304 pages | 234x153mm
978-0-19-870259-7 | Hardback | August 2015 (estimated)
A comprehensive yet succinct look at the development of conceptions of number from ancient Greece to the beginning of the twentieth century
The history of mathematics has been a very active and changing field of research over the last 25 years
Accessible to undergraduate students of mathematics and the sciences, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be?
In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century.
Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.
Readership: The intended readership of this book includes undergraduate students of mathematics and the sciences, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.
1: The System of Numbers: An Overview
2: Writing Numbers: Now and Back Then
3: Numbers and Magnitudes in the Greek Mathematical Tradition
4: Construction Problems and Numerical Problems in the Greek Mathematical Tradition
5: Numbers in the Tradition of Medieval Islam
6: Numbers in Europe from the 12th to the 16th Centuries
7: Number and Equations at the Beginning of the Scientific Revolution
8: Number and Equations in theWorks of Descartes, Newton, and their Contemporaries
9: New Definitions of Complex Numbers in the Early 19th Century
10: "What are numbers and what should they be?" Understanding Numbers in the Late 19th Century
11: Exact Definitions for the Natural Numbers: Dedekind, Peano and Frege
12: Numbers, Sets and Infinity. A Conceptual Breakthrough at the Turn of the Twentieth Century
13: Epilogue: Numbers in Historical Perspective
February 2015 1472 pages
Series: SAGE Benchmarks in Social Research Methods
Hardcover ISBN: 9781446294604
This four-volume Major Work contains texts which explore both the foundations of latent variables and factor analysis, and specific contemporary
hallenges in the field.
The collection has been designed as a multi-disciplinary resource, with literature drawn from many different areas of study, such as sociology, psychology, education and political science.
In the editorfs introductory essay, a general approach to the meaning and use of latent variables in the social sciences is laid out, the basics of factor analysis and how it works are explained, and the logic that guided the selection of literature included in the collection is elaborated upon. The combination of these elements makes for a truly comprehensive and user-friendly research tool, invaluable to social scientists across a range of disciplines.
Volume One: The Conceptualization and Operationalization of Variables
Volume Two: Applications of Unmeasured Variables
Volume Three: Factor Analysis for Latent Variables
Volume Four: Advanced Topics
Series: SpringerBriefs in Applied Sciences and Technology
Subseries: SpringerBriefs in Mathematical Methods
2015, 100 p. 30 illus.
Information
ISBN 978-3-319-15397-1
Due: July 10, 2015
The target audience for this book consists of graduate students, researchers and practitioners in the field, both mathematicians and computer scientists
This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and to their analysis
The state space of a concurrent program is described as a higher-dimensional space whose topology encodes the essential properties of the system
This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and to their analysis. The state space of a concurrent program is described as a higher-dimensional space whose topology encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than gjusth topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a consequence, tools and concepts from topology have to be extended to take privileged directions into account.
With a point of departure in well-known discrete models for concurrent processes with resource management, the book develops refinements in terms of combinatorial and topological models. Along the line, it motivates and develops tools and invariants for the new discipline directed algebraic topology that is driven by fundamental research interests as well as by applications in primarily the static analysis of concurrent programs.
The target audience for this book consists of graduate students, researchers and practitioners in the field, both mathematicians and computer scientists.
Content Level â Research
Keywords â ALCOOL Tool - Concurrency Theory - Directed Algebraic Topology - Distributed Networks - Geometrical Models for Execution Spaces - Higher Dimensional Automata - Models for Concurrency - State space Reduction - Static Analysis of Concurrent Programs
Related subjects â Complexity - Geometry & Topology - Theoretical Computer Science
Clearly describes the Hamiltonian quantization for constrained physical systems
Bridges the gap between the development and application of advanced Dirac quantization associated with BRST symmetries
A valuable source of information for researchers of various branches in quantum field theories
Makes connections among Hamiltonian quantization, BRST symmetry, hadron phenomenology and de Rham cohomology
Emphases both topological and phenomenological aspects of the subject
This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. It offers a critical overview of the research in this area and unifies the existing literature, employing a consistent notation.
Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST quantization for constrained physical systems and its corresponding de Rham cohomology group structure. These were studied by theoretical physicists from the early 1960s and appeared in attempts to quantize rigorously some physical theories such as solitons and other models subject to geometrical constraints. In particular, phenomenological soliton theories such as Skyrmion and chiral bag models have seen a revival following experimental data from the SAMPLE and HAPPEX Collaborations, and these are discussed. The book describes how these model predictions were shown to include rigorous treatments of geometrical constraints because these constraints affect the predictions themselves. The application of the BRST symmetry to the de Rham cohomology contributes to a deep understanding of Hilbert space of constrained physical theories.
Aimed at graduate-level students in quantum field theory, the book will also serve as a useful reference for those working in the field. An extensive bibliography guides the reader towards the source literature on particular topics.
Content Level â Research
Keywords â BRST Extension - BRST Symmetry - Chiral Bag Model - De Rham Cohomology - Hamilton-Jacobi Quantization - Hamiltonian Quantization - Noncommutative D-brane System - Schrodinger Representation - Skyrmion Model - Soliton Model
Related subjects â Particle and Nuclear Physics - Theoretical, Mathematical & Computational Physics
Preface.
1. Introduction.
2. Hamiltonian quantization with constraints.
2.1 Hamiltonian quantization of free particle on sphere. 2.2 Hamiltonian quantization of free particle on torus.
3. BRST symmetry in constrained systems.
3.1 BRST symmetry in free particle system on sphere. 3.2 BRST symmetry in free particle system on torus.
4. Symplectic embedding and Hamilton-Jacobi quantization.
4.1 . Symplectic embedding of free particle system on torus. 4.2 Hamilton-Jacobi quantization of nonholonomic system. 4.3 Symplectic embedding and Hamilton-Jacobi analysis of Proca model.
5. Hamiltonian quantization and BRST symmetry of soliton models.
5.1 Hamiltonian and semi-classical quantization of O(3) nonlinear sigma model. 5.2 Schrodinger representation of O(3) nonlinear sigma model. 5.3 BRST symmetry in SU(3) linear sigma model. 5.4 BRST extension of Faddeev model.
6. Hamiltonian quantization and BRST symmetry of Skyrmion models.
6.1 Hamiltonian quantization of SU(2) Skyrmion. 6.2 BRST Symmetry of SU(2) Skyrmion. 6.3 Hamiltonian quantization of SU(3) Skyrmion. 6.4 Flavor symmetry breaking effect on SU(3) Skyrmion.
7. Hamiltonian structure of other models.
7.1 Bosonization of QCD at high density. 7.2 Gauge symmetry enhancement of enlarged CP(,N) model.
8. Phenomenological soliton.
8.1 Sum rules for strange form factors and flavor singlet axial charges. 8.2 Sum rules for baryon decuplet magnetic moments.
9. De Rham cohomology in constrained physical system.
9.1 De Rham cohomology in algebraic topology. 9.2 De Rham cohomology in 't Hooft-Polyakov monopole.
Series: SpringerBriefs in Statistics
Subseries: JSS Research Series in Statistics
2015, Approx. 125 p. 20 illus.
Softcover
ISBN 978-4-431-55458-5
Due: July 7, 2015
Presents the first comprehensive treatment of maximal ranks and typical ranks over the real number file
Provides interesting ideas of determinant polynomials, determinantal ideals, absolutely nonsingular tensors and absolutely full column rank tensors
Includes numerical methods of determining ranks by simultaneous singular value decomposition through a theory of matrix star algebra
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions.
Content Level â Research
Keywords â Computational Aspects of Tensor Ranks - Full Rank Tensors - Maximal Rank of Real Tensors - Simultaneous Singular Value Decomposition - Typical Rank of Real Tensors
Related subjects â Computational Statistics - Physical & Information Science - Social Sciences & Law
1. Basics of Tensor Rank -2. Characterizations of Tensor Ranks -3. Evaluations of Small Three Tensors -4. A Group Action and Determinant Polynomials -5. Maximal Ranks -6. Typical Ranks -7. Global Theory of Tensor Ranks -8. 2 x 2 x ... x 2 Tensors -9 Block Diagonalizations .
Series: Atlantis Studies in Variational Geometry, Vol. 2
2015, Approx. 250 p.
Hardcover
ISBN 978-94-6239-108-6
Due: September 8, 2015
Unified exposition of the inverse variational problem for ordinary and partial differential equations and for equations on manifolds
First systematic contribution to the global inverse problem of the calculus of variations based on modern differential geometry and algebraic topology
Selected applications of the inverse problem in geometry, optimal control theory and modern theoretical physics (higher-order mechanics and general relativity)
Prepares the reader for research in the local and global inverse problem using variational sequence theory and its consequences based on elementary sheaf theory
The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).
Content Level â Research
Keywords â Euler-Lagrange form - Helmholtz conditions - Lagrangian - Source form - Variational sequence
Related subjects â Analysis - Geometry & Topology - Mathematics - Theoretical, Mathematical & Computational Physics
Series: Atlantis Studies in Differential Equations, Vol. 5
2015, Approx. 150 p. 10 illus.
Hardcover
ISBN 978-94-6239-120-8
Due: October 8, 2015
First monograph on the subject
Many examples to illustrate the theory
Open problems to work on
This monograph covers the existing results regarding Greenfs functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Greenfs functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Greenfs function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.
Content Level â Research
Keywords â Differential Equations with reflection - Functional-Differential Equations of Carleman type - Green's functions - Maximum principles - Ordinary Differential Equations with involutions
Related subjects â Dynamical Systems & Differential Equations - Theoretical, Mathematical & Computational Physics