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SPIRES-BOOKS: FIND KEYWORD CATEGORY THEORY MATHEMATICS *END*INIT* use /tmp/qspiwww.webspi1/13323.59 QRY 131.225.70.96 . find keyword "category theory mathematics" ( in books using www Cover
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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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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
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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
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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
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Note:This text deals with A1-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 A1-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 A1-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
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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
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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
Note:Springer e-book platform
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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