This book provides a comprehensive collection of problems together with their detailed solutions in the field of Theoretical and Mathematical Physics. All modern fields in Theoretical and Mathematical Physics are covered. It is the only book which covers all the new techniques and methods in theoretical and mathematical physics.
Third edition updated with: Exercises in: Hilbert space theory, Lie groups, Matrix-valued differential forms, Bose?Fermi operators and string theory. All other chapters have been updated with new problems and materials. Most chapters contain an introduction to the subject discussed in the text.
Volume I:
Complex Numbers and Functions
Sums and Product
Discrete Fourier Transform
Algebraic and Transcendental Equations
Vector and Matrix Calculations
Matrices and Groups
Matrices and Eigenvalue Problems
Functions of Matrices
Transformations
L'Hospital's Rule
Lagrange Multiplier Method
Linear Difference Equations
Linear Differential Equations
Integration
Continuous Fourier Transform
Complex Analysis
Special Functions
Inequalities
Functional Analysis
Combinatorics
Convex Sets and Functions
Optimization
Volume II:
Groups
Kronecker and Tensor Products
Nambu Mechanics
Gateaux and Frechet Derivatives
Stability and Bifurcations
Nonlinear Ordinary Difference Equations
Nonlinear Ordinary Differential Equations
Lax Representations in Classical Mechanics
Hilbert Spaces
Generalized Functions
Linear Partial Differential Equations
Nonlinear Partial Differential Equations
Symmetries and Group Theoretical Reductions
Soliton Equations
Backlund Transformations
Lax Pairs for Partial Differential Equations
Hirota Technique
Painleve Test
Lie Algebras
Lie Groups
Differential Forms
Matrix-Valued Differential Forms
Lie Derivative
Metric Tensor Fields
Killing Vector Fields
Inequalities
Ising Model and Heisenberg Model
Number Theory
Combinatorial Problems
Fermi Operators
Bose Operators
Bose?Fermi Systems
Lax Representations and Bethe Ansatz
Gauge Transformations
Chaos, Fractals and Complexity
Readership: Undergraduates, graduate students, academics and researchers in physics and mathematics.
Vol. I
250pp (approx.) Pub. date: Scheduled Fall 2009
ISBN 978-981-4282-14-7
ISBN 978-981-4282-15-4(pbk)
Vol. II
410pp (approx.) Pub. date: Scheduled Fall 2009
ISBN 978-981-4282-16-1
ISBN 978-981-4282-17-8(pbk)
Murray Gell-Mann is one of the leading physicists in the world. He was awarded the Nobel Prize in Physics in 1969 for his work on the SU(3) symmetry. His list of publications, albeit relatively short, is highly impressive ? he has written mainly papers, which have become landmarks in physics. In 1953, Gell-Mann introduced the strangeness quantum number. In 1954, he proposed, together with F Low, the idea of the renormalization group. In 1958, Gell-Mann wrote, together with R Feynman, an important paper on the V-A theory of weak interactions. In 1961, Gell-Mann published his ideas on the SU(3) symmetry. In 1964, he proposed the quark model for hadrons. In 1971, Gell-Mann, together with H Fritzsch, proposed the color quantum number; and in 1972, the theory of QCD. These major publications of Gell-Mann are collected in this volume, thus providing physicists with easy access to the important publications of Gell-Mann.
The Garden of Live Flowers
Strangeness
Quantum Electrodynamics at Small Distances
Theory of the Fermi Interaction
The Eightfold Way: A Theory of Strong Interaction Symmetry
Symmetries of Baryons and Mesons
A Schematic Model of Baryons and Mesons
Current Topics in Particle Physics
Quarks: Developments in the Theory of Hadrons
Current Algebra: Quarks and What Else?
Particle Theory from S-Matrix to Quarks
Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology
Progress in Elementary Particle Theory, 1950?1964
Nature Conformable to Herself
Quarks, Color and QCD
Effective Complexity
and other papers
Readership: Researchers in high energy physics and theoretical physics.
300pp Pub. date: Jul 2009
ISBN: 978-981-283-684-7
981-283-684-5
Stochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics.
The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject.
Introduction: Stochastic Analysis and Stochastic Dynamics
A Glimpse of Stochastic Dynamical Systems
Progress in White Noise Analysis
Dynamical Systems Driven by Fractional Brownian Motion
Dynamical Systems Driven by Non-Gaussian Noise
Stochastic Dynamical Systems with Memory
Simulation of Stochastic Dynamical Systems
Readership: Applied mathematicians, statisticians, scientists and engineers, mathematical modelers, and other professionals who are interested in stochastic modeling, analysis, simulation and prediction.
400pp Pub. date: Oct 2009
ISBN: 978-981-4277-25-9
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
ISBN: 9781439800218
Publication Date: 21/05/2009
Pages: 232
Although ROC curves have become ubiquitous in many application areas, the various advances have been scattered across disparate articles and texts. ROC Curves for Continuous Data is the first book solely devoted to the subject, bringing together all the relevant material to provide a clear understanding of how to analyze ROC curves.
The fundamental theory of ROC curves
The book first discusses the relationship between the ROC curve and numerous performance measures and then extends the theory into practice by describing how ROC curves are estimated. Further building on the theory, the authors present statistical tests for ROC curves and their summary statistics. They consider the impact of covariates on ROC curves, examine the important special problem of comparing two ROC curves, and cover Bayesian methods for ROC analysis.
Special topics
The text then moves on to extensions of the basic analysis to cope with more complex situations, such as the combination of multiple ROC curves and problems induced by the presence of more than two classes. Focusing on design and interpretation issues, it covers missing data, verification bias, sample size determination, the design of ROC studies, and the choice of optimum threshold from the ROC curve. The final chapter explores applications that not only illustrate some of the techniques but also demonstrate the very wide applicability of these techniques across different disciplines.
With nearly 5,000 articles published to date relating to ROC analysis, the explosive interest in ROC curves and their analysis will continue in the foreseeable future. Embracing this growth of interest, this timely book will undoubtedly guide present and future users of ROC analysis.
Introduction. Population ROC Curves. Estimation. Further Inference on Single Curves. ROC Curves and Covariates. Comparing ROC Curves. Bayesian Methods. Beyond the Basics. Design and Interpretation Issues. Substantive Applications. Appendix. References.
ISBN: 9781420079333
Publication Date: 04/08/2009
Pages: 376
Binding(s): Paperback
Like its bestselling predecessor, A Handbook of Statistical Analyses Using R, Second Edition provides a guide to data analysis using the R system for statistical computing. Each chapter includes a brief account of the relevant statistical background, along with appropriate references.
New chapters on graphical displays, generalized additive models, and simultaneous inference
A new section on generalized linear mixed models that completes the discussion on the analysis of longitudinal data where the response variable does not have a normal distribution
New examples and additional exercises in several chapters
A new version of the HSAUR package (HSAUR2), which is available from CRAN
This edition continues to offer straightforward descriptions of how to conduct a range of statistical analyses using R, from simple inference to recursive partitioning to cluster analysis. Focusing on how to use R and interpret the results, it provides students and researchers in many disciplines with a self-contained means of using R to analyze their data.
An Introduction to R. Data Analysis Using Graphical Displays. Simple Inference. Conditional Inference. Analysis of Variance. Simple and Multiple Linear Regression. Logistic Regression and Generalized Linear Models. Density Estimation. Recursive Partitioning. Scatterplot Smoothers and Generalized Additive Models. Survival Analysis. Analyzing Longitudinal Data I. Analyzing Longitudinal Data II. Simultaneous Inference and Multiple Comparisons. Meta-Analysis. Principal Component Analysis. Multidimensional Scaling. Cluster Analysis. Bibliography. Index.
International Series of Monographs on Physics 101
248 pages | 234x156mm
978-0-19-956640-2 | Paperback | 07 May 2009
This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.
Readership: Graduate students of quantum theory (both mathematicians and physicists). Researchers in mathematical physics and related areas.
States and observables
Quantum theory
The relativistic symmetry
Local observables
Scattering theory
Sector theory
Appendix A: Hilbert space and operators
Appendix B: Operator algebras
Appendix C: Free fields
608 pages | 40 illustrations | 234x156mm
978-0-19-923257-4 | Hardback | November 2009 (estimated)
Stochastic Geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, their probability theory, and the challenging problems raised by their statistical analysis. It has grown rapidly in response to challenges in all kinds of applied science, from image analysis through to materials science. Recently, still more stimulus has arisen from exciting new links with rapidly developing areas of mathematics, from fractals through percolation theory to randomized allocation schemes. Coupled with many ongoing developments arising from all sorts of applications, the area is changing and developing rapidly. This book is intended to lay foundations for future research directions, by collecting together 17 chapters contributed by leading researchers in the field, both theoreticians and people involved in applications, surveying these new developments both in theory and in applications. It will introduce and lay foundations for appreciating the fresh perspectives, new ideas and interdisciplinary connections now arising from Stochastic Geometry and from other areas of mathematics now connecting to this area. This will benefit young researchers wishing to gain quick access to the area, scientists from other fields wanting perspectives on what the area has to offer their own speciality, and workers already active in the field who will enjoy and profit from the coverage of a wide and rapidly developing field.
Readership: Graduates and researchers in mathematics and probability.
Preface
1: Rolf Schneider & Wolfgang Weil: Classical stochastic geometry
I NEW DEVELOPMENTS IN CLASSICAL STOCHASTIC GEOMETRY
2: Matthias Reitzner: Random polytopes
3: Gunter Last: Modern random measures: Palm theory and related models
4: Tomasz Schreiber: Limit theorems in stochastic geometry
5: P. Calka: Tessellations
II STOCHASTIC GEOMETRY AND MODERN PROBABILITY
6: Remco van der Hofstad: Percolation and random graphs
7: Mathew D. Penrose & Andrew R. Wade: Random directed and on-line networks
8: Peter Morters: Random fractals
III STATISTICS AND STOCHASTIC GEOMETRY
9: Jesper Moller: Inference
10: W.S. Kendall & Huiling Le: Statistical shape theory
11: Antonio Cuevas & Ricardo Fraiman: Set estimation
12: Ignacio Cascos: Data depth: multivariate statistics and geometry
IV APPLICATIONS
13: M.N.M. van Lieshout: Applications of stochastic geometry in image analysis
14: Werner Nagel: Stereology
15: Klaus Mecke: Physics of spatially structured materials
16: Sergei Zuyev: Stochastic geometry and telecommunications networks
17: Ilya Molchanov: Random sets in finance and econometrics
Index
Oxford Graduate Texts in Mathematics 19
368 pages | 35 illustrations | 234x156mm
978-0-19-857062-2 | Hardback | December 2009 (estimated)
978-0-19-857063-9 Paperback
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations.
The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.
Readership: Suitable for advanced undergraduate and research students, as well as experts in soliton theory and differential geometry.
Preface
1: Integrability in classical mechanics
2: Soliton equations and the Inverse Scattering Transform
3: The hamiltonian formalism and the zero-curvature representation
4: Lie symmetries and reductions
5: The Lagrangian formalism and field theory
6: Gauge field theory
7: Integrability of ASDYM and twistor theory
8: Symmetry reductions and the integrable chiral model
9: Gravitational instantons
10: Anti-self-dual conformal structures
Appendix A: Manifolds and Topology
Appendix B: Complex analysis
Appendix C: Overdetermined PDEs
Index