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SPIRES-BOOKS: FIND KEYWORD FIELD THEORY AND POLYNOMIALS *END*INIT* use /tmp/qspiwww.webspi1/11392.8 QRY 131.225.70.96 . find keyword field theory and polynomials ( in books using www Cover
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Call number:SPRINGER-2016-9783319304519:ONLINE Show nearby items on shelf
Title:Symmetries in Graphs, Maps, and Polytopes 5th SIGMAP Workshop, West Malvern, UK, July 2014
Author(s):
Date:2016
Edition:1st ed. 2016
Size:1 online resource (332 p.)
Note:10.1007/978-3-319-30451-9
ISBN:9783319304519
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 159
Keywords: Mathematics , Algebra , Field theory (Physics) , Topological groups , Lie groups , Graph theory , Mathematics , Graph Theory , Field Theory and Polynomials , Topological Groups, Lie Groups
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Call number:SPRINGER-2016-9783319273235:ONLINE Show nearby items on shelf
Title:Non-Archimedean Operator Theory
Author(s): Toka Diagana
Date:2016
Size:1 online resource (156 p.)
Note:10.1007/978-3-319-27323-5
ISBN:9783319273235
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Field theory (Physics) , Functional analysis , Operator theory , Functions of real variables , Mathematics , Operator Theory , Functional Analysis , Field Theory and Polynomials , Real Functions
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Call number:SPRINGER-2016-9783319259017:ONLINE Show nearby items on shelf
Title:Perturbative Algebraic Quantum Field Theory An Introduction for Mathematicians
Author(s): Kasia Rejzner
Date:2016
Edition:1st ed. 2016
Size:1 online resource (180 p.)
Note:10.1007/978-3-319-25901-7
Contents:Introduction -- Algebraic approach to quantum theory -- Algebraic quantum mechanics -- Causality -- Haag-Kastler axioms -- pAQFT axioms -- LCQFT -- Kinematical structure -- The space of field configurations -- Functionals on the
configuration space -- Fermionic field configurations -- Vector fields -- Functorial interpretation -- Classical theory -- Dynamics -- Natural Lagrangians -- Homological characterization of the solution space -- The net of topological
Poisson algabras -- Analogy with classical mechanics -- Deformation quantization -- Star products -- The star product on the space of multivector fields -- Kähler structure -- Interaction -- Outline of the approach -- Scatering matrix
and time ordered products -- Renormalization group -- Interacting local nets -- Explicit construction -- Gauge theories -- Classical gauge theory -- Gauge-fixing -- BV formalism -- Effective quantum gravity -- From LCQFT to quantum
gravity -- Dynamics and symmetries -- Linearized theory -- Quantization -- Relational observables -- Background independence
ISBN:9783319259017
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Algebra , Field theory (Physics) , Mathematical physics , Quantum field theory , String theory , Physics , Quantum Field Theories, String Theory , Mathematical Physics , Field Theory and Polynomials
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Call number:SPRINGER-2014-9783319052540:ONLINE Show nearby items on shelf
Title:Trends in Contemporary Mathematics [electronic resource]
Author(s): Vincenzo Ancona
Elisabetta Strickland
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book covers a wide spectrum of hot topics and current trends in mathematics, including noncommutative algebra via deformation theory, optimal transportation, nonlinear potential theory,kinetic theory and gas dynamics,geometric numerical integrat ion, finite simple groups of small essential dimension, optimal control problems, extended Dynkin diagrams, spin glasses, aspherical closed manifolds, Boltzmann systems, birational geometry of projectivevarieties and directed graphs, nonlinear diffusion, geometric constructions of extremal metrics on complex manifolds, and Pells equation in polynomials. The book comprises a selection of contributions by leading internationalmathematicians who were speakers at the INdAM Day, an initiative dating back to 20 04 at which the most recent developments in contemporary mathematics are presented
Contents:1 F. Guerra: Interpolation and comparison methods in the mean field spin glass model
2 A. De Sole, V.G. Kac, D. Valeri: Integrability of dirac reduced Bi
Hamiltonian equations
3 W. Luck: Some open problems about aspherical closed manifolds abstract
4 P. Etingof: Exploring noncommutative algebras via deformation theory
5 G. Lancia: Mathematical models and solutions for the analysis of human genotypes
6 M. Manetti: Kodaira
Spencer formality of products of complex manifolds
7 O. Debarre, B. Lass: Monomial transformations of the projective space
8 J.L. Vazquez: Progress in the
ISBN:9783319052540
Series:eBooks
Series:SpringerLink
Series:Springer INdAM Series, 2281-518X : v8
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Global analysis (Mathematics) , Differential equations, partial , Computer science Mathematics
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Call number:SPRINGER-2014-9783319035185:ONLINE Show nearby items on shelf
Title:Networks of Networks: The Last Frontier of Complexity [electronic resource]
Author(s): Gregorio D'Agostino
Antonio Scala
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The present work is meant as a reference to provide an organic and comprehensive view of the most relevant results in the exciting new field of Networks of Networks (NetoNets). Seminal papers have recently been published posingthe basis to study what happens when different networks interact, thus providing evidence for the emergence of new, unexpected behaviors and vulnerabilities. From those seminal works, the awareness on the importance understandingNetworks of Networks (NetoNets) has spread to the entire community of Complexity Science. The reader will benefit from the experience of some of the most well-recognized leaders in this field. The contents have been aggregated underfour headings General Theory, Phenomenology, Applications and Risk Asses sment. The reader will be impressed by the different applications of the general paradigm that span from physiology, to financial risk, to transports. We arecurrently making the first steps to reduce the distance between the language and the way of thinki ng of the two communities of experts in real infrastructures and the complexity scientists. Although this path may prove to be long, itis extremely promising, both in extending our understanding of complex systems and in finding concrete applications that can enhance the life quality of millions of people
Contents:Part I Theoretical Approaches
Network of Interdependent Networks: Overview of Theory and Applications (18 April 2013)
Avalanches in Multiplex and Interdependent Networks
Multiple Networks
Modeling Interconnected Networks as Random Graphs: Connectivity and Systemic Risk
Thresholds and Complex Dynamics of Interdependent Cascading Infrastructure Systems
Part II Applications
Characterizing Relevant Network Structure with Reliability Polynomials
Spatial Effects: Transport on Interdependent Networks
Electrical Networks An Introduction
Smart Grid as Multi
Layer In
ISBN:9783319035185
Series:eBooks
Series:SpringerLink
Series:Understanding Complex Systems, 1860-0832
Series:Physics and Astronomy (Springer-11651)
Keywords: Engineering , Economics, Mathematical
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Call number:SPRINGER-2014-9781493909254:ONLINE Show nearby items on shelf
Title:Commutative Algebra [electronic resource] : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions
Author(s): Marco Fontana
Sophie Frisch
Sarah Glaz
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point tofuture directions of rese arch in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics andresearch methods include Noetherian and non- Noetheri an ring theory as well as integer-valued polynomials and functions. Specific topics include: Homological dimensions of Prfer-like rings Quasi complete rings Total graphs of rings Properties of prime ideals over various rings Bases for integer-valued p olynomials Boolean subrings The portable property of domains Probabilistic topics inIntn(D) Closure operations in Zariski-Riemann spaces of valuation domains Stability of domains Non-Noetherian grade Homotopy in integer-valued polynomials Localiza tions of global propertiesof rings Topics in integral closure Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees ofthe conferen ce in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Grazconference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere
Contents:Preface
Weak global dimension of Prfer
like rings (K. Adarbeh, S
E. Kabbaj)
Quasi
complete semilocal rings and modules (D.D. Anderson)
On the total graph of a ring and its related graphs: A survey (A. Badawi)
Prime ideals in polynomials and power series rings over Noetherian domains
Integer
valued polynomials: Looking for regular bases (J
L. Chabert)
On Boolean subrings of rings (I. Chajda, G. Eigenthaler)
On a new class of integral domains with the portable property (D.E. Dobbs, G. Picavet, M. Picavet
L'Hermitte)
The probability that Intn(D) is free (J. Elliott
ISBN:9781493909254
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algebraic topology
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Call number:SPRINGER-2014-9781493902583:ONLINE Show nearby items on shelf
Title:Analytic Number Theory, Approximation Theory, and Special Functions [electronic resource] : In Honor of Hari M. Srivastava
Author(s): Gradimir V Milovanovi
Michael Th Rassias
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematicalcommunity, including bot h research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions andquadratures, orthogonality, and special and co mplex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results,methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fieldsof mathematics, physics, and other computational and applied sciences
Contents:Part I. Analytic Number Theory, Combinatorics, and Special Sequences of Numbers and Polynomials
The mean values of the Riemann Zeta function on the critical line (A. Ivi)
Explicit bounds concerning non
trivial zeros of the Riemann Zeta function (M. Hassani)
On the value
distribution of logarithmic derivatives of Dirichlet L
functions (Y. Ihara, K. Matsumoto)
Multiple Gamma functions and their applications (J. Choi)
On partition functions of hyperbolic three
geometry and associated Hilbert schemes (A.A. Bytsenko and E. Elizalde)
Families of twisted Bernoulli numbers, twisted
ISBN:9781493902583
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional equations , Functional analysis , Number theory
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Call number:SPRINGER-2013-9789491216862:ONLINE Show nearby items on shelf
Title:Single Variable Differential and Integral Calculus [electronic resource] : Mathematical Analysis
Author(s): Elimhan Mahmudov
Date:2013
Publisher:Paris : Atlantis Press : Imprint: Atlantis Press
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book Single variable Differential and Integral Calculus is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book isunique in the field of mathemat ical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important businessfields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequencesof functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems andexamples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Sti eltjes and Lebesque integrals are studied together and compared
Note:Springer eBooks
Contents:Introduction to Numbers and Set Theory
Sequences and Series
Limits and Continuity of Functions
Differential Calculus
Some Basic Properties of Differentiable Functions
Polynomials and Interpolations
Applications of Differential Calculus to Limit Calculations and Extremum Problems
The Indefinite Integral
The Definite Integral
Applications of the Definite Integral
ISBN:9789491216862
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations
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Call number:SPRINGER-2013-9781461469711:ONLINE Show nearby items on shelf
Title:Graphs on Surfaces [electronic resource] : Dualities, Polynomials, and Knots
Author(s): Joanna A Ellis-Monaghan
Iain Moffatt
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:Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate theinterdependency between dualit y, medial graphs and knots how this interdependency is reflected in algebraic invariants of graphs and knots and how it can be exploited to solve problems in graph and knot theory. Taking aconstructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructionsto obtain full extensions of them to embedded graphs. The authors demonstrate the bene fits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces:Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knottheorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students an d researchers in either area. Because the area is advancing so rapidly, the authors give acomprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages ofconsidering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise
Note:Springer eBooks
Contents:1. Embedded Graphs
2. Generalised Dualities
3. Twisted duality, cycle family graphs, and embedded graph equivalence
4. Interactions with Graph Polynomials
5. Applications to Knot Theory
References
Index
ISBN:9781461469711
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology
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Call number:SPRINGER-2013-9781461466789:ONLINE Show nearby items on shelf
Title:The Fundamentals of Atomic and Molecular Physics [electronic resource]
Author(s): Robert L Brooks
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:The Fundamentals of Atomic and Molecular Physics is intended as an introduction to the field for advanced undergraduates who have taken quantum mechanics. Each chapter builds upon the previous, using the same tools and methodsthroughout. As the stude nts progress through the book, their ability to use these tools will steadily increase, along with their confidence in their efficacy. The book treats the two-electron atom as the simplest example of themany-electron atomas opposed to using techniques tha t are not applicable to many-electron atomsso that it is unnecessary to develop additional equations when turning to multielectron atoms, such as carbon. External fields aretreated using both perturbation theory and direct diagonalization and spontaneous emission is developed from first principles. Only diatomic molecules are considered with the hydrogen molecular ion and neutral molecule treated in somedetail. This comprehensive coverage of the quantum mechanics of complex atoms and simple diatomic molec ules, developed from the very basic components, is extremely useful for students considering graduate studies in any area ofphysics
Note:Springer eBooks
Contents:Part I: Atoms
Central Forces and Angular Momentum
Complex Atoms
Electro
and Magnetostatic Interactions
Transition Probabilities
Part II: Molecules
Electronic Structure of Diatomic Molecules
Vibrations and Rotations of Diatomic Molecules
Appendix A. Some Atomic Constants
Appendix B. Polynomials and Spherical Harmonics
Appendix C. Some Tensor Background
Appendix D. Magnetic Dipole Interaction Energy
ISBN:9781461466789
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Lecture Notes in Physics, 2192-4791
Series:Physics and Astronomy (Springer-11651)
Keywords: Chemistry , Mathematical physics
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Call number:SPRINGER-2013-9781461463931:ONLINE Show nearby items on shelf
Title:Advances in Applied Mathematics and Approximation Theory [electronic resource] : Contributions from AMAT 2012
Author(s): George A Anastassiou
Oktay Duman
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:Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the bestarticlespresented at Applied Mathematics and Approximation Theory 2012, an international conference heldin Ankara, Turkey, May 17-20, 20 12. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators,statistical approximation, fuzzy approximation, fracti onal analysis, semigroups, inequalities, special functions and summability. The collection willbe a useful resource for researchers in applied mathematics, engineering andstatistics
Note:Springer eBooks
Contents:Approximation by Neural Networks Iterates. George A. Anastassiou
Univariate Hardy Type Fractional Inequalities. George A. Anastassiou
Statistical Convergence on Time Scales and its Characterizations. Ceylan Turan and Oktay Duman
On the g
Jacobi Matrix Functions Bayram C ekim and Esra Erkus
Duman
Linear Combinations of Genuine Szasz
Mirakjan
Durrmeyer Operators. Margareta Heilmann and Gancho Tachev
Extensions of Schurs Inequality for the Leading Coefficient of Bounded Polynomials with Two Prescribed Zeros. Heinz
Joachim Rack
An Example of Optimal Nodes for Interpolati
ISBN:9781461463931
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v41
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2013-9781447148630:ONLINE Show nearby items on shelf
Title:Symmetries, Integrable Systems and Representations [electronic resource]
Author(s): Kenji Iohara
Sophie Morier-Genoud
Bertrand Rmy
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume is the result of two international workshops Infinite Analysis 11 Frontier of Integrability held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems andRepresentations held at Universit Claude Be rnard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some reviewarticles. The subjects discussed range across diverse areas such as algeb raic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through thesetopics, the readerwill find some recent developments in the field of mathematical physics and thei r interactions with several other domains
Note:Springer eBooks
Contents:A presentation of the deformed W1+1 algebra
Generating series of the Poincar polynomials of quasihomogeneous Hilbert schemes
PBW filtration over Z and compatible bases for VZ(_) in type An and Cn
On the subgeneric restricted blocks of affine category O at the critical level
Slavnov determinants, Yang
Mills structure constants, and discrete KP
Monodromy of partial KZ functors for rational Cherednik algebras
Category of finite dimensional modules over an orthosymplectic Lie superalgebra: small rank examples
Monoidal categorifications of cluster algebras of type A and D
ISBN:9781447148630
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v40
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Functions, special , Combinatorics , Mathematical physics
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Call number:SPRINGER-2012-9783642348853:ONLINE Show nearby items on shelf
Title:Analytic Tools for Feynman Integrals [electronic resource]
Author(s): Vladimir A. Smirnov
Date:2012
Publisher:Springer Berlin Heidelberg
Size:1 online resource
Note:Monograph
Note:Springer 2012 Physics and Astronomy eBook collection
Note:Springer e-book platform
ISBN:9783642348853
Series:Springer Tracts in Modern Physics
Series:e-books
Keywords: Particle and Nuclear Physics , Quantum Physics , Field Theory and Polynomials , Numerical and Computational Physics
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Call number:SPRINGER-2012-9783642252952:ONLINE Show nearby items on shelf
Title:Mathematical Modeling for Complex Fluids and Flows [electronic resource]
Author(s): Michel O Deville
Thomas B Gatski
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so itsupplies the means to de sign mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar andturbulent flow of non-Newtonian fluids such as thos e required in food processing and polymeric flows. The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian,viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory,especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeli ng strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomialrepresentations and accounting for non-inertial and curvature effects. Ranging from fundamental concepts to practical methodology, a nd including discussion of emerging technologies, this book is ideal for those requiring asingle-source assessment of current practice in this intricate yet vital field
Note:Springer eBooks
Contents:1. Introduction
2. Tensor Analysis, Invariants, and Representations
3. Kinematics and Dynamics
4. Constitutive Equations: General Principles
5. Non
Newtonian and Viscoelastic Fluids
6. Turbulent Flows
7. The Boltzmann Equation
8. Properties of the Hermite Polynomials
Table of symbols
References
ISBN:9783642252952
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer simulation
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Call number:SPRINGER-2012-9783034804318:ONLINE Show nearby items on shelf
Title:A Comprehensive Treatment of q-Calculus [electronic resource]
Author(s): Thomas Ernst
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom theywere written. This c onfusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new andinteresting notation for q-calculus based on logar ithms. For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see theconnection between q-hypergeometric functions and the q-gamma function, somethi ng that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations.Beyond a thorough review of the historical development of q-calculus, italso presents the domains of m odern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few
Note:Springer eBooks
Contents:1 Introduction
2 The different languages of q
3 Pre q
Analysis
4 The q
umbral calculus and the semigroups. The Nrlund calculus of finite diff
5 q
Stirling numbers
6 The first q
functions
7 An umbral method for q
hypergeometric series
8 Applications of the umbral calculus
9 Ciglerian q
Laguerre polynomials
10 q
Jacobi polynomials
11 q
Legendre polynomials and Carlitz
AlSalam polynomials
12 q
functions of many variables
13 Linear partial q
difference equations
14 q
Calculus and physics
15 Appendix: Other philosophies
ISBN:9783034804318
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions, special , Number theory
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Call number:SPRINGER-2011-9783642194924:ONLINE Show nearby items on shelf
Title:Combinatorial Aspects of Commutative Algebra and Algebraic Geometry [electronic resource] : The Abel Symposium 2009
Author(s): Gunnar Flystad
Trygve Johnsen
Andreas Leopold Knutsen
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The Abel Symposium 2009 Combinatorial aspects of Commutative Algebra and Algebraic Geometry, held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presentingcontributions on syzygies, trop ical geometry, Boij-Sderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorialgames and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour
Note:Springer eBooks
Contents:The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two: M.Boij, G.Flystad
Koszul Cycles: W.Bruns, A.Conca, T.Rmer
Boij
Sderberg Theory: D.Eisenbud, F
O.Schreyer
Powers of Componentwise Linear Ideals: J.Herzog, T.Hibi, H.Ohsugi
Modules With 1
Dimensional Socle and Components of Lusztig Quiver Varieties in Type A.: J.Kamnitzer, C.Sadanand
Realization Spaces for Tropical Fans: E.Katz, S.Payne
A Relation Between Symmetric Polynomials and the Algebra of Classes, Motivated by Equivariant Schubert Calculus: D.Laksov
Theory and Applications of Lattice Po
ISBN:9783642194924
Series:e-books
Series:SpringerLink (Online service)
Series:Abel Symposia : v6
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Combinatorics
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Call number:SPRINGER-2011-9783642156373:ONLINE Show nearby items on shelf
Title:The Mathematics of Knots [electronic resource] Theory and Application
Author(s): Markus Banagl
Denis Vogel
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursuedareas of mathematical kn ot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented numerous illustrations support the text. The book will be of great interest toresearchers in topology, geometry, and mathemat ical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands
Note:Springer eBooks
Contents:Preface
1 Knots, Singular Embeddings, and Monodromy
2 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus
3 A Survey of Twisted Alexander Polynomials
4 On Two Categorifications of the Arrow Polynomial for Virtual Knots
5 An Adelic Extension of the Jones Polynomial
6 Legendrian Grid Number One Knots and Augmentations of their Differential Algebras
7 Embeddings of Four
Valent Framed Graphs into 2
Surfaces
8 Geometric Topology and Field Theory on 3
Manifolds
9 From Goeritz Matrices to Quasi
Alternating Links
10 An Overview of Property 2R
11 DNA, Knot
ISBN:9783642156373
Series:e-books
Series:SpringerLink (Online service)
Series:Contributions in Mathematical and Computational Sciences : v1
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Physiology Mathematics , Global differential geometry , Topology , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9783834893291:ONLINE Show nearby items on shelf
Title:Discrete Mathematics in Statistical Physics [electronic resource] : Introductory Lectures
Author(s): Martin Loebl
Date:2010
Publisher:Wiesbaden : Vieweg+Teubner
Size:1 online resource
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Note:The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the establishedconnections, some exciting activi ties in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strongtrend in both research communities recently. It also nat urally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers.Basic concepts - Introduction to Graph Theory - Trees and electrical networks Matroids - Geometric representations of graphs - Game of dualities - The zeta function and graph polynomials Knots - 2D Ising and dimer models -Advanced Graduate Students in Mathematics, Physics and Computer Sciences - Researchers Prof. Dr. Martin Loeb l, Dept. of Mathematics, Charles University, Prague
Note:Springer eBooks
ISBN:9783834893291
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2010-9783034601801:ONLINE Show nearby items on shelf
Title:Recent Advances in Operator Theory in Hilbert and Krein Spaces [electronic resource]
Author(s): Jussi Behrndt
Karl-Heinz Frster
Carsten Trunk
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:The present book is a memorial volume devoted to Peter Jonas. It displays recent advances in modern operator theory in Hilbert and Krein spaces and contains a collection of original research papers written by many well-knownspecialists in this field. The papers contain new results for problems close to the area of research of Peter Jonas: Spectral and perturbation problems for operators in inner product spaces, generalized Nevanlinna functions anddefinitizable functions, scattering theory, extension theory for symmetric operators, fixed points, hyperbolic matrix polynomials, moment problems, indefinite spectral and Sturm-Liouville problems, and invariant subspace problems. Thisbook is written for researchers and postgraduates interested in functional analysis and differential operators
Note:Springer eBooks
ISBN:9783034601801
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory
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Call number:SPRINGER-2010-9780817649388:ONLINE Show nearby items on shelf
Title:Representation Theory and Complex Geometry [electronic resource]
Author(s): Neil Chriss
Victor Ginzburg
Date:2010
Edition:1st
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometrically-oriented treatment of the subject is very timely and has long been desired, especially since thediscovery of D-module s in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Liegroups, and quantum field theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. The book is largelyself-contained. . . . There is a nice introduction to symplectic geometry and a cha rming exposition of equivariant K-theory. Both are enlivened by examples related to groups. . . . An attractive feature is the attempt to convey someinformal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory. . . it hasalready proved successful in introducing a new generation to the subject. --- Bulletin of the American Mathematical Society Th e authors have tried to help readers by adopting an informal and easily accessible style. . . . The book willprovide a guide to those who wish to penetrate into subject-matter which, so far, was only accessible in difficult papers. . . . The book is quite suitable as a basis for an advanced course or a seminar, devoted to the material of oneof the chapters of the book. --- Mededelingen van het Wiskundig Genootschap Represents an important and very interesting addition to the literature. --- Mathematical R eviews
Note:Springer eBooks
Contents:Preface
Chapter 0. Introduction
Chapter 1. Symplectic Geometry
Chapter 2. Mosaic
Chapter 3. Complex Semisimple Groups
Chapter 4. Springer Theory
Chapter 5. Equivariant K
Theory
Chapter 6. Flag Varieties, K
Theory, and Harmonic Polynomials
Chapter 7. Hecke Algebras and K
Theory
Chapter 8. Representations of Convolution Algebras
Bibliography
ISBN:9780817649388
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780387894881:ONLINE Show nearby items on shelf
Title:Stochastic Partial Differential Equations [electronic resource] : A Modeling, White Noise Functional Approach
Author(s): Helge Holden
Bernt ksendal
Jan Ube
Tusheng Zhang
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by space-time Brownian motion noise. In this, the second edition, theauthors extend the the ory to include SPDEs driven by space-time Lvy process noise, and introduce new applications of the field. Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually ofthe distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection betweenwhite noise theory and SPDEs is that integration with respect to Browni an random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarlywith Lvy processes. The first part of the book deals with the classical Brownian motion case . The second extends it to the Lvy white noise case. For SPDEs of the Wick type, a general solution method is given by means of the Hermitetransform, which turns a given SPDE into a parameterized family of deterministic PDEs. Applications of this theory a re emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as areapplications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.From the reviews of the first edition: The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully w ritten and the details of the proofs are basically spelled out...This is a rich and demanding book It will be of great value for students of probability theory or SPDEs with an interest in the
Note:Springer eBooks
Contents:Preface to the Second Edition
Preface to the First Edition
Introduction
Framework
Applications to stochastic ordinary differential equations
Stochastic partial differential equations driven by Brownian white noise
Stochastic partial differential equations driven by Lvy white noise
Appendix A. The Bochner
Minlos theorem
Appendix B. Stochastic calculus based on Brownian motion
Appendix C. Properties of Hermite polynomials
Appendix D. Independence of bases in Wick products
Appendix E. Stochastic calculus based on Lvy processes
References
List of frequently
ISBN:9780387894881
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Differential equations, partial , Distribution (Probability theory)
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Call number:SPRINGER-2009-9783642008375:ONLINE Show nearby items on shelf
Title:Lectures on Topological Fluid Mechanics [electronic resource]
Author(s): Mitchell A Berger
Louis H Kauffman
Boris Khesin
H. Keith Moffatt
Renzo L Ricca
De Witt Sumners
Renzo L Ricca
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developmentshave given topologic al fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume containsa wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamicsand magnetohydrodynamics, integrability issues, Hamiltonian stru ctures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modernbraid theory and knot polynomials, as well as more advanced topics in knot classification , provides an invaluable addition to this material
Note:Springer eBooks
Contents:Braids and Knots
Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants
Tangles, Rational Knots and DNA
The Group and Hamiltonian Descriptions of Hydrodynamical Systems
Singularities in Fluid Dynamics and their Resolution
Structural Complexity and Dynamical Systems
Random Knotting: Theorems, Simulations and Applications
ISBN:9783642008375
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1973
Series:Mathematics and Statistics (Springer-11649)
Keywords: Differentiable dynamical systems , Differential equations, partial , Topology , Thermodynamics
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Call number:SPRINGER-2009-9780387894928:ONLINE Show nearby items on shelf
Title:Functional Equations and Inequalities with Applications [electronic resource]
Author(s): Palaniappan Kannappan
Date:2009
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch ofmathematics with far- reaching applications it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering. Thisself-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, andmany other basic tools in analysis. Each chapter examines a particular f amily of equations and gives an in-depth study of its applications as well as examples and exercises to support the material. The book is intended as a referencetool for any student, professional (researcher), or mathematician studying in a field where fu nctional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be aninspiring entre into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition
Note:Springer eBooks
Contents:Basic Equations: Cauchy and Pexider Equations
Matrix Equations
Trigonometric Functional Equations
Quadratic Functional Equations
Characterization of Inner Product Spaces
Stability
Characterization of Polynomials
Nondifferentiable Functions
Characterization of Groups, Loops, and Closure Conditions
Functional Equations from Information Theory
Abel Equations and Generalizations
Regularity ConditionsChristensen Measurability
Difference Equations
Characterization of Special Functions
Miscellaneous Equations
General Inequalities
Applications
ISBN:9780387894928
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional equations , Functional analysis
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Call number:SPRINGER-2009-9780387747255:ONLINE Show nearby items on shelf
Title:A Concrete Introduction to Higher Algebra [electronic resource]
Author(s): Lindsay N Childs
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strongemphasis on congruence clas ses leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, error correction,integration, and especially to elementary and compu tational number theory. The later chapters include expositions of Rabin's probabilistic primality test, quadratic reciprocity, the classification of finite fields, and factoringpolynomials over the integers. Over 1000 exercises, ranging from routine examp les to extensions of theory, are found throughout the book hints and answers for many of them are included in an appendix. The new edition includes topicssuch as Luhn's formula, Karatsuba multiplication, quotient groups and homomorphisms, Blum-Blum-Shub p seudorandom numbers, root bounds for polynomials, Montgomery multiplication, and more. At every stage, a wide variety ofapplications is presented...The user-friendly exposition is appropriate for the intended audience - T.W. Hungerford, Mathematical Revie ws The style is leisurely and informal, a guided tour through the foothills, the guide unable toresist numerous side paths and return visits to favorite spots... - Michael Rosen, American Mathematical Monthly
Note:Springer eBooks
Contents:Preface
Numbers
Induction
Euclid's Algorithm
Unique Factorization
Congruence
Congruence Classes
Rings and Fields
Matrices and Codes
Fermat's and Euler's Theorems
Applications of Fermat's and Euler's Theorems
Groups
The Chinese Remainder Theorem
Polynomials
Unique Factorization
The Fundamental Theorem of Algebra
Polynomials in Q[x]
Congruences and the CRT
Fast Polynomial Multiplication
Cyclic Groups and Cryptography
Carmichael Numbers
Quadratic Reciprocity
Quadratic Applications
Congruence Classes Modulo a Polynomial
Homom
ISBN:9780387747255
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2009-9780387689029:ONLINE Show nearby items on shelf
Title:Maximum Penalized Likelihood Estimation [electronic resource] : Volume II: Regression
Author(s): Vincent N LaRiccia
Paul P Eggermont
Date:2009
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This is the second volume of a text on the theory and practice of maximum penalized likelihood estimation. It is intended for graduate students in statistics, operations research and applied mathematics, as well as for researchersand practitioners in the field. The present volume deals with nonparametric regression. The emphasis in this volume is on smoothing splines of arbitrary order, but other estimators (kernels, local and global polynomials) pass review aswell. Smoothing splines and local polyno mials are studied in the context of reproducing kernel Hilbert spaces. The connection between smoothing splines and reproducing kernels is of course well-known. The new twist is that letting theinnerproduct depend on the smoothing parameter opens up new p ossibilities. It leads to asymptotically equivalent reproducing kernel estimators (without qualifications), and thence, via uniform error bounds for kernel estimators, touniform error bounds for smoothing splines and via strong approximations, to confiden ce bands for the unknown regression function. The reason for studying smoothing splines of arbitrary order is that one wants to use them for dataanalysis. Regarding the actual computation, the usual scheme based on spline interpolation is useful for cubic smoothing splines only. For splines of arbitrary order, the Kalman filter is the most important method, the intricacies ofwhich are explained in full. The authors also discuss simulation results for smoothing splines and local and global polynomials for a variety of test problems as well as results on confidence bands for the unknown regression functionbased on undersmoothed quintic smoothing splines with remarkably good coverage probabilities. P.P.B. Eggermont and V.N. LaRiccia are with the Statistics P rogram of the Department of Food and Resource Economics in the College ofAgriculture and Natural Resources at the University of Delaware, and the authors of Maximum Penalized Likelihood Estimation: Volu
Note:Springer eBooks
Contents:Smoothing splines of arbitrary order
Deterministic and random designs
Reproducing kernel Hilbert spaces, equivalent reproducing kernel estimators
Strong approximation and confidence bands
Computing: the Bayesian model and the Kalman filter
Other estimators: kernels, sieves, local polynomials, least
absolute deviations, total
variation penalized least squares
Simulations and examples
ISBN:9780387689029
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Series in Statistics, 0172-7397
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics , Biometrics , Statistical methods , Computer science Mathematics , Mathematical statistics , Econometrics
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Call number:SPRINGER-2008-9783540683490:ONLINE Show nearby items on shelf
Title:Interpolation Processes [electronic resource] : Basic Theory and Applications
Author(s): Giuseppe Mastroianni
Gradimir V Milovanovi
Date:2008
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs,recent results on conver gent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In thisspecial, but fundamental and important field of r eal analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthogonal polynomials, moduli ofsmoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. Beside the basic propertiesof the classical orthogonal polynomials the book provides new results on nonclassical ortho gonal polynomials including methods for their numerical construction
Note:Springer eBooks
Contents:1. Constructive Elements and Approaches in Approximation Theory
1.1 Introduction to Approximation Theory
1.2 Basic Facts on Trigonometric Approximation
1.3 Chebyshev Systems and Interpolation
1.4 Interpolation by Algebraic Polynomials
2. Orthogonal Polynomials and Weighted Polynomial Approximation
2.1 Orthogonal Systems and Polynomials
2.2 Orthogonal Polynomials on the Real Line
2.3 Classical Orthogonal Polynomials
2.4 Nonclassical Orthogonal Polynomials
2.5 Weighted Polynomial Approximation
3. Trigonometric Approximation
3.1 Approximating Properties of Oper
ISBN:9783540683490
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Integral equations , Sequences (Mathematics) , Functions, special
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Call number:SPRINGER-2008-9783211742808:ONLINE Show nearby items on shelf
Title:Diophantine Approximation [electronic resource] : Festschrift for Wolfgang Schmidt
Author(s): Hans Peter Schlickewei
Klaus Schmidt
Robert F Tichy
Date:2008
Publisher:Vienna : Springer Vienna
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation. This includes contributions to Wolfgang Schmidt's subspace theorem and its applications to diophantine equationsand to the study of l inear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavour. Several articles deal with estimates for the number of solutions ofdiophantine equations as well as with cong ruences and polynomials. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and discrepancy theory. The articlesare based on lectures given at a conference at the Erwin Schrdi nger-Institute (Vienna, 2003), where many leading experts in the field of diophantine approximation participated
Note:Springer eBooks
ISBN:9783211742808
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, 1389-2177 : v16
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Computer science Mathematics , Number theory
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Call number:SPRINGER-2007-9780817646134:ONLINE Show nearby items on shelf
Title:Advanced Algebra [electronic resource] : Along with a companion volume Basic Algebra
Author(s): Anthony W Knapp
Date:2007
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a globalview of algebra and its r ole in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementarytheory of modules as developed in Basic Algebra *Ch apters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, andalgebraic geometry *Sections in two chapters relate the theory to the su bject of Grbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra andother branches of mathematics, particularly topology and complex analysis *Book carries on two prom inent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationshipbetween number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete s olutions for most of the problems *The exposition proceeds from the particular to the general, often providingexamples well before a theory that incorporates them it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forward-looking way that takesinto account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topicsdeveloped in Basic Algebra
Note:Springer eBooks
Contents:Transition to Modern Number Theory
WedderburnArtin Ring Theory
Brauer Group
Homological Algebra
Three Theorems in Algebraic Number Theory
Reinterpretation with Adeles and Ideles
Infinite Field Extensions
Background for Algebraic Geometry
The Number Theory of Algebraic Curves
Methods of Algebraic Geometry
ISBN:9780817646134
Series:e-books
Series:SpringerLink (Online service)
Series:Cornerstones
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Field theory (Physics) , Number theory
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Call number:SPRINGER-2007-9780387498942:ONLINE Show nearby items on shelf
Title:Number Theory [electronic resource] : Volume II: Analytic and Modern Tools
Author(s): Henri Cohen
Date:2007
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally inalgebraic numbers. Thi s theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. The first is the local aspect: one can do analysisin p-adic fields, and here the author start s by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and inparticular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study ofelliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analoguesis treated at length in the third part of the book, including many interesting and original applications. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, theauthor has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. Th ese chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, SamirSiksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms. Thebook contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and
Note:Springer eBooks
Contents:Bernoulli Polynomials and the Gamma Functions
Dirichlet Series
Applications of Linear Forms in Logarithms
Rational Points on Higher Genus Curves
The Modular Approach to Diophantine Equations
The Superfermat Equation
Catalans Equation
Bibliography
Index
ISBN:9780387498942
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v240
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Field theory (Physics) , Algebra , Computer science Mathematics , Algorithms , Number theory
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Call number:SPRINGER-2006-9781846281815:ONLINE Show nearby items on shelf
Title:Fields and Galois Theory [electronic resource]
Author(s): John M Howie
Date:2006
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they usedwere, in the end, more im portant than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra. This book provides a gentle introduction to Galois theory suitable for third- and fourth-yearundergraduates and beginning graduates. The appr oach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic byradicals is linked to the fact that the alternating group of degree 5 is s imple - which is assuredly not the way Galois would have expressed the connection. Topics covered include: rings and fields integral domains and polynomialsfield extensions and splitting fields applications to geometry finite fields the Galois group equat ions Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed upwith worked examples and more than 100 exercises, for which full solutions are provided
Note:Springer eBooks
Contents:Rings and Fields
Integral Domains Polynomials
Field Extensions
Applications to Geometry
Splitting Fields
Finite Fields
The Galois Group
Equations and Groups
Some Group Theory
Groups and Equations
Regular Polygons
Solutions
Bibliography
List of Symbols
Index
ISBN:9781846281815
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics)
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Call number:SPRINGER-2006-9780817645298:ONLINE Show nearby items on shelf
Title:Basic Algebra [electronic resource]
Author(s): Anthony W Knapp
Date:2006
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a globalview of algebra and its r ole in mathematics as a whole. Key topics and features of Basic Algebra: *Linear algebra and group theory build on each other continually *Chapters on modern algebra treat groups, rings, fields, modules, andGalois groups, with emphasis on methods of compu tation throughout *Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linearalgebra and group theory, and the relationship between number theory and ge ometry *Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them includes blocks of problems that introduce additional topics and applications for further study*Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of th e Jordan canonical form in solving linear systems of ordinary differential equations, and constructions ofinterest in mathematical physics) appear in sequences of problems Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semesteradvanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding ofthe geometry and reduction of linear equations, and an acquaintance with proofs
Note:Springer eBooks
Contents:Preliminaries about the Integers, Polynomials, and Matrices
Vector Spaces over ?, ?, and ?
Inner
Product Spaces
Groups and Group Actions
Theory of a Single Linear Transformation
Multilinear Algebra
Advanced Group Theory
Commutative Rings and Their Modules
Fields and Galois Theory
Modules over Noncommutative Rings
ISBN:9780817645298
Series:e-books
Series:SpringerLink (Online service)
Series:Cornerstones
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics) , Group theory , Matrix theory
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Call number:SPRINGER-2006-9780387367170:ONLINE Show nearby items on shelf
Title:Multiplicative Ideal Theory in Commutative Algebra [electronic resource] : A Tribute to the Work of Robert Gilmer
Author(s): James W Brewer
Sarah Glaz
William J Heinzer
Bruce M Olberding
Date:2006
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:For over forty years, Robert Gilmers numerous articles and books have had a tremendous impact on research in commutative algebra. It is not an exaggeration to say that most articles published today in non-Noetherian ringtheory, and some in Noetherian ring theory as well, originated in a topic that Gilmer either initiated or enriched by his work. This volume, a tribute to his work, consists of twenty-four articles authored by Robert Gilmers mostprominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. In a concluding article, Robert Gilmerpoints out directions for future research, highlighting the open problems in t he areas he considers of importance. Robert Gilmers article is followed by the complete list of his published works, his mathematical genealogical tree,information on the writing of his four books, and reminiscences about Robert Gilmers contributions to t he stimulating research environment in commutative algebra at Florida State in the middle 1960s. The entire collection providesan in-depth overview of the topics of research in a significant and large area of commutative algebra. Audience This book is int ended for researchers and graduate students in the field of commutative algebra
Note:Springer eBooks
Contents:Commutative rngs
Robert Gilmers work on semigroup rings
Numerical semigroup algebras
Prfer rings
Subrings of zero
dimensional rings
Old problems and new questions around integer
valued polynomials and factorial sequences
Robert Gilmers contributions to the theory of integer
valued polynomials
Progress on the dimension question for power series rings
Some research on chains of prime ideals influenced by the writings of Robert Gilmer
Direct
sum decompositions over one
dimensional Cohen
Macaulay local rings
An historical overview of Kronecker function rings,
ISBN:9780387367170
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2006-9780387276786:ONLINE Show nearby items on shelf
Title:Field Theory [electronic resource]
Author(s): Steven Roman
Date:2006
Edition:Second Edition
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 presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course inabstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity. For this new edition, the author has rewritten the text based on his experiences teaching from the first edition.There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis,Berlekamp's algorithm for factoring polynomials over Zp and nat ural and accessory irrationalities. From the reviews of the first edition: The book is written in a clear and explanatory style...the book is recommended for a graduatecourse in field theory as well as for independent study. - T. Albu, Mathematical Review s ...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduatecourse in field theory, but also for a student who wishes to take a field theory course as independent study. - J .N.Mordeson, Zentralblatt
Note:Springer eBooks
Contents:Preliminaries
Preliminaries
Field Extensions
Polynomials
Field Extensions
Embeddings and Separability
Algebraic Independence
Galois Theory
Galois Theory I: An Historical Perspective
Galois Theory II: The Theory
Galois Theory III: The Galois Group of a Polynomial
A Field Extension as a Vector Space
Finite Fields I: Basic Properties
Finite Fields II: Additional Properties
The Roots of Unity
Cyclic Extensions
Solvable Extensions
The Theory of Binomials
Binomials
Families of Binomials
ISBN:9780387276786
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v158
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics) , Number theory
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Call number:SPRINGER-2005-9780817644482:ONLINE Show nearby items on shelf
Title:Approximation Theory [electronic resource] : From Taylor Polynomials to Wavelets
Author(s): Ole Christensen
Khadija L Christensen
Date:2005
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This concisely written book gives an elementary introduction to a classical area of mathematicsapproximation theoryin a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather thantechnical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in wordsrather than mathematical symbols * Elementary intro duction to approximation using polynomials (Weierstrass and Taylors theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introductionto Fourier analysis * Numerous classical, illustrative examples and constructio ns * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBIs use of wavelets to store fingerprints *Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate course s on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbookor self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Rea ders will find motivation and background material pointing toward advanced literature and research topicsin pure and applied harmonic analysis and related areas
Note:Springer eBooks
Contents:Preface
Approximation with Polynomials
Infinite Series
Fourier Analysis
Wavelets and Applications
Wavelets and their Mathematical Properties
Appendix A
Appendix B
References
Index
ISBN:9780817644482
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functional analysis
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Call number:SPRINGER-2005-9780817644475:ONLINE Show nearby items on shelf
Title:Number Fields and Function FieldsTwo Parallel Worlds [electronic resource]
Author(s): Gerard Geer
Ben Moonen
Ren Schoof
Date:2005
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeperunderstanding of this analo gy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with thefinite ones gave a new impetus and led to spectacula r success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights inthe more arithmetically-oriented world of number fields, or vice versa. Th ese invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range fromArakelov geometry, the search for a theory of varieties over the field with one element, via Eis enstein series to Drinfeld modules, and t-motives. This volume is aimed at a wide audience of graduate students, mathematicians, andresearchers interested in geometry and arithmetic and their connections. Contributors: G. Bckle T. van den Bogaart H. Brenn er F. Breuer K. Conrad A. Deitmar C. Deninger B. Edixhoven G. Faltings U. Hartl R. de Jong K.Khler U. Khn J.C. Lagarias V. Maillot R. Pink D. Roessler and A. Werner
Note:Springer eBooks
Contents:Arithmetic over Function Fields: A Cohomological Approach
Algebraic Stacks Whose Number of Points over Finite Fields is a Polynomial
On a Problem of Miyaoka
Monodromy Groups Associated to Non
Isotrivial Drinfeld Modules in Generic Characteristic
Irreducible Values of Polynomials: A Non
Analogy
Schemes over
Line Bundles and p
Adic Characters
Arithmetic Eisenstein Classes on the Siegel Space: Some Computations
Uniformizing the Stacks of Abelian Sheaves
Faltings Delta
Invariant of a Hyperelliptic Riemann Surface
A Hirzebruch Proportionality Principle in Arakelov
ISBN:9780817644475
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v239
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Number theory , Mathematical physics
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Call number:SPRINGER-2005-9780387274751:ONLINE Show nearby items on shelf
Title:Undergraduate Algebra [electronic resource]
Author(s): Serge Lang
Date:2005
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:Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory,and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance eachother. Illustrative examples accompany the gene ral theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text. For the third edition, the author has included new material onproduct structure for matrices (e.g. the Iwasawa and polar decompositio ns), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snydersproof of the Mason-Stothers polynomial abc theorem. About the First Edition: The exposition is dow n-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-termcourse...the flavor of modern mathematics is sprinkled here and there. - Hideyuki Matsumura, Zentralblatt
Note:Springer eBooks
Contents:Foreword
The Integers
Groups
Rings
Polynomials
Vector Spaces and Modules
Some Linear Groups
Field Theory
Finite Fields
The Real and Complex Numbers
Sets
Appendix
Index
ISBN:9780387274751
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics)
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Call number:SPRINGER-2005-9780387235349:ONLINE Show nearby items on shelf
Title:Progress in Galois Theory [electronic resource] : Proceedings of John Thompsons 70th Birthday Conference
Author(s): Helmut Voelklein
Tanush Shaska
Date:2005
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:A recent trend in the field of Galois theory is to tie the previous theory of curve coverings (mostly of the Riemann sphere) and Hurwitz spaces (moduli spaces for such covers) with the theory of algebraic curves and their modulispaces. A general surv ey of this is given in the article by Voelklein. Further exemplifications come in the articles of Guralnick on automorphisms of modular curves in positive characteristic, of Zarhin on the Galois module structureof the 2-division points of hyperelliptic cu rves and of Krishnamoorthy, Shashka and Voelklein on invariants of genus 2 curves. Abhyankar continues his work on explicit classes of polynomials in characteristic p>0 whose Glaois groupscomprise entire families of Lie type groups in characteristic p. In his article, he proves a characterization of sympletic groups required for the identification of the Galois group of certain polynomials. The more abstract aspectscome into play when considering the totality of Galois extensions of a given field. This le ads to the study of absolute Galois groups and (profinite) fundamental groups. Haran and Jarden present a result on the problem of finding agroup-theoretic characterization of absolute Galois groups. In a similar spirit, Boston studies infinite p-extensio ns of number fields unramified at p and makes a conjecture about a group-theoretic characterization of their Galoisgroups. He notes connections with the Fontaine-Mazur conjecture, knot theory and quantum field theory. Nakamura continues his work on relati onships between the absolute Galois group of the rationals and the Grothendieck-Teichmllergroup. Finally, Fried takes us on a tour of places where classical tropics like modular curves and j-line covers connect to the genus zero problems which was the sta rting point of the Guralnick-Thompson Conjecture. Audience This volumeis suitable for graduate students and researchers in the field
Note:Springer eBooks
Contents:Preface
Supplementary Thoughts on Symplectic Groups
Automorphisms of the Modular Curve
Reducing the Fontaine
Mazur Conjecture to Group Theory
Relating Two Genus 0 Problems of John Thompson
Relatively Projective Groups as Absolute Galois Groups
Invariants of Binary Forms
Some Classical Views on the Parameters of GT
The Image of a Hurwitz Space under the Moduli Map
Very Simply Presentation: Variations on a Theme of Clifford
ISBN:9780387235349
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, 1389-2177 : v12
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Group theory
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Call number:SPRINGER-2004-9783662054123:ONLINE Show nearby items on shelf
Title:Proofs from THE BOOK
Author(s): Martin Aigner
Date:2004
Edition:Third Edition
Size:1 online resource (239 p.)
Note:10.1007/978-3-662-05412-3
Contents:Number Theory -- 1. Six proofs of the infinity of primes -- 2. Bertrand’s postulate -- 3. Binomial coefficients are (almost) never powers -- 4. Representing numbers as sums of two squares -- 5. Every finite division ring is a field --
6. Some irrational numbers -- 7. Three times ?2/6 -- Geometry -- 8. Hilbert’s third problem: decomposing polyhedra -- 9. Lines in the plane and decompositions of graphs -- 10. The slope problem -- 11. Three applications of Euler’s
formula -- 12. Cauchy’s rigidity theorem -- 13. Touching simplices -- 14. Every large point set has an obtuse angle -- 15. Borsuk’s conjecture -- Analysis -- 16. Sets, functions, and the continuum hypothesis -- 17. In praise of
inequalities -- 18. A theorem of Pólya on polynomials -- 19. On a lemma of Littlewood and Offord -- 20. Cotangent and the Herglotz trick -- 21. Buffon’s needle problem -- Combinatorics -- 22. Pigeon-hole and double counting -- 23.
Three famous theorems on finite sets -- 24. Shuffling cards -- 25. Lattice paths and determinants -- 26. Cayley’s formula for the number of trees -- 27. Completing Latin squares -- 28. The Dinitz problem -- 29. Identities versus
bijections -- Graph Theory -- 30. Five-coloring plane graphs -- 31. How to guard a museum -- 32. Turán’s graph theorem -- 33. Communicating without errors -- 34. Of friends and politicians -- 35. Probability makes counting (sometimes)
easy -- About the Illustrations
ISBN:9783662054123
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Computer science , Mathematical analysis , Analysis (Mathematics) , Geometry , Number theory , Combinatorics , Mathematics , Mathematics, general , Number Theory , Geometry , Combinatorics , Analysis , Computer Science, general
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Call number:SPRINGER-2004-9783540446460:ONLINE Show nearby items on shelf
Title:The Valuative Tree
Author(s): Charles Favre
Date:2004
Size:1 online resource (244 p.)
Note:10.1007/b100262
Contents:1 Generalities -- 1.1 Setup -- 1.2 Valuations -- 1.3 Krull Valuations -- 1.4 Plane Curves -- 1.5 Examples of Valuations -- 1.6 Valuations Versus Krull Valuations -- 1.7 Sequences of Blowups and Krull Valuations -- 2 MacLane’s Method
-- 2.1 Sequences of Key Polynomials -- 2.2 Classification -- 2.3 Graded Rings and Numerical Invariants -- 2.4 From Valuations to SKP’s -- 2.5 A Computation -- 3 Tree Structures -- 3.1 Trees -- 3.2 Nonmetric Tree Structure on V -- 3.3
Parameterization of V by Skewness -- 3.4 Multiplicities -- 3.5 Approximating Sequences -- 3.6 Thinness -- 3.7 Value Semigroups and Approximating Sequences -- 3.8 Balls of Curves -- 3.9 The Relative Tree Structure -- 4 Valuations
Through Puiseux Series -- 4.1 Puiseux Series and Valuations -- 4.2 Tree Structure -- 4.3 Galois Action -- 4.4 A Tale of Two Trees -- 4.5 The Berkovich Projective Line -- 4.6 The Bruhat-Tits Metric -- 4.7 Dictionary -- 5 Topologies --
5.1 The Weak Topology -- 5.2 The Strong Topology on V -- 5.3 The Strong Topology on Vqm -- 5.4 Thin Topologies -- 5.5 The Zariski Topology -- 5.6 The Hausdorff-Zariski Topology -- 5.7 Comparison of Topologies -- 6 The Universal Dual
Graph -- 6.1 Nonmetric Tree Structure -- 6.2 Infinitely Near Points -- 6.3 Parameterization and Multiplicity -- 6.4 The Isomorphism -- 6.5 Proof of the Isomorphism -- 6.6 Applications -- 6.7 The Dual Graph of the Minimal
Desingularization -- 6.8 The Relative Tree Structure -- 7 Tree Measures -- 7.1 Outline -- 7.2 More on the Weak Topology -- 7.3 Borel Measures -- 7.4 Functions of Bounded Variation -- 7.5 Representation Theorem I -- 7.6 Complex Tree
Potentials -- 7.7 Representation Theorem II -- 7.8 Atomic Measures -- 7.9 Positive Tree Potentials -- 7.10 Weak Topologies and Compactness -- 7.11 Restrictions to Subtrees -- 7.12 Inner Products -- 8 Applications of the Tree Analysis
-- 8.1 Zariski’s Theory of Complete Ideals -- 8.2 The Voûte étoilée -- A Infinitely Singular Valuations -- A.1 Characterizations -- A.2 Constructions -- B The Tangent Space at a Divisorial Valuation -- C Classification -- D
Combinatorics of Plane Curve Singularities -- D.1 Zariski’s Terminology for Plane Curve Singularities -- D.2 The Eggers Tree -- E.1 Completeness -- E.2 The Residue Field -- References
ISBN:9783540446460
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1853
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Topology , Discrete mathematics , Mathematics , Discrete Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Topology
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Call number:SPRINGER-2004-9783034879347:ONLINE Show nearby items on shelf
Title:Polynomial Identity Rings
Author(s): Vesselin Drensky
Date:2004
Size:1 online resource (200 p.)
Note:10.1007/978-3-0348-7934-7
Contents:A Combinatorial Aspects in PI-Rings -- Vesselin Drensky -- 1 Basic Properties of PI-algebras -- 2 Quantitative Approach to PI-algebras -- 3 The Amitsur-Levitzki Theorem -- 4 Central Polynomials for Matrices -- 5 Invariant Theory of
Matrices -- 6 The Nagata-Higman Theorem -- 7 The Shirshov Theorem for Finitely Generated PI-algebras -- 8 Growth of Codimensions of PI-algebras -- B Polynomial Identity Rings -- Edward Formanek -- 1 Polynomial Identities -- 2 The
Amitsur-Levitzki Theorem -- 3 Central Polynomials -- 4 Kaplansky’s Theorem -- 5 Theorems of Amitsur and Levitzki on Radicals -- 6 Posner’s Theorem -- 7 Every PI-ring Satisfies a Power of the Standard Identity -- 8 Azumaya Algebras -- 9
Artin’s Theorem -- 10 Chain Conditions -- 11 Hilbert and Jacobson PI-Rings -- 12 The Ring of Generic Matrices -- 13 The Generic Division Ring of Two 2 x 2 Generic Matrices -- 14 The Center of the Generic Division Ring -- 15 Is the
Center of the Generic Division Ring a Rational Function Field?
ISBN:9783034879347
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Associative rings , Rings (Algebra) , Combinatorics , Mathematics , Associative Rings and Algebras , Combinatorics
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Call number:SPRINGER-2004-9781461302490:ONLINE Show nearby items on shelf
Title:Galois Theory and Modular Forms
Author(s):
Date:2004
Size:1 online resource (394 p.)
Note:10.1007/978-1-4613-0249-0
Contents:I. Arithmetic geometry -- The arithmetic of Weierstrass points on modular curves X0(p) -- Semistable abelian varieties with small division fields -- Q-curves with rational j-invariants and jacobian surfaces of GL2-type -- Points
defined over cyclic quartic extensions on an elliptic curve and generalized Kummer surfaces -- The absolute anabelian geometry of hyperbolic curves -- II. Galois groups and Galois extensions -- Regular Galois realizations of PSL2(p2)
over ?(T) -- Middle convolution and Galois realizations -- On the essential dimension of p-groups -- Explicit constructions of generic polynomials for some elementary groups -- On dihedral extensions and Frobenius extensions -- On the
non-existence of certain Galois extensions -- Frobenius modules and Galois groups -- III. Algebraic number theory -- On quadratic number fields each having an unramified extension which properly contains the Hilbert class field of its
genus field -- Distribution of units of an algebraic number field -- On capitulation problem for 3-manifolds -- On the Iwasawa ?-invariant of the cyclotomic ?p-extension of certain quartic fields -- IV. Modular forms and arithmetic
functions -- Quasimodular solutions of a differential equation of hypergeometric type -- Special values of the standard zeta functions -- p-adic properties of values of the modular j-function -- Thompson series and Ramanujan’s
identities -- Generalized Rademacher functions and some congruence properties
ISBN:9781461302490
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Developments in Mathematics: 11
Keywords: Mathematics , Algebraic geometry , Algebra , Field theory (Physics) , Group theory , Mathematics , Field Theory and Polynomials , Algebraic Geometry , Group Theory and Generalizations
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Call number:SPRINGER-2004-9781461220589:ONLINE Show nearby items on shelf
Title:Approximation Theory Using Positive Linear Operators
Author(s): Radu Păltănea
Date:2004
Size:1 online resource (202 p.)
Note:10.1007/978-1-4612-2058-9
Contents:1 Introduction -- 1.1 Operators and functionals. Moduli of continuity -- 1.2 Approximation of functions by sequences of positive linear operators -- 2 Estimates with Second Order Moduli -- 2.1 A general approach -- 2.2 Estimates with
moduli ?2? and ?2? -- 2.3 Estimates with modulus ?2d -- 2.4 Estimates with modulus ?2dd -- 2.5 Estimates with Ditzian—Totik modulus -- 3 Absolute Optimal Constants -- 3.1 Introduction -- 3.2 Discrete functionals and the classical
second order modulus ?2 -- 3.3 General functionals and the second order modulus with parameter ?2? -- 4 Estimates for the Bernstein Operators -- 4.1 Various types of estimates -- 4.2 Best constant in the estimate with modulus ?2 -- 4.3
Global smoothness preservation -- 5 Two Classes of Bernstein Type Operators -- 5.1 Generalized Brass type operators -- 5.2 Generalized Durrmeyer type operators -- 6 Approximation Operators for Vector-Valued Functions -- 6.1
Approximation of functions with real argument -- 6.2 Approximation of functions with vector argument -- References
ISBN:9781461220589
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Field theory (Physics) , Approximation theory , Functional analysis , Integral transforms , Operational calculus , Operator theory , Applied mathematics , Engineering mathematics , Mathematics , Approximations and Expansions , Field Theory and Polynomials , Functional Analysis , Integral Transforms, Operational Calculus , Operator Theory , Applications of Mathematics
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Call number:SPRINGER-2004-9781402026607:ONLINE Show nearby items on shelf
Title:P-adic Deterministic and Random Dynamics
Author(s): Andrei Yu Khrennikov
Date:2004
Size:1 online resource (270 p.)
Note:10.1007/978-1-4020-2660-7
Contents:1. On Applications of P-Adic Analysis -- 2. P-Adic Numbers and P-Adic Analysis -- 3. P-Adic Dynamical Systems -- 4. Perturbation of Monomial Systems -- 5. Dynamical Systems in Finite Extensions of ? P -- 6. Conjugate Maps -- 7. P-Adic
Ergodicity -- 8. P-Adic Neural Networks -- 9. Dynamics in Ultra-Pseudometric Spaces -- 10. Random Dynamics -- 11. Dynamics of Probability Distributions on the P-Adic Mental Space -- 12. Ultrametric Wavelets and Their Applications --
13. Theory of P-Adic Valued Probability -- References
ISBN:9781402026607
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications : 574
Keywords: Physics , Algebraic geometry , Algebra , Field theory (Physics) , Functional analysis , Mechanics , Cognitive psychology , Physics , Mechanics , Field Theory and Polynomials , Mathematical Methods in Physics , Cognitive Psychology , Functional Analysis , Algebraic Geometry
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Call number:SPRINGER-2004-9781402021879:ONLINE Show nearby items on shelf
Title:Abel’s Theorem in Problems and Solutions Based on the lectures of Professor V.I. Arnold
Author(s): V.B Alekseev
Date:2004
Size:1 online resource (270 p.)
Note:10.1007/1-4020-2187-9
Contents:From the contents: Preface for the English edition V.I. Arnold -- Preface -- Introduction -- 1: Groups -- 2: The complex numbers -- 3: Hints, Solutions and Answers -- Appendix. Solvability of equations by explicit formulae A.
Khovanskii -- Bibliography -- Appendix V.I. Arnold -- Index
ISBN:9781402021879
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Field theory (Physics) , Group theory , Topological groups , Lie groups , Functions of complex variables , Mathematics , Group Theory and Generalizations , Functions of a Complex Variable , Field Theory and Polynomials , Topological Groups, Lie Groups
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Call number:SPRINGER-2004-9781402020292:ONLINE Show nearby items on shelf
Title:Resolution of Curve and Surface Singularities in Characteristic Zero
Author(s): K Kiyek
Date:2004
Size:1 online resource (486 p.)
Note:10.1007/978-1-4020-2029-2
Contents:I Valuation Theory -- 1 Marot Rings -- 2 Manis Valuation Rings -- 3 Valuation Rings and Valuations -- 4 The Approximation Theorem For Independent Valuations -- 5 Extensions of Valuations -- 6 Extending Valuations to Algebraic
Overfields -- 7 Extensions of Discrete Valuations -- 8 Ramification Theory of Valuations -- 9 Extending Valuations to Non-Algebraic Overfields -- 10 Valuations of Algebraic Function Fields -- 11 Valuations Dominating a Local Domain --
II One-Dimensional Semilocal Cohen-Macaulay Rings -- 1 Transversal Elements -- 2 Integral Closure of One-Dimensional Semilocal Cohen-Macaulay Rings -- 3 One-Dimensional Analytically Unramified and Analytically Irreducible CM-Rings -- 4
Blowing up Ideals -- 5 Infinitely Near Rings -- III Differential Modules and Ramification -- 1 Introduction -- 2 Norms and Traces -- 3 Formally Unramified and Unramified Extensions -- 4 Unramified Extensions and Discriminants -- 5
Ramification For Quasilocal Rings -- 6 Integral Closure and Completion -- IV Formal and Convergent Power Series Rings -- 1 Formal Power Series Rings -- 2 Convergent Power Series Rings -- 3 Weierstraß Preparation Theorem -- 4 The
Category of Formal and Analytic Algebras -- 5 Extensions of Formal and Analytic Algebras -- V Quasiordinary Singularities -- 1 Fractionary Power Series -- 2 The Jung-Abhyankar Theorem: Formal Case -- 3 The Jung-Abhyankar Theorem:
Analytic Case -- 4 Quasiordinary Power Series -- 5 A Generalized Newton Algorithm -- 6 Strictly Generated Semigroups -- VI The Singularity Zq = XYp -- 1 Hirzebruch-Jung Singularities -- 2 Semigroups and Semigroup Rings -- 3 Continued
Fractions -- 4 Two-Dimensional Cones -- 5 Resolution of Singularities -- VII Two-Dimensional Regular Local Rings -- 1 Ideal Transform -- 2 Quadratic Transforms and Ideal Transforms -- 3 Complete Ideals -- 4 Factorization of Complete
Ideals -- 5 The Predecessors of a Simple Ideal -- 6 The Quadratic Sequence -- 7 Proximity -- 8 Resolution of Embedded Curves -- VIII Resolution of Singularities -- 1 Blowing up Curve Singularities -- 2 Resolution of Surface
Singularities I: Jung’s Method -- 3 Quadratic Dilatations -- 4 Quadratic Dilatations of Two-Dimensional Regular Local Rings -- 5 Valuations of Algebraic Function Fields in Two Variables -- 6 Uniformization -- 7 Resolution of Surface
Singularities II: Blowing up and Normalizing -- Appendices -- A Results from Classical Algebraic Geometry -- 1 Generalities -- 1.1 Ideals and Varieties -- 1.2 Rational Functions and Maps -- 1.3 Coordinate Ring and Local Rings -- 1.4
Dominant Morphisms and Closed Embeddings -- 1.5 Elementary Open Sets -- 1.6 Varieties as Topological Spaces -- 1.7 Local Ring on a Subvariety -- 2 Affine and Finite Morphisms -- 3 Products -- 4 Proper Morphisms -- 4.1 Space of
Irreducible Closed Subsets -- 4.3 Proper Morphisms -- 5 Algebraic Cones and Projective Varieties -- 6 Regular and Singular Points -- 7 Normalization of a Variety -- 8 Desingularization of a Variety -- 9 Dimension of Fibres -- 10
Quasifinite Morphisms and Ramification -- 10.1 Quasifinite Morphisms -- 10.2 Ramification -- 11 Divisors -- 12 Some Results on Projections -- 13 Blowing up -- 14 Blowing up: The Local Rings -- B Miscellaneous Results -- 1 Ordered
Abelian Groups -- 1.1 Isolated Subgroups -- 1.2 Initial Index -- 1.3 Archimedean Ordered Groups -- 1.4 The Rational Rank of an Abelian Group -- 2 Localization -- 3 Integral Extensions -- 4 Some Results on Graded Rings and Modules --
4.1 Generalities -- 4.3 Homogeneous Localization -- 4.4 Integral Closure of Graded Rings -- 5 Properties of the Rees Ring -- 6 Integral Closure of Ideals -- 6.1 Generalities -- 6.2 Integral Closure of Ideals -- 6.3 Integral Closure of
Ideals and Valuation Theory -- 7 Decomposition Group and Inertia Group -- 8 Decomposable Rings -- 9 The Dimension Formula -- 10 Miscellaneous Results -- 10.1 The Chinese Remainder Theorem -- 10.2 Separable Noether Normalization -- 10.3
The Segre Ideal -- 10.4 Adjoining an Indeterminate -- 10.5 Divisor Group and Class Group -- 10.6 Calculating a Multiplicity -- 10.7 A Length Formula -- 10.8 Quasifinite Modules -- 10.9 Maximal Primary Ideals -- 10.10 Primary
Decomposition in Non-Noetherian Rings -- 10.11 Discriminant of a Polynomial -- Index of Symbols
ISBN:9781402020292
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Algebras and Applications: 4
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Functions of complex variables , Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Field Theory and Polynomials , Several Complex Variables and Analytic Spaces
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Call number:SPRINGER-2004-9780817681708:ONLINE Show nearby items on shelf
Title:Arithmetic of Higher-Dimensional Algebraic Varieties
Author(s):
Date:2004
Edition:1
Size:1 online resource (287 p.)
Note:10.1007/978-0-8176-8170-8
Contents:Diophantine equations: progress and problems -- Rational points and analytic number theory -- Weak approximation on algebraic varieties -- Counting points on varieties using universal torsors -- The Cox ring of a Del Pezzo surface --
Counting rational points on threefolds -- Remarques sur l’approximation faible sur un corps de fonctions d’une variable -- K3 surfaces over number fields with geometric Picard number one -- Jumps in Mordell-Weil rank and Arithmetic
Surjectivity -- Universal torsors and Cox rings -- Random diophantine equations -- Descent on simply connected surfaces over algebraic number fields -- Rational points on compactifications of semi-simple groups of rank 1 -- Weak
Approximation on Del Pezzo surfaces of degree 4 -- Transcendental Brauer-Manin obstruction on a pencil of elliptic curves
ISBN:9780817681708
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 226
Keywords: Mathematics , Algebraic geometry , Algebra , Field theory (Physics) , Functions of complex variables , Number theory , Mathematics , Number Theory , Algebraic Geometry , Field Theory and Polynomials , Several Complex Variables and Analytic Spaces
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Call number:SPRINGER-2004-9780387218311:ONLINE Show nearby items on shelf
Title:Integers, Polynomials, and Rings A Course in Algebra
Author(s): Ronald S Irving
Date:2004
Size:1 online resource (288 p.)
Note:10.1007/b97633
Contents:Introduction: The McNugget Problem -- Introduction: The McNugget Problem -- Integers -- Induction and the Division Theorem -- The Euclidean Algorithm -- Congruences -- Prime Numbers -- Rings -- Euler’ Theorem -- Binomial Coefficients
-- Polynomials -- Polynomials and Roots -- Polynomials with Real Coefficients -- Polynomials with Rational Coefficients -- Polynomial Rings -- Quadratic Polynomials -- Polynomial Congruence Rings -- All Together Now -- Euclidean Rings
-- The Ring of Gaussian Integers -- Finite Fields
ISBN:9780387218311
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Field theory (Physics) , Mathematics , Algebra , Associative Rings and Algebras , Field Theory and Polynomials
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Call number:SPRINGER-2004-9780306485176:ONLINE Show nearby items on shelf
Title:Applications of Fibonacci Numbers Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications
Author(s):
Date:2004
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource (311 p.)
Note:10.1007/978-0-306-48517-6
Contents:Universal Bernoulli Polynomials and P-Adic Congruences -- A Generalization of Durrmeyer-Type Polynomials and their Approximation Properties -- Fibinomial Identities -- Recounting Binomial Fibonacci Identities -- The Fibonacci Diatomic
Array Applied to Fibonacci Representations -- On Purple Parrots, Fibonacci Numbers, and Color Theory -- Finding Fibonacci in a Fractal -- Positive Integers (a2 + b2)/(ab + 1) are Squares -- On the Fibonacci Length of Powers of Dihedral
Groups -- Some Sums Related to Sums of Oresme Numbers -- Some Thoughts on Rook Polynomials on Square Chessboards -- Pythagorean Quadrilaterals -- A General Lacunary Recurrence Formula -- Ordering Words and Sets of Numbers: The
Fibonacci Case -- Some Basic Properties of a Tribonacci Line-Sequence -- A Type of Sequence Constructed from Fibonacci Numbers -- Cullen Numbers in Binary Recurrent Sequences -- A Generalization of Euler’s Formula and its Connection to
Fibonacci Numbers -- Extensions of Generalized Binomial Coefficients -- Some Parity Results Regarding t-Core Partitions -- Generalized Pell Numbers and Polynomials -- A Further Note on Lucasian Numbers -- Some Constructions and
Theorems in Goldpoint Geometry -- Some Applications of Triangle Transformations in Fibonacci Geometry -- Cryptography and Lucas Sequence Discrete Logarithms -- Divisibility of an F-L Type Convolution -- Generating Functions of
Convolution Matrices -- F-L Representation of Division of Polynomials over a Ring
ISBN:9780306485176
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Computer science , Algebra , Field theory (Physics) , Special functions , Number theory , Combinatorics , Mathematics , Number Theory , Combinatorics , Special Functions , Field Theory and Polynomials , Discrete Mathematics in Computer Science
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Call number:SPRINGER-2003-9789401703376:ONLINE Show nearby items on shelf
Title:Proceedings of the Third International Algebra Conference June 16–July 1, 2002 Chang Jung Christian University, Tainan, Taiwan
Author(s): Yuen Fong
Date:2003
Size:1 online resource (268 p.)
Note:10.1007/978-94-017-0337-6
ISBN:9789401703376
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Group theory , Nonassociative rings , Mathematics , Field Theory and Polynomials , Commutative Rings and Algebras , Associative Rings and Algebras , Non-associative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-2003-9783540450962:ONLINE Show nearby items on shelf
Title:Almost Ring Theory
Author(s):
Date:2003
Size:1 online resource (318 p.)
Note:10.1007/b10047
Contents:Introduction -- Homological Theory -- Almost Ring Theory -- Fine Study of Almost Projective Modules -- Henselian Pairs -- Valuation Theory -- Analytic Geometry -- Appendix -- References -- Index
ISBN:9783540450962
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1800
Keywords: Mathematics , Algebra , Algebraic geometry , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Field theory (Physics) , Mathematics , Algebra , Commutative Rings and Algebras , Algebraic Geometry , Category Theory, Homological Algebra , Field Theory and Polynomials
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