Modules | |
A Note on Polynomial Rings over Nil Rings | |
QI | |
modules | |
Corings with Exact Rational Functors and Injective Objects | |
Preradicals of Associative Algebras and their Connections with Pr | |
ISBN: | 9783764387426 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2008-9783540719625:ONLINE Show nearby items on shelf |
Title: | Combinatorial Algebraic Topology [electronic resource] |
Author(s): |
Dmitry Kozlov |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part ofthe book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - willprobably find particularly useful the sec ond part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existingtexts. In addition, several new themes, such as spectral sequ ences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing thetopological structure theory for graph homomorphisms. The main benefit for the read er will be the prospect of fairly quickly getting to the forefront of modern research in this active field |
Note: | Springer eBooks |
Contents: | Concepts of Algebraic Topology |
Overture | |
Cell Complexes | |
Homology Groups | |
Concepts of Category Theory | |
Exact Sequences | |
Homotopy | |
Cofibrations | |
Principal ? | |
Bundles and StiefelWhitney Characteristic Classes | |
Methods of Combinatorial Algebraic Topology | |
Combinatorial Complexes Melange | |
Acyclic Categories | |
Discrete Morse Theory | |
Lexicographic Shellability | |
Evasiveness and Closure Operators | |
Colimits and Quotients | |
Homotopy Colimits | |
Spectral Sequences | |
Complexes of Graph Homomorphisms | |
Chromatic Numbers and the Kneser Conjecture | |
Structural Theory of Mo | |
ISBN: | 9783540719625 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algorithms and Computation in Mathematics, 1431-1550 : v21 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Combinatorics , Algebraic topology |
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Call number: | SPRINGER-2008-9780387789019:ONLINE Show nearby items on shelf |
Title: | Lattices and Ordered Sets [electronic resource] |
Author(s): |
Steven Roman |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study.Prerequisites are ke pt to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on wellordering and ordinal numbers, which is not u sually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises. Topic coverage includes: modular, semimodular anddistributive lattices, boolean algebras, representation of distr ibutive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more. Steven Roman is the author of manysuccessful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), F ield Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004) |
Note: | Springer eBooks |
Contents: | Preface |
Partially Ordered Sets | |
Well | |
Ordered Sets | |
Lattices | |
Modular and Distributive Lattices | |
Boolean Algebras | |
The Representation of Distributive Lattices | |
Algebraic Lattices | |
Prime and Maximal Ideals: Separation Theorems | |
Congruence Relations on Lattices | |
Duality for Distributive Lattices: The Priestley Topology | |
Free Lattices | |
Fixed | |
Point Theorems | |
Appendix A: A Bit of Topology | |
Appendix B: A Bit of Category Theory | |
References | |
Index of Symbols | |
Index | |
ISBN: | 9780387789019 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2007-9783764375249:ONLINE Show nearby items on shelf |
Title: | Tool and Object [electronic resource] : A History and Philosophy of Category Theory |
Author(s): |
Ralf Krmer |
Date: | 2007 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematicalsubdisciplines (above all algebraic topology and algebraic geometry) is analyzed. Category theory also has an important philosophical aspect: on the one hand its set-theoretical foundation is less obvious than for other mathematicaltheories, and on the other hand it unifies concep tually a large part of modern mathematics and may therefore be considered as somewhat fundamental itself. The role of this philosophical aspect in the historical development is thesecond focus of the book. Relying on the historical analysis, the author de velops a philosophical interpretation of the theory of his own, intending to get closer to how mathematicians conceive the significance of their activity thantraditional schools of philosophy of science. The book is the first monography exclusively devote d to the history of category theory. To a substantial extent it considers aspects never studied before. The author uses (and justifies theuse of) a methodology combining historical and philosophical approaches. The analysis is not confined to general rema rks, but goes into considerable mathematical detail. Hence, the book provides an exceptionally thorough case studycompared with other works on history or philosophy of mathematics. The philosophical position developed here (inspired by Peircean pragmatism and Wittgenstein) is an interesting alternative to traditional approaches in philosophy ofmathematics like platonism, formalism and intuitionism |
Note: | Springer eBooks |
Contents: | Prelude: Poincar, Wittgenstein, Peirce, and the use of concepts |
Category theory in Algebraic Topology | |
Category theory in Homological Algebra | |
Category theory in Algebraic Geometry | |
From tool to object: full | |
fledged category theory | |
Categories as sets: problems and solutions | |
Categorial foundations | |
Pragmatism and category theory | |
ISBN: | 9783764375249 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Science Networks. Historical Studies : v32 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Mathematics_$xHistory |
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Call number: | SPRINGER-2007-9783540368243:ONLINE Show nearby items on shelf |
Title: | Algebraic Cobordism [electronic resource] |
Author(s): |
Marc Levine Fabien Morel |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (incharacteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over theLazard ring by the elements of positive degrees. Th is implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications |
Note: | Springer eBooks |
Contents: | Introduction |
I. Cobordism and oriented cohomology | |
1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism | |
II. The definition of algebraic cobordism. 2.1. Oriented Borel | |
Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism | |
III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extende | |
ISBN: | 9783540368243 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , K-theory |
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Call number: | SPRINGER-2007-9780817645830:ONLINE Show nearby items on shelf |
Title: | Metric Structures for Riemannian and Non-Riemannian Spaces [electronic resource] |
Author(s): |
Mikhail Gromov |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups andprobability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metrictheory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the GromovHausdorff distance between Riemannian manifolds. This distanceorganizes Riemannian manifolds of all possible topological types into a singl e connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya,Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced ne w invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degreesof maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosi s, stimulated by the LevyMilman concentration phenomenon, encompassing the law of large numbers for metricspaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which tur ned into the famous Green Book by Lafontaine and Pansu (1979). The present Englishtranslation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendicesby Gromov on Levy's inequality, by Pansu o n quasiconvex domains, by Katz on systoles ofRiemannian manifolds, and by Semmes overviewing analysis on metric spaces with measuresas well as an extensive bibliography and index round o |
Note: | Springer eBooks |
Contents: | Preface to the French Edition |
Preface to the English Edition | |
Introduction: Metrics Everywhere | |
Length Structures: Path Metric Spaces | |
Degree and Dilatation | |
Metric Structures on Families of Metric Spaces | |
Convergence and Concentration of Metrics and Measures | |
Loewner Rediscovered | |
Manifolds with Bounded Ricci Curvature | |
Isoperimetric Inequalities and Amenability | |
Morse Theory and Minimal Models | |
Pinching and Collapse | |
Appendix A: Quasiconvex Domains in Rn | |
Appendix B: Metric Spaces and Mappings Seen at Many Scales | |
Appendix C: Paul Levy's Isoperimetric Inequalit | |
ISBN: | 9780817645830 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global differential geometry , Distribution (Probability theory) , Algebraic topology , Cell aggregation Mathematics |
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Call number: | SPRINGER-2007-9780817645748:ONLINE Show nearby items on shelf |
Title: | The Grothendieck Festschrift [electronic resource] A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck |
Author(s): |
Pierre Cartier Luc Illusie Nicholas M Katz Grard Laumon Yuri I Manin Kenneth A Ribet |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The many diverse articles presented in these three volumes, collected on the occasion of Alexander Grothendiecks sixtieth birthday and originally published in 1990, were offered as a tribute to one of the worlds greatestliving mathematicians. Grothen dieck changed the very way we think about many branches of mathematics. Many of his ideas, revolutionary when introduced, now seem so natural as to have been inevitable. Indeed, it is difficult to fullygrasp the influence his vast contributions to modern mathematics have subsequently had on new generations of mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundationalto the subject. Topics addressed by these top-notch contributors match th e breadth of Grothendiecks own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory,K-theory, category theory, and homological algebra. CONTRIBUTORS to Volume I: A. Altman M. Artin V. Bala ji A. Beauville A.A. Beilinson P. Berthelot J.-M. Bismut S. Bloch L. Breen J.-L. Brylinski J. Dieudonn H. Gillet A.B.Goncharov K. Kato S. Kleiman W. Messing V.V. Schechtman C.S. Seshadri C. Soul J. Tate M. van den Bergh and A.N. Varchenko |
Note: | Springer eBooks |
Contents: | Foreword |
Bibliographie d'Alexander Grothendieck | |
Dieudonne | |
Altman and Kleiman | |
Artin, Tate, and van den Bergh | |
Balaji and Seshadri | |
Beauville | |
Beilinson, Goncharov, Schechtman, and Varchenko | |
Berthelot and Messing | |
Bismut, Gillet, and Soule | |
Bloch and Kato | |
Breen | |
Brylinski | |
ISBN: | 9780817645748 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , K-theory , Functional analysis , Number theory , Algebraic topology |
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