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SPIRES-BOOKS: FIND KEYWORD ALGEBRAS,LINEAR *END*INIT* use /tmp/qspiwww.webspi1/5918.631 QRY 131.225.70.96 . find keyword algebras,linear ( 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:9783319428130:ONLINE Show nearby items on shelf
Title:Positive Operator Semigroups From Finite to Infinite Dimensions
Author(s): András Bátkai
Date:2017
Size:1 online resource (XVIII, 364 p p.)
Contents:1 An Invitation to Positive Matrices -- 2 Functional Calculus -- 3 Powers of Matrices -- 4 Matrix Exponential Function -- 5 Positive Matrices -- 6 Applications of Positive Matrices -- 7 Positive Matrix Semigroups and Applications -- 8
Positive Linear Systems -- 9 Banach Lattices -- 10 Positive Operators -- 11 Operator Semigroups -- 12 Generation Properties -- 13 Spectral Theory for Positive Semigroups I -- 14 Spectral Theory for Positive Semigroups II -- 15 An
application to linear transport equations -- Appendices -- Index
ISBN:9783319428130
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Matrix theory , Algebra , Operator theory , Mathematics , Operator Theory , Linear and Multilinear Algebras, Matrix Theory
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Call number:TA347.L5S97 Show nearby items on shelf
Title:An engineering approach to linear algebra
Author(s): Walter Warwick Sawyer 1911
Date:1972
Publisher:University Press, Cambridge [Eng
Size:304
Contents:1. Mathematics and Engineers, 2. Mappings, 3. The Nature of the Generalization, 4. Symbolic Conditions for Linearity, 5. Graphical Representation, 6. Vectors in a Plane, 7. Bases, 8. Calculations in a Vector Space, 9. Change of Axes, 10. Specification of a Linear Mapping, 11. Transformations, 12. choice of Basis, 13. Complex Numbers, 14. Calculations with Complex Numbers, 15. complex Numbers and Trigonometry, 16 Trigonometry and Exponentials, 17. complex Numbers and Convergence, 18. Complex Numbers: Terminology, 19. The Logic of Complex Numbers, 20. The Algebra of Transformations, 21. Subtraction of Transformations, 22. Matrix Notation, 23. An Application of Matrix Multiplication, 24. An Application of Linearity, 25. Procedure for Finding Invariant Lines, Eigenvectors and Eigenvalues, 26. Determinant and Inverse, 27. Properties of Determinants, 28. Matrices Other than Square: Partitions, 29. Subscript and Summation Notation, 30. row and Column Vectors, 31. Affine and Euclidean Geometry, 32. Scalar Products, 33. Transpose: Quadratic Forms, 34. Maxiumum and Minimum Principles, 35. Formal Laws of Matrix Algebra, 36. Orthogonal Transformations, 37. Finding the Simplest Expressions for Quadratic Forms, 38. Principal Axes and Eigenvectors, 39. Lines, Planes and Subspaces: Vector Product, 40. Systems of Linear Equations, 41. Null Space, Column Space, Row Space of a Matrix, 42. Illustrating the Importance of Orthogonal Matrices, 43. Linear Programming, 44. Linear Programming continued
ISBN:0521084768
Keywords: Algebras, Linear.
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Call number:SPRINGER-2016-9783319318424:ONLINE Show nearby items on shelf
Title:Hasse-Schmidt Derivations on Grassmann Algebras With Applications to Vertex Operators
Author(s): Letterio Gatto
Date:2016
Size:1 online resource (195 p.)
Note:10.1007/978-3-319-31842-4
Contents:Prologue -- Generic Linear Recurrence Sequences -- Algebras and Derivations -- Hasse-Schmidt Derivations on Exterior Algebras -- Schubert Derivations -- Decomposable Tensors in Exterior Powers -- Vertex Operators via Generic LRS -- Index
ISBN:9783319318424
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:IMPA Monographs : 4
Keywords: Mathematics , Matrix theory , Algebra , Operator theory , Differential equations , Mathematics , Linear and Multilinear Algebras, Matrix Theory , Ordinary Differential Equations , Operator Theory
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Call number:SPRINGER-2016-9783319301808:ONLINE Show nearby items on shelf
Title:Infinite Matrices and Their Recent Applications
Author(s): P.N Shivakumar
Date:2016
Size:1 online resource (118 p.)
Note:10.1007/978-3-319-30180-8
Contents:Introduction -- Finite Matrices and their Nonsingularity -- Infinite Linear Equations -- Generalized Inverses: Real or Complex Field -- Generalized Inverses: Quaternions -- M-matrices over Infinite Dimensional Spaces -- Infinite Linear Programming -- Applications.
ISBN:9783319301808
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Matrix theory , Algebra , Mathematics , Linear and Multilinear Algebras, Matrix Theory
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Call number:SPRINGER-2016-9783319284835:ONLINE Show nearby items on shelf
Title:Iterative Solution of Large Sparse Systems of Equations
Author(s): Wolfgang Hackbusch
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (11 p.)
Note:10.1007/978-3-319-28483-5
Contents:Part I: Linear Iterations -- Introduction -- Iterative Methods -- Classical Linear Iterations in the Positive Definite Case -- Analysis of Classical Iterations Under Special Structural Conditions -- Algebra of Linear Iterations -- Analysis of Posit ive Definite Iterations -- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods -- Semi-Iterative Methods -- Gradient Methods -- Conjugate Gradient Methods and Generalizations -- Part III: Special Iterations -- Multigrid Iterations -- Dom ain Decomposition and Subspace Methods -- H-LU Iteration -- Tensor-based Methods -- Appendices
ISBN:9783319284835
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Applied Mathematical Sciences: 95
Keywords: Mathematics , Matrix theory , Algebra , Partial differential equations , Numerical analysis , Mathematics , Numerical Analysis , Linear and Multilinear Algebras, Matrix Theory , Partial Differential Equations
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Call number:SPRINGER-2014-9783319079684:ONLINE Show nearby items on shelf
Title:Representation Theory [electronic resource] : A Homological Algebra Point of View
Author(s): Alexander Zimmermann
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra andrepresentations of groups to block the ory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more generalalgebras, such as symmetric finite dimensional algebras over a fie ld. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their maininvariants and links between them. Group theoretical applications of these theories are given such as the structure of blocks of cyclic defect groups whenever appropriate. Overall, many methods from the representation theory ofalgebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups andalgebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use
Contents:Rings, Algebras and Modules
Modular Representations of Finite Groups
Abelian and Triangulated Categories
Morita theory
Stable Module Categories
Derived Equivalences
ISBN:9783319079684
Series:eBooks
Series:SpringerLink
Series:Algebra and Applications, 1572-5553 : v19
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2014-9783319067285:ONLINE Show nearby items on shelf
Title:Functional Analysis [electronic resource] : An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras
Author(s): Joseph Muscat
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonovregularization, shoul d appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers themain topics, based upon the classical seque nce and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis the latter is redone in the light of metric spaces. Itcontains more than a thousand worked examples and exercises, which mak e up the main body of the book
Contents:Introduction
Distance
Convergence and Continuity
Completeness and Separability
Connectedness
Compactness
Normed Spaces
Continuous Linear Maps
Main Examples
Hilbert Spaces
Banach Spaces
Differentiation and Integration
Banach Algebras
Spectral Theory
C
Algebras
ISBN:9783319067285
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Operator theory
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Call number:SPRINGER-2014-9783319056487:ONLINE Show nearby items on shelf
Title:Spectral Mapping Theorems [electronic resource] : A Bluffer's Guide
Author(s): Robin Harte
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several andmany variables. The basic algebraic systems semigroups, rings and linear algebras are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. SpectralMapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory
Contents:Algebra
Topology
Topological algebra
Spectral theory
Several variables
Many Variables
ISBN:9783319056487
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory
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Call number:SPRINGER-2014-9783319052243:ONLINE Show nearby items on shelf
Title:Descriptive Topology and Functional Analysis [electronic resource] : In Honour of Jerzy Kakols 60th Birthday
Author(s): Juan Carlos Ferrando
Manuel Lpez-Pellicer
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topologicalAbelian groups, linear top ological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapterpresents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area
Contents:1Some aspects in the Mathematical work of Jerzy Kakol
2Weak barrelledness vs. P
spaces
3On the topology of the sets of the real projections of the zeros ofexponential polynomials
4The density character of the space Cp(X)
5Compactness and distances to spaces of continuous functions andFrchet spaces
6Two classes of metrizable spaces lc
invariant
7Characteristics of the Mackey topology for abelian topologicalgroups
8Bowens Entropy for Endomorphisms of Totally Bounded Abelian
9On preserved and unpreserved extreme pointsGroups
10Cantor set
ISBN:9783319052243
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v80
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functional analysis , Operator theory , Topology
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Call number:SPRINGER-2014-9783319048703:ONLINE Show nearby items on shelf
Title:Combinatorial Algebraic Geometry [electronic resource] : Levico Terme, Italy 2013, Editors: Sandra Di Rocco, Bernd Sturmfels
Author(s): Aldo Conca
Sandra Di Rocco
Jan Draisma
June Huh
Bernd Sturmfels
Filippo Viviani
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions, and enumerative geometry. The aim of this volume is tointroduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varietiesendowed with a rich combinatorial structure. Rele vant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications
Contents:Koszul algebras, Koszul homology and syzygies
Infinite
dimensional systems of polynomial equations with symmetry
Maximum Likelihood Geometry
Linear Toric fibrations and Cayley polytopes
Toroidal compactifications and tropicalizations of moduli spaces
ISBN:9783319048703
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2108
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Combinatorics
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Call number:SPRINGER-2014-9783319041506:ONLINE Show nearby items on shelf
Title:Introduction to Matrix Analysis and Applications [electronic resource]
Author(s): Fumio Hiai
Dnes Petz
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced bypositive semidefinite matri ces. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After anintroduction to matrices and functional analysis, it c overs more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introductionto Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information,statistics, engineering and economics
Contents:Fundamentals of operators and matrices
Mappings and algebras
Functional calculus and derivation
Matrix monotone functions and convexity
Matrix means and inequalities
Majorization and singular values
Some applications
ISBN:9783319041506
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory
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Call number:SPRINGER-2014-9783319021119:ONLINE Show nearby items on shelf
Title:The Art of Science [electronic resource] : From Perspective Drawing to Quantum Randomness
Author(s): Rossella Lupacchini
Annarita Angelini
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Like linear perspective, complex numbers and probability are notable discoveries of the Renaissance. History has been quick to recognize the crucial impact of linear perspective on painting, but reluctant to acknowledge theimportance of complex numbe rs and probability. Both were treated with a great deal of suspicion by the scientific establishment and overlooked for many years. It was only in the twentieth century, when quantum theory defined the notionof complex probability amplitude, that complex numbers merged with probability and transformed the image of the physical world. From a theoretical point of view, however, the space opened to painting by linear perspective and thespace opened to science by complex numbers are equally valuable and share significant characteristics. By exploring that common ground, The Art of Science will lead the reader to complement Leonardos vision of painting as a scienceand to see science as an art. Its aim is to restore a visual dimension to mathematical sciences an element dulled, if not obscured, by historians, philosophers, and scientists themselves
Contents:From Perspective Drawing to the Eighth Dimension
Seeing Reality in Perspective: The Art of Optics and the Science of Painting
The Role of Perspective in the Transformation of European Culture
Visual DifferentialGeometry and Beltramis Hyperbolic Plane
All Done by Mirrors: Symmetries, Quaternions, Spinors, and Clifford Algebras
Artists & Gamblers on the Way to Quantum Physics
Radices Sophisticae, Racines Imaginaires: The Origins of Complex Numbers in the Late Renaissance
Random, Complex, and Quantum
ISBN:9783319021119
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Science Philosophy , Quantum theory , Humanities
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Call number:SPRINGER-2014-9783034808163:ONLINE Show nearby items on shelf
Title:Operator Theory, Operator Algebras and Applications [electronic resource]
Author(s): M. Amlia Bastos
Amarino Lebre
Stefan Samko
Ilya M Spitkovsky
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i)operator theory and ha rmonic analysis (singular integral operators with shifts pseudodifferential operators, factorization of almost periodic matrix functions inequalities Cauchy type integrals maximal and singular operators ongeneralized Orlicz-Morrey spaces the Riesz potenti al operator modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras inner endomorphisms of some semi group,crossed products C*-algebras generated by mappings which have finite orbits Foln er sequences in operator algebras arithmetic aspect of C*_r SL(2) C*-algebras of singular integral operators algebras of operator sequences) and (iii)mathematical physics (operator approach to diffraction from polygonal-conical screens Poisson geometry of difference Lax operators)
Contents:Flner Sequences in Operator Theory and Operator Algebras
On the Factorization of Some Block Triangular Almost Periodic Matrix Functions
A C
algebra of Singular Integral Operators with Shifts Similar to Affine Mappings
On Cauchy Type Integrals Related to the Cimmino System of Partial Differential Equations
Singular Integral Operators with Linear Fractional Shifts on the Unit Circle
Diffraction from Polygonal
Conical Screens, An Operator Approach
Boundedness of the Maximal and Singular Operators on Generalized Orlicz
Morrey Spaces
On a Question by Markus Seidel
Inver
ISBN:9783034808163
Series:eBooks
Series:SpringerLink
Series:Operator Theory: Advances and Applications, 0255-0156 : v242
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory , Differential equations, partial
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Call number:SPRINGER-2014-9783034805025:ONLINE Show nearby items on shelf
Title:Algebraic Methods in Functional Analysis [electronic resource] : The Victor Shulman Anniversary Volume
Author(s): Ivan G Todorov
Lyudmila Turowska
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011. The conference was held in honour of Professor Victor Shulman on the occasion of his65th birthday. The pape rs included in the volume covera large variety of topics, among them the theory of operator ideals, linear preservers, C*-algebras, invariant subspaces, non-commutative harmonic analysis, and quantum groups,andreflect recent developments in these areas. T he book consists of bothoriginal research papers and high quality survey articles, allofwhich werecarefully refereed
Contents:Introduction
Victor Shulman: The Gentle Art of Mathematics
Operators Splitting the Arveson Spectrum
Singly Generated Operator Algebras Satisfying Weakened Versions of Amenability
Operator Algebras and C*
correspondences: A Survey
Some Operator Algebras from Semigroups
Lifting Algebraic Contractions in C*
algebras
The Second Local Multiplier Algebra of a Separable C*
algebra
Test
space Characterizations of Some Classes of Banach Spaces
Splittings of Masa
bimodules
Noncommutative Analogues of Stein Spaces of Finite Embedding Dimension
Idempotent States on Locally C
ISBN:9783034805025
Series:eBooks
Series:SpringerLink
Series:Operator Theory: Advances and Applications, 0255-0156 : v233
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Operator theory
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Call number:SPRINGER-2013-9788847028357:ONLINE Show nearby items on shelf
Title:Spectral Theory and Quantum Mechanics [electronic resource] : With an Introduction to the Algebraic Formulation
Author(s): Valter Moretti
Date:2013
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given tospectral theory features t hat are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in oneplace a number of useful rigorous statements on t he mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out toMaster's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. Thebook should benefit established researchers to organise and present the profusion of advanced ma terial disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly
Note:Springer eBooks
Contents:Introduction and mathematical backgrounds
Normed and Banach spaces, examples and applications
Hilbert spaces and bounded operators
Families of compact operators on Hilbert spaces and fundamental properties
Densely
defined unbounded operators on Hilbert spaces
Phenomenology of quantum systems and Wave Mechanics: an overview
The first 4 axioms of QM: propositions, quantum states and observables
Spectral Theory I: generalities, abstract C
algebras and operators in B(H)
Spectral theory II: unbounded operators on Hilbert spaces
Spectral Theory III: applications
Mathem
ISBN:9788847028357
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Mathematical physics
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Call number:SPRINGER-2013-9783642343698:ONLINE Show nearby items on shelf
Title:Positive Linear Maps of Operator Algebras [electronic resource]
Author(s): Erling Strmer
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 volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the studyof entanglement in quan tum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps ofoperator algebras into the bounded operators on a H ilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps positivity properties,as well as their associated linear functionals together with their density o perators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of mattersrelating to positive linear maps, of which a large proportion is relevant and applicable to today s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a wholeappeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.
Note:Springer eBooks
Contents:Introduction
1 Generalities for positive maps
2 Jordan algebras and projection maps
3 Extremal positive maps
4 Choi matrices and dual functionals
5 Mapping cones
6 Dual cones
7 States and positive maps
8 Norms of positive maps
Appendix: A.1 Topologies on B(H)
A.2 Tensor products
A.3 An extension theorem
Bibliography
Index
ISBN:9783642343698
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Functional analysis , Mathematical physics
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Call number:SPRINGER-2013-9783642310904:ONLINE Show nearby items on shelf
Title:Poisson Structures [electronic resource]
Author(s): Camille Laurent-Gengoux
Anne Pichereau
Pol Vanhaecke
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:Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of thesecontexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to theproblem in nearly all cases. Poisson Structu res is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures.The first part coverssolid foundations,the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications ofPoisson structures (integrable systems and deformation quantization). The clear structure of th e book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researcherswhoare interested in anintroduction to the many facets and applications of Poisson structures
Note:Springer eBooks
Contents:Part I Theoretical Background:1.Poisson Structures: Basic Definitions
2.Poisson Structures: Basic Constructions
3.Multi
Derivations and Khler Forms
4.Poisson (Co)Homology
5.Reduction
Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds
7.Linear Poisson Structures and Lie Algebras
8.Higher Degree Poisson Structures
9.Poisson Structures in Dimensions Two and Three
10.R
Brackets and r
Brackets
11.PoissonLie Groups
Part III Applications:12.Liouville Integrable Systems
13.Deformation Quantization
A Multilinear Algebra
B Real
ISBN:9783642310904
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v347
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global analysis (Mathematics) , Global differential geometry
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Call number:SPRINGER-2013-9783642309946:ONLINE Show nearby items on shelf
Title:Linear Algebra and Geometry [electronic resource]
Author(s): Igor R Shafarevich
Alexey O Remizov
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements ofmatrix theory and continue s with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but areusually not covered in such courses: exterior alge bras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitelygenerated periodic modules (similar to Jordan normal forms of linear opera tors). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equationsand differential geometry, as well as from mechanics and physics
Note:Springer eBooks
Contents:Preface
Preliminaries
1. Linear Equations
2. Matrices and Determinants
3. Vector Spaces
4. Linear Transformations of a Vector Space to Itself
5. Jordan Normal Form
6. Quadratic and Bilinear Forms
7. Euclidean Spaces
8. Affine Spaces
9. Projective Spaces
10. The Exterior Product and Exterior Algebras
11. Quadrics
12. Hyperbolic Geometry
13. Groups, Rings, and Modules
14. Elements of Representation Theory
Historical Note
References
Index
ISBN:9783642309946
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory , Geometry
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Call number:SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf
Title:Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations
Author(s): Sadri Hassani
Date:2013
Edition:2nd ed. 2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
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Note:The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences.
Note:Springer eBooks
Contents:Mathematical Preliminaries
I Finite
Dimensional Vector Spaces
1 Vectors and Linear Maps
2 Algebras
3 Operator Algebra
4 Matrices
5 Spectral Decomposition
II Infinite
Dimensional Vector Spaces
6 Hilbert Spaces
7 Classical Orthogonal Polynomials
8 Fourier Analysis
III Complex Analysis
9 Complex Calculus
10 Calculus of Residues
11 Advanced Topics
IV Differential Equations
12 Separation of Variables in Spherical Coordinates
13 Second
Order Linear Differential Equations
14 Complex Analysis of SOLDEs
15 Integral Transforms and Differential Equ
ISBN:9783319011950
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematics , Mathematical physics
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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-2013-9781461469988:ONLINE Show nearby items on shelf
Title:Algebraic Combinatorics [electronic resource] : Walks, Trees, Tableaux, and More
Author(s): Richard P Stanley
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the authors extensiveknowledge of combinatori cs and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfoundknowledge to mathematical, engineering, and bus iness models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory.Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints toselected exercises. Key topics include walks on graphs, cubes and the Radon transform, the MatrixTree Th eorem, de Bruijn sequences, the Erds-Moser conjecture, electrical networks, and the Sperner property. There are also threeappendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and t he enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics atthe Massachusetts Institute of Technology. Stanley has received several awards including the George Plya Prize in applied combinatorics, the Guggenheim Fello wship, and the Leroy P. Steele Prize for mathematical exposition. Also bythe author: Combinatorics and Commutative Algebra, Second Edition, Birkhuser
Note:Springer eBooks
Contents:Preface
Notation
1. Walks in graphs
2. Cubes and the Radon transform
3. Random walks
4. The Sperner property
5. Group actions on boolean algebras
6. Young diagrams and q
binomial coefficients
7. Enumeration under group action
8. A glimpse of Young tableaux
Appendix. The RSK algorithm
Appendix. Plane partitions
9. The MatrixTree Theorem
Appendix. Three elegant combinatorial proofs
10. Eulerian diagraphs and oriented trees
11. Cycles, bonds, and electrical networks
12. Miscellaneous gems of algebraic combinatorics
Hints
References
ISBN:9781461469988
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Combinatorics
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Call number:SPRINGER-2013-9781461464068:ONLINE Show nearby items on shelf
Title:Asymptotic Geometric Analysis [electronic resource] : Proceedings of the Fall 2010 Fields Institute Thematic Program
Author(s): Monika Ludwig
Vitali D Milman
Vladimir Pestov
Nicole Tomczak-Jaegermann
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as thedimension tends to inf inity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in theFall of 2010 continued an established traditi on of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces *Concentration of measure and isoperimetric inequalities, optimal transport ation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Randommatrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working ina wide range of mathematical sciencesin particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science
Note:Springer eBooks
Contents:Preface
The Variance Conjecture on Some Polytopes (D. Alonso Gutirrez, J. Bastero)
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures (D. Bartosova)
On the Lyapounov Exponents of Schrodinger Operators Associated with the Standard Map (J. Bourgain)
Overgroups of the Automorphism Group of the Rado Graph (P. Cameron, C. Laflamme, M. Pouzet, S. Tarzi, R. Woodrow)
On a Stability Property of the Generalized Spherical Radon Transform (D. Faifman)
Banach Representations and Affine Compactification of Dynamical Systems (E. Glasner, M. Megrelishvili)
F
ISBN:9781461464068
Series:e-books
Series:SpringerLink (Online service)
Series:Fields Institute Communications, 1069-5265 : v68
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functional analysis , Operator theory , Discrete groups , Distribution (Probability theory)
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Call number:SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf
Title:New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number
Author(s): Garret Sobczyk
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s
Note:Springer eBooks
Contents:1 Modular Number Systems
2 Complex and Hyperbolic Numbers
3 Geometric Algebra
4 Vector Spaces and Matrices
5 Outer Product and Determinants
6 Systems of Linear Equations
7 Linear Transformations on R^n
8 Structure of a Linear Operator
9 Linear and Bilinear Forms
10 Hermitian Inner Product Spaces
11 Geometry of Moving Planes
12 Representations of the Symmetric Group
13 Calculus on m
Surfaces
14 Differential Geometry of Curves
15 Differential Geometry of k
Surfaces
16 Mappings Between Surfaces
17 Non
Euclidean and Projective Geometries
18 Lie Gr
ISBN:9780817683856
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2012-9783642225970:ONLINE Show nearby items on shelf
Title:Topics in Noncommutative Algebra [electronic resource] : The Theorem of Campbell, Baker, Hausdorff and Dynkin
Author(s): Andrea Bonfiglioli
Roberta Fulci
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, NumericalAnalysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: 1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra ornot) to understand and apply the statements and numero us corollaries of the main result 2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view andnotation 3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincar, Pascal, Campbell, Baker, Hausdorff and Dynkin 4) give an outlook on theapplications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) 5 ) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modernliterature concerning a theorem which, though having its roots in the beginning of the20th century, has not ceased to provide new problems an d applications. The book assumes some undergraduate-level knowledge of algebra and analysis,but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool fo r beginners in Algebra
Note:Springer eBooks
Contents:1 Historical Overview
Part I Algebraic Proofs of the CBHD Theorem
2 Background Algebra
3 The Main Proof of the CBHD Theorem
4 Some Short Proofs of the CBHD Theorem
5 Convergence and Associativity for the CBHD Theorem
6 CBHD, PBW and the Free Lie Algebras
Part II Proofs of the Algebraic Prerequisites
7 Proofs of the Algebraic Prerequisites
8 Construction of Free Lie Algebras
9 Formal Power Series in One Indeterminate
10 Symmetric Algebra
ISBN:9783642225970
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2034
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry
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Call number:SPRINGER-2012-9783034804172:ONLINE Show nearby items on shelf
Title:Advances in Applied Analysis [electronic resource]
Author(s): Sergei V Rogosin
Anna A Koroleva
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book contains survey papers based on the lectures presented at the 3rd International Winter School Modern Problems of Mathematics and Mechanics held in January 2010 at the Belarusian State University, Minsk. Theselectures are devoted to differen t problems of modern analysis and its applications. An extended presentation of modern problems of applied analysis will enable the reader to get familiar with new approaches of mostly interdisciplinarycharacter. The results discussed are application orie nted and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics
Note:Springer eBooks
Contents:Introduction
Kisil, Vladimir V.: Erlangen Program at Large: Brief Outline
Laurincikas, A.: The Riemann zeta
function: approximation of analytic functions
Luchko, Yury: Anomalous diffusion: models, their analysis, and interpretation
Mityushev, Vladimir, V.: R
linear and Riemann
Hilbert problems for multiply connected domains
Plaksa, S. A.: Commutative algebras associated with classic equations of mathematical physics
Rogosin, Sergei V.: 2D Free Boundary Value Problems
ISBN:9783034804172
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Mathematics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Differential equations, partial , Number theory
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Call number:SPRINGER-2012-9781441999825:ONLINE Show nearby items on shelf
Title:Introduction to Smooth Manifolds [electronic resource]
Author(s): John M Lee
Date:2012
Edition:2nd ed. 2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific researchsmoothstructures, tangent vector s and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. Theapproach is as concrete as possible, with pictu res and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. Thissecond edition has been extensively revised and clarified, and the topic s have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, muchearlier so that they can be used throughout the book. A few new topics have been added, notably Sards theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study offirst-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds , and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, thefundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis
Note:Springer eBooks
Contents:Preface
1 Smooth Manifolds
2 Smooth Maps
3 Tangent Vectors
4 Submersions, Immersions, and Embeddings
5 Submanifolds
6 Sard's Theorem
7 Lie Groups
8 Vector Fields
9 Integral Curves and Flows
10 Vector Bundles
11 The Cotangent Bundle
12 Tensors
13 Riemannian Metrics
14 Differential Forms
15 Orientations
16 Integration on Manifolds
17 De Rham Cohomology
18 The de Rham Theorem
19Distributions and Foliations
20 The Exponential Map
21 Quotient Manifolds
22 Symplectic Manifolds
Appendix A: Review of Topology
Appendix B: Review
ISBN:9781441999825
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v218
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry
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Call number:SPRINGER-2011-9781441978929:ONLINE Show nearby items on shelf
Title:Geometric Design of Linkages [electronic resource]
Author(s): J. Michael McCarthy
Gim Song Soh
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the movement of a workpiece, or end effector, ofthe system. The function of the device is prescribed as a set of positions to be reachable by the end effector and the mechanical constraints are formed by joints that limit relative movement. The goal is to find all the devices thatcan achieve a specific task. Formulated in thi s way the design problem is purely geometric in character. Robot manipulators, walking machines, and mechanical hands are examples of articulated mechanical systems that rely on simplemechanical constraints to provide a complex workspace for the end effec tor. This new edition includes research results of the past decade on the synthesis of multiloop planar and spherical linkages, and the use of homotopy methods andClifford algebras in the synthesis of spatial serial chains. One new chapter on the synthesi s of spatial serial chains introduces the linear product decomposition of polynomial systems andpolynomial continuation solutions. The secondnew chapter introduces the Clifford algebra formulation of the kinematics equations of serial chain robots. Exampl es are used throughout to demonstrate the theory. Review of First Edition: ...I found the author had provided anexcellent text that enabled me to come to terms with the subject. Readers with an interest in the area will find the volume rewarding. -The Mat hematical Gazette (2001)
Note:Springer eBooks
Contents:Introduction
Analysis of Planar Linkages
Graphical Synthesis in the Plane
Planar Kinematics
Algebraic Synthesis of Planar
Multiloop Planar Linkages
Analysis of Spherical Linkages
Spherical Kinematics
Algebraic Synthesis of Spherical Chains
Multiloop Spherical
Analysis of Spatial Chains
Spatial Kinematics
Algebraic Synthesis of Spatial
Synthesis of Spatial Chains with Reachable Surface
Clifford Algebra Synthesis of Spatial Chains
Platform Manipulators
References
ISBN:9781441978929
Series:e-books
Series:SpringerLink (Online service)
Series:Interdisciplinary Applied Mathematics, 0939-6047 : v11
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Systems theory
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Call number:SPRINGER-2011-9781441974006:ONLINE Show nearby items on shelf
Title:An Introduction to Manifolds [electronic resource]
Author(s): Loring W Tu
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classicalmechanics, general relativity , and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By theend of the book the reader should be able to comput e, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessaryfor further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for aone-semester graduate or advanced undergraduate course, as well as by students engaged in sel f-study. The requisite point-set topology is included in an appendix of twenty-five pages other appendices review facts from real analysisand linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal un dergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for the author'spublication with Raoul Bott, Differential Forms in Algebraic Topology.
Note:Springer eBooks
Contents:Preface to the Second Edition
Preface to the First Edition
Chapter 1. Euclidean Spaces
Chapter 2. Manifolds
Chapter 3. The Tangent Space
Chapter 4. Lie Groups and Lie Algebras
Chapter 5. Differential Forms
Chapter 6. Integration
Chapter 7. De Rham Theory
Appendices
A. Point
Set Topology
B. The Inverse Function Theorem on R(N) and Related Results
C. Existence of a Partition of Unity in General
D. Linear Algebra
E. Quaternions and the Symplectic Group
Solutions to Selected Exercises
Hints and Solutions to Selected End
of
Section Problems
List of Sym
ISBN:9781441974006
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9781441969507:ONLINE Show nearby items on shelf
Title:Concrete Functional Calculus [electronic resource]
Author(s): R. M Dudley
R Norvaia
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- oroperator-valued coefficient f unction into a solution of a system of linear differential equations with the given coefficients. For nonlinear integral equations with respect to possibly discontinuous functions having unboundedvariation, existence and uniqueness of solutions are proved under suitable assumptions. Key features and topics: * Extensive usage of p-variation of functions * Applications to stochastic processes. This work will serve as a thoroughreference on its main topics for researchers and graduate students with a backgro und in real analysis and, for Chapter 12, in probability
Note:Springer eBooks
Contents:Preface
1 Introduction and Overview
2 Definitions and Basic Properties of Extended Riemann
Stieltjes Integrals
3 Phi
variation and p
variation Inequalities for Integrals
4 Banach Algebras
5 Derivatives and Analyticity in Normed Spaces
6 Nemytskii Operators on Some Function Spaces
7 Nemytskii Oerators on Lp Spaces
8 Two
Function Composition
9 Product Integration
10 Nonlinear Differential and Integral Equations
11 Fourier Series
12 Stochastic Processes and Phi
Variation
Appendix Nonatomic Measure Spaces
References
Subject Index
Author Index
Ind
ISBN:9781441969507
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Integral equations , Operator theory
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Call number:SPRINGER-2011-9780817647155:ONLINE Show nearby items on shelf
Title:An Introduction to Tensors and Group Theory for Physicists [electronic resource]
Author(s): Nadir Jeevanjee
Date:2011
Edition:1
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:An Introduction to Tensors and Group Theory for Physicists provides bothan intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystifytensors and provide a unif ied framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulationfound in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition oftensors, and concludes with applications to classical and quantum physics th rough the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that ofPart I by introducing representation theory.Exercises and examplesare provided throughout for go od practice in applying the presented definitions and techniques. Advanced undergraduate and graduate students in physics and appliedmathematics will find clarity and insight into the subject in this textbook
Note:Springer eBooks
Contents:PartI Linear Algebra and Tensors
A Quick Introduction to Tensors
Vector Spaces
Tensors
Part II Group Theory
Groups, Lie Groups, and Lie Algebras
Basic Representation Theory
The Winger
Echart Theorem and Other Applications
Appendix Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R
References
Index
ISBN:9780817647155
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Quantum theory , Mathematical physics
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Call number:SPRINGER-2010-9783764385149:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators and Symmetries [electronic resource] : Background Analysis and Advanced Topics
Author(s): Michael Ruzhansky
Ville Turunen
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim oftackling a number of import ant problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach byusing global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on thetorus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyz ed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups andhomogeneous spaces. The exposition of the book is self-contained and provides the reader with the backgro und material surrounding the theory and needed for working with pseudo-differential operators in different settings. Thebackground section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous ex amples and exercises
Note:Springer eBooks
Contents:Preface
Introduction
Part I Foundations of Analysis
A Sets, Topology and Metrics
B Elementary Functional Analysis
C Measure Theory and Integration
D Algebras
Part II Commutative Symmetries
1 Fourier Analysis on Rn
2 Pseudo
differential Operators on Rn
3 Periodic and Discrete Analysis
4 Pseudo
differential Operators on Tn
5 Commutator Characterisation of Pseudo
differential Operators
Part III Representation Theory of Compact Groups
6 Groups
7 Topological Groups
8 Linear Lie Groups
9 Hopf Algebras
Part IV Non
commutative Symmetries
10 Pseu
ISBN:9783764385149
Series:e-books
Series:SpringerLink (Online service)
Series:Pseudo-Differential Operators, Theory and Applications : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Differential equations, partial
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Call number:SPRINGER-2010-9783642111754:ONLINE Show nearby items on shelf
Title:Introduction to Complex Reflection Groups and Their Braid Groups [electronic resource]
Author(s): Michel Brou
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra. It has recently beendiscovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductivegroups. It is now also broadly agreed upon that ma ny of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic propertiesof complex reflection groups (characterization, Steinberg theorem, Gutki n-Opdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basicdefinitions and properties of the associated braid groups, as well as a quick introduction to Bes sis' lifting of Springer theory to braid groups
Note:Springer eBooks
Contents:1 Preliminaries
2 Prerequsites and Complements in Commutative Algebra
3 Polynomial Invariants of Finite Linear Groups
4 Finite Reflection Groups in Characteristic Zero
5 Eigenspaces and Regular Elements
ISBN:9783642111754
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1988
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Algebraic topology
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Call number:SPRINGER-2010-9781441962119:ONLINE Show nearby items on shelf
Title:Quadratic Forms, Linear Algebraic Groups, and Cohomology [electronic resource]
Author(s): Jean-Louis Colliot-Thlne
Skip Garibaldi
R Sujatha
Venapally Suresh
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This volume of invited works collects the most recent research and developments in quadratic forms, linear algebraic groups, and cohomology topics that are each at the intersection of algebra, number theory and algebraicgeometry. The contributions to this volume are the work of renowned experts and present new results related to the research of Raman Parimala, to whom this collection is dedicated. Some specific topics presented in this volume include,Iwasawa theory, Witt groups and sheafs, Chow motiv es, quaternion algebras, p-adic curves, and progress on the Kato conjecture as well as topics of recent interest such as field patching and a proof of the Serre's Conjecture II forfunction fields of complex surfaces. This volume is intended for researcher s and graduate students specializing in algebra, number theory, and algebraic geometry and may be suitable for supplementary use in an advanced graduatecourse
Note:Springer eBooks
Contents:Foreword
Surveys
Multiples of forms (Eva Bayer
Fluckiger)
On Saltmans p
adic curves papers (Eric Brussel)
Serres Conjecture II: a survey (Philippe Gille)
Field patching, factorization, and local
global principles (Daniel Krashen)
Deformation theory and rational points on rationally connected varieties (Max Lieblich)
Recent progress on the Kato Conjecture (Shuji Saito)
Elliptic curves and Iwasawas =0 conjecture (R. Sujatha)
Cohomological invariants of central simple algebras with involution (Jean
Pierre Tignol)
Witt groups of varieties and the purity p
ISBN:9781441962119
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt, 1389-2177 : v18
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Number theory
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Call number:SPRINGER-2010-9780387788661:ONLINE Show nearby items on shelf
Title:Groups and Symmetries [electronic resource] : From Finite Groups to Lie Groups
Author(s): Yvette Kosmann-Schwarzbach
Date:2010
Edition:First
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Key Topics: Brisk review of the basicdefinitions of group theory, wi th examples Representation theory of finite groups: character theory Representations of compact groups using the Haar measure Lie algebras and linear Lie groups Detailed study of SO(3) andSU(2), and their representations Spherical harmonics Represen tations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group This book is illustrated with portraitsand a few historical remarks. With only linear algebra and calculus as prerequisites, Grou ps and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be ofinterest to beginning graduate students. Exercises for each chapter and a collection of problems with complete sol utions make this an ideal text for the classroom and for independent study
Note:Springer eBooks
Contents:Introduction
Acknowledgments
General Facts about Groups
Representations of Finite Groups
Representations of Compact Groups
Lie Groups and Lie Algebras
Lie groups SU(2) and SO(3)
Representations of SU(2) and SO(3)
Spherical Harmonics
Representations of SU(3) and Quarks
Problems and Solutions
Bibliography
Index
ISBN:9780387788661
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Quantum theory , Crystallography
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Call number:SPRINGER-2009-9783642027802:ONLINE Show nearby items on shelf
Title:Quantum Field Theory on Curved Spacetimes [electronic resource] : Concepts and Mathematical Foundations
Author(s): Christian Br
Klaus Fredenhagen
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:After some decades of work a satisfactory theory of quantum gravity is still not available moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, tofirst approximation, one i s left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions,the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure,and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is anoutgrowth of a compact course given by the editors and contributing authors to an audience of adva nced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysison the part of the reader
Note:Springer eBooks
Contents:C*
algebras
Lorentzian Manifolds
Linear Wave Equations
Microlocal Analysis
Quantum Field Theory on Curved Backgrounds
ISBN:9783642027802
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v786
Series:Physics and Astronomy (Springer-11651)
Keywords: Cell aggregation Mathematics , Mathematical physics , Quantum theory
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Call number:SPRINGER-2009-9781402096136:ONLINE Show nearby items on shelf
Title:Bilinear Control Systems [electronic resource] : Matrices in Action
Author(s): David Elliott
Date:2009
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
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Note:A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the 1960s and has since developed into afascinating field, vita l for the solution of many challenging practical control problems. Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and thestudy of Lie semigroups. The first half of th e book is based upon matrix analysis, introducing Lie algebras and the Campbell-Baker-Hausdorff Theorem. Individual chapters are dedicated to topics such as discrete-time systems,observability and realization, examples from science and engineering, linear ization of nonlinear systems, and input-output analysis. Written by one of the leading researchers in the field in a clear and comprehensible manner and ladenwith proofs, exercises and Mathematica scripts, this involving text will be a vital and thorough introduction to the subject for first-year graduate students of control theory. It will also be of great value to academics andresearchers with an interest in matrix analysis, Lie algebra, and semigroups
Note:Springer eBooks
Contents:1. Introduction
2. Lie Algebras, Lie Groups
3. Systems in Drift
4. Discrete Time Bilinear Systems
5. Systems with Outputs
6. Examples
7. Linearization
8. Input Structures
A. Matrix Algebra
B. Lie Algebras and Groups
C. Algebraic Geometry
D. Transitive Lie Algebras
References
Index
ISBN:9781402096136
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Mathematical Sciences, 0066-5452 : v169
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra Data processing , Matrix theory , Topological Groups , Systems theory
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Call number:SPRINGER-2009-9780817649166:ONLINE Show nearby items on shelf
Title:Fourier Analysis on Finite Abelian Groups [electronic resource]
Author(s): Bao Luong
Date:2009
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thoroughlook at the Fourier tr ansform, one of the most useful tools in applied mathematics. With countless examples and unique exercise sets at the end of most sections, Fourier Analysis on Finite Abelian Groups is a perfect companion for afirst course in Fourier analysis. The first t wo chapters provide fundamental material for a strong foundation to deal with subsequent chapters. Special topics covered include: * Computing eigenvalues of the Fourier transform *Applications to Banach algebras * Tensor decompositions of the Fourier tra nsform * Quadratic Gaussian sums This book provides a useful introduction for well-prepared undergraduate and graduate students and powerful applications thatmay appeal to researchers and mathematicians. The only prerequisites are courses in group theory and linear algebra
Note:Springer eBooks
Contents:Preface
Overview
Chapter 1: Foundation Material
Results from Group Theory
Quadratic Congruences
Chebyshev Systems of Functions
Chapter 2: The Fourier Transform
A Special Class of Linear Operators
Characters
The Orthogonal Relations for Characters
The Fourier Transform
The Fourier Transform of Periodic Functions
The Inverse Fourier Transform
The Inversion Formula
Matrices of the Fourier Transform
Iterated Fourier Transform
Is the Fourier Transform a Self
Adjoint Operator?
The Convolutions Operator
Banach Algebra
The Uncertainty Principle
ISBN:9780817649166
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Fourier analysis
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Call number:SPRINGER-2009-9780387855295:ONLINE Show nearby items on shelf
Title:Elementary Functional Analysis [electronic resource]
Author(s): Barbara MacCluer
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This text is intended for a one-semester introductory course in functional analysis for graduate students and well-prepared advanced undergraduates in mathematics and related fields. It is also suitable for self-study, and couldbe used for an indepen dent reading course for undergraduates preparing to start graduate school. While this book is relatively short, the author has not sacrificed detail. Arguments are presented in full, and many examples arediscussed, making the book ideal for the reader who may be learning the material on his or her own, without the benefit of a formal course or instructor. Each chapter concludes with an extensive collection of exercises. The choice oftopics presented represents not only the author's preferences, but also h er desire to start with the basics and still travel a lively path through some significant parts of modern functional analysis. The text includes some historicalcommentary, reflecting the author's belief that some understanding of the historical context o f the development of any field in mathematics both deepens and enlivens one's appreciation of the subject. The prerequisites for this bookinclude undergraduate courses in real analysis and linear algebra, and some acquaintance with the basic notions of po int set topology. An Appendix provides an expository discussion of the more advanced real analysis prerequisites,which play a role primarily in later sections of the book. Barbara MacCluer is Professor of Mathematics at University of Virginia. She also co -authored a book with Carl Cowen, Composition Operators on Spaces of Analytic Functions (CRC1995)
Note:Springer eBooks
Contents:Preface
Hilbert Space Preliminaries
Operator Theory Basics
The Big Three
Compact Operators
Banach and C+
Algebras
The Spectral Theorem
Real Analysis Topics
References
Index
ISBN:9780387855295
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v253
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis
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Call number:SPRINGER-2009-9780387798523:ONLINE Show nearby items on shelf
Title:Symmetry, Representations, and Invariants [electronic resource]
Author(s): Roe Goodman
Nolan R Wallach
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on thegeometry and basic theory o f Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lietheory, representation theory, invariant theory, and a lgebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e.,presenting the principal theorems of representation theory for the classical matr ix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete argumentsnow given in the general case. Key Features of Symmetry, Representations, and Invariants: Early chapte rs suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, andadvanced calculus Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (sym metric group and Young tableaux) Self-contained chapters, appendices, comprehensive bibliography More than 350 exercises (most with detailed hints for solutions) further explore main concepts Serves as an excellent main text for a one-year course in Lie group theory Benefits physicists as well as mathematicians as areference work
Note:Springer eBooks
Contents:Preface
Organization and Notation
Lie Groups and Algebraic Groups
Structure of Classical Groups
Highest
Weight Theory
Algebras and Representations
Classical Invariant Theory
Spinors
Character Formulas
Branching Laws
Tensor Representations of GL(n)
Tensor Representations of O(V) and Sp(V)
Algebraic Groups and Homogeneous Spaces
Representations on Function Spaces
Algebraic Geometry
Linear and Multilinear Algebra
Associative Algebras and Lie Algebras
Manifolds and Lie Groups
References
Index of Symbols
Subject Index
ISBN:9780387798523
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v255
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Topological Groups , Mathematical physics
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Call number:SPRINGER-2008-9783540770541:ONLINE Show nearby items on shelf
Title:Integrable Hamiltonian Hierarchies [electronic resource] : Spectral and Geometric Methods
Author(s): V.S Gerdjikov
G Vilasi
A.B Yanovski
Date:2008
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it isdemonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to awide readership: from researchers in the fiel d of nonlinear completely integrable evolution equations to graduate and post-graduate students
Note:Springer eBooks
Contents:Introduction
Lax Representation and AKNS Approach
The Direct Scattering Problem
The Inverse Scattering Problem
The Generalized Fourier Transforms
Fundamental Properties of the Solvable NLEEs
Hierarchies of Hamiltonian Structures
The NLEEs and Gauge Transformations
The Classical R
Matrix Method
Smooth Manifolds
Hamiltonian Dynamics
Vector
Valued Differential Forms
Integrability and Nijenhuis Tensors
Poisson
Nijenhuis Structures Related to GZS System
Linear Bundles of Lie Algebras and Compatible Poisson Structures
ISBN:9783540770541
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v748
Series:Physics and Astronomy (Springer-11651)
Keywords: Global analysis (Mathematics) , Geometry , Mathematical physics
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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-2008-9780387782157:ONLINE Show nearby items on shelf
Title:Naive Lie Theory [electronic resource]
Author(s): John Stillwell
Date:2008
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called classical groups''that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach toLie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduceimportant results beyond those proved in the book, as part of an infor mal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regardedbooks published by Springer, including The Four Pillars of Geometry (2005), Elements of Num ber Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994)
Note:Springer eBooks
Contents:Geometry of complex numbers and quaternions
Groups
Generalized rotation groups
The exponential map
The tangent space
Structure of Lie algebras
The matrix logarithm
Topology
Simply connected Lie groups
ISBN:9780387782157
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups
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Call number:SPRINGER-2008-9780387728315:ONLINE Show nearby items on shelf
Title:Advanced Linear Algebra [electronic resource]
Author(s): Steven Roman
Date:2008
Edition:Third Edition
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over afinite field (Wedderbu rn's theorem) polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products) upgraded some proofs that wereoriginally done only for finite-dimensional/ra nk cases added new theorems, including the spectral mapping theorem considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviewsof the second edition: In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of manytopics of linear algebra and related fields...the exercises are rewritten and expanded....Ov erall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book. Ali-Akbar Jafarian,ZentralblattMATH This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints givenfor the solution of trickier problems...It represents linear algebra and does so comprehensively. Henry Ricardo, MAA Online
Note:Springer eBooks
Contents:Basic Linear Algebra
Vector Spaces
Linear Transformations
The Isomorphism Theorems
Modules I: Basic Properties
Modules II: Free and Noetherian Modules
Modules over a Principal Ideal Domain
The Structure of a Linear Operator
Eigenvalues and Eigenvectors
Real and Complex Inner Product Spaces
Structure Theory for Normal Operators
Topics
Metric Vector Spaces: The Theory of Bilinear Forms
Metric Spaces
Hilbert Spaces
Tensor Products
Positive Solutions to Linear Systems: Convexity and Separation
Affine Geometry
Singular Values and the MoorePen
ISBN:9780387728315
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v135
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory
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Call number:SPRINGER-2008-9780387724881:ONLINE Show nearby items on shelf
Title:Algebra [electronic resource] : Fields with Structure, Algebras and Advanced Topics
Author(s): Falko Lorenz
Date:2008
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by afirst course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions andalgebraic geometry. The main focus of the seco nd volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of afield, the calculus of Witt vectors, the Schur group of a field, a nd local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the Germanversion: This is a charming textbook, introducing the reader to the classical parts of algebr a. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at leastin the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews
Note:Springer eBooks
Contents:Ordered Fields and Real Fields
Hilbert's Seventeenth Problem and the Real Nullstellensatz
Orders and Quadratic Forms
Absolute Values on Fields
Residue Class Degree and Ramification Index
Local Fields
Witt Vectors
The Tsen Rank of a Field
Fundamentals of Modules
Wedderburn Theory
Crossed Products
The Brauer Group of a Local Field
Local Class Field Theory
Semisimple Representations of Finite Groups
The Schur Group of a Field
ISBN:9780387724881
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics) , Matrix theory , Number theory
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Call number:SPRINGER-2008-9780387481012:ONLINE Show nearby items on shelf
Title:An Introduction to Manifolds [electronic resource]
Author(s): Loring W Tu
Date:2008
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classicalmechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By theend of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessaryfor further study of geometry and topology. The requisite point-set topolo gy is included in an appendix of twenty pages other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many ofthe exercises and problems. This work may be used as the text for a one-semester graduate or adva nced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, AnIntroduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology
Note:Springer eBooks
Contents:Euclidean Spaces
Smooth Functions on a Euclidean Space
Tangent Vectors in Rn as Derivations
Alternating k
Linear Functions
Differential Forms on Rn
Manifolds
Manifolds
Smooth Maps on a Manifold
Quotients
Lie Groups and Lie Algebras
The Tangent Space
Submanifolds
Categories and Functors
The Rank of a Smooth Map
The Tangent Bundle
Bump Functions and Partitions of Unity
Vector Fields
Lie Groups and Lie Algebras
Lie Groups
Lie Algebras
Differential Forms
Differential 1
Forms
Differential k
Forms
The Exterior Derivative
Integra
ISBN:9780387481012
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2007-9783764382650:ONLINE Show nearby items on shelf
Title:Spectral Theory of Linear Operators [electronic resource] : and Spectral Systems in Banach Algebras
Author(s): Vladimir Mller
Date:2007
Edition:Second edition
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
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Note:This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements.Typical examples are t he one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the firsttime in a monograph. The material is self-cont ained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theoryand to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book isdedicated to the spectral theory of linear operators on Banach spaces and of elements in Banac h algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examplesare the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theor y is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph.The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The present sec ond edition contains a number of new results, in particular, concerning orbits and their relationsto the invariant subspace problem. Due to its very clear style and the careful organization of the material, this truly brilliant book may serve as an introd uction into the field, yet it also provides an excellent source of informationon specific topics in spectral theory for the working mathematician. Review of the first edition by M. Grosser, Vienna Monat
Note:Springer eBooks
Contents:Preface
I. Banach Algebras
II. Operators
III. Essential Spectrum
IV. Taylor Spectrum
V. Orbits and Capacity
Appendix
Bibliography
ISBN:9783764382650
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v139
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory
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Call number:SPRINGER-2007-9783764377960:ONLINE Show nearby items on shelf
Title:Functional Identities [electronic resource]
Author(s): Matej Brear
Mikhail A Chebotar
Wallace S Martindale
Date:2007
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The theory of functional identities (FIs) is a relatively new one - the first results were published at the beginning of the 1990s, and this is the first book on this subject. An FI can be informally described as an identicalrelation involving arbitr ary elements in an associative ring together with arbitrary (unknown) functions. The goal of the general FI theory is to describe these functions, or, when this is not possible, to describe the structure of thering admitting the FI in question. This abstr act theory has turned out to be a powerful tool for solving a variety of problems in ring theory, Lie algebras, Jordan algebras, linear algebra, and operator theory. The book is divided intothree parts. Part I is an introductory one. Part II is the core o f the book. It gives a full account of the general FI theory, which is based on the concept of a d-free set various constructions and concrete examples of d-free setsare given, and FIs on d-free sets are thoroughly studied. Part III deals with application s. Its main purpose is to demonstrate how one can find FIs when considering different problems, and then effectively use the general theoryexposed in Part II. Perhaps the most illuminating example of the applicability are solutions of long-standing Herste ins conjectures on Lie homomorphisms and Lie derivations - in the proofs practically the entire FI theory is used
Note:Springer eBooks
Contents:Part I. An Introductory Course
What is a functional identity?
Strong degree and FI
degree
Part II. The General Theory
Constructing d
free sets
FIs on d
free sets
FIs in (semi
) prime rings
Part III. Applications
Lie maps and related topics
Linear Preserver Problems
Further Applications to Lie Algebras
Appendices
Bibliography
ISBN:9783764377960
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Functional analysis
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Call number:SPRINGER-2007-9783540399469:ONLINE Show nearby items on shelf
Title:Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces [electronic resource]
Author(s): Lajos Molnr
Date:2007
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Over the past several decades, the territory of preserver problems has been continuously enlarging within the frame of linear analysis. The aim of this work is to present a sort of cross-section of the modern theory of preserverson infinite dimension al spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is put on preserver problems concerning some structures of Hilbert space operators which appear inquantum mechanics. Moreover, local automorphisms and local isometries of operator algebras and function algebras are discussed in details
Note:Springer eBooks
Contents:Preface
Introduction
1. Some Linear and Multiplicative Preserver Problems on Operator Algebras and Function Algebras
2. Preservers on Quantum Structures
3. Local Automorphisms and Local Isometries of Operator Algebras and Function Algebras
Appendix
Recent Results Added in Revision
References
Index
ISBN:9783540399469
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1895
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Quantum theory
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Call number:SPRINGER-2007-9781402054952:ONLINE Show nearby items on shelf
Title:The Linear Algebra a Beginning Graduate Student Ought to Know [electronic resource]
Author(s): Jonathan S Golan
Date:2007
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entailsan extensive corpus o f theoretical results as well as a large body of computational techniques. The book is intended to be used in one of several possible ways: (1) as a self-study guide (2) as a textbook for a course in advancedlinear algebra, either at the upper-class under graduate level or at the first-year graduate level or (3) as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifyingexams. The volume is self-contained to the extent that it does not assu me any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, suchas the solution of a small system of linear equations over the real numbers. More important ly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many ofwhich are very challenging
Note:Springer eBooks
Contents:Notation and terminology
Fields
Vector spaces over a field
Algebras over a field
Linear independence and dimension
Linear transformations
The endomorphism algebra of a vector space
Representation of linear transformations by matrices
The algebra of square matrices
Systems of linear equations
Determinants
Eigenvalues and eigenvectors
Krylov subspaces
The dual space
Inner product spaces
Orthogonality
Selfadjoint Endomorphisms
Unitary and Normal endomorphisms
Moore
Penrose pseudoinverses
Bilinear transformations and forms
ISBN:9781402054952
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Electronic data processing , Algebra , Matrix theory , Algorithms
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