Series: Advanced Courses in Mathematics - CRM Barcelona,
2005, VIII, 264 p., Softcover
ISBN: 3-7643-7264-8
A Birkhauser book
About this textbook
The solution of the distortion problem for the Hilbert space, the unconditional basic sequence problem for Banach spaces, and the Banach homogeneous space problem are samples of the most important recent advances where Ramsey methods are used. The main goal of this book is to expose the general principles and methods that lie hidden behind and are most likely useful for further developments.
Written for:
Graduate students and researchers
Keywords:
Banach spaces
Ramsey method
Table of contents
Series: International Series of Numerical Mathematics, Vol. 152
2005, Approx. 256 p., Hardcover
ISBN: 3-7643-7238-9
About this book
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
Table of contents
Preface.- I Basic Concepts: Introduction. Problem Formulations. Convex and Lagrangian Relaxations. Decomposition Methods. Semidefinite Relaxations. Convex Underestimators. Cuts, Lower Bounds and Box Reduction. Local and Global Optimality Criteria. Adaptive Discretization of Infinite Dimensional MINLPs.- II Algorithms: Overview of Global Optimization Methods. Deformation Heuristics. Rounding, Partitioning and Lagrangian Heuristics. Branch-Cut-and-Price Algorithms. LaGO.- Bibliography.- Index.
Series: Cambridge Monographs on Mathematical Physics
Paperback (ISBN 052101736X)
Also available in Hardback
available from May 2005
This graduate/research level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantisation of strings, gravity and topological field theory. With chapters on random walks, random surfaces, two- and higher dimensional quantum gravity, topological quantum field theories and Monte Carlo simulations of random geometries, the text provides a self-contained account of quantum geometry from a statistical field theory point of view. The approach uses discrete approximations and develops analytical and numerical tools. Continuum physics is recovered through scaling limits at phase transition points and the relation to conformal quantum field theories coupled to quantum gravity is described. The most important numerical work is covered, but the main aim is to develop mathematically precise results that have wide applications. Many diagrams and references are included.
? First book on the subject
? Authors leading pioneers in research in the topics covered by the book
Contents
Preface; 1. Introduction; 2. Random walks; 3. Random surfaces; 4. Two-dimensional gravity; 5. Monte Carlo simulations; 6. Gravity in higher dimensions; 7. Topological quantum field theories; References; Index.
Series: Cambridge Studies in Probability, Induction and Decision Theory
Hardback (ISBN-10: 0521444705)
Paperback (ISBN-10: 052144912X)
available from July 2005
This volume brings together a collection of essays on the history and philosophy of probability and statistics by one of the eminent scholars in these subjects. Written over the last fifteen years, they fall into three broad categories. The first deals with the use of symmetry arguments in inductive probability, in particular, their use in deriving rules of succession (Carnap’s ‘continuum of inductive methods’). The second group deals with four outstanding individuals who made lasting contributions to probability and statistics in very different ways: Frank Ramsey, R. A. Fisher, Alan Turing, and Abraham de Moivre. The last group of essays deals with the problem of ‘predicting the unpredictable’ - making predictions when the range of possible outcomes is unknown in advance. The essays weave together the history and philosophy of these subjects and document the fascination that they have exercised for more than three centuries.
? Interweaving of history, philosophy and mathematics
? Focus on important Cambridge personalities: Ramsey, Fisher, and Turing
? Explains the origins of modern subjective probability
Contents
Part I. Probability: 1. Symmetry and its discontents; 2. The rule of succession; 3. Buffon, Price, and Laplace: scientific attribution in the eighteenth century; 4. W. E. Johnson’s sufficientness postulate. Part II. Personalities: 5 Abraham De Moivre and the birth of the Central Limit Theorem; 6 Ramsey, truth, and probability; 7. R. A. Fisher on the history of inverse probability; 8. R. A. Fisher and the fiducial argument; 9. Alan Turing and the Central Limit Theorem; Part III. Prediction: 10. Predicting the unpredictable; 11. The continuum of inductive methods revised.
Hardback (ISBN-10: 0521854830)
Paperback (ISBN-10: 0521671051)
- available from August 2005 (Stock level updated: 05:54 GMT, 17 May 2005)
Textbook
Lecturers can request inspection copies of this title.
This lively and engaging textbook provides the knowledge required to read empirical papers in the social and health sciences, as well as the techniques needed to build statistical models. The author explains the basic ideas of association and regression, and describes the current models that link these ideas to causality. He focuses on applications of linear models, including generalized least squares and two-stage least squares. The bootstrap is developed as a technique for estimating bias and computing standard errors. Careful attention is paid to the principles of statistical inference. There is background material on study design, bivariate regression, and matrix algebra. To develop technique, there are computer labs, with sample computer programs. The book's discussion is organized around published studies, as are the numerous exercises - many of which have answers included. Relevant papers reprinted at the back of the book are thoroughly appraised by the author.
? Enormously respected and well-known author
? Features plenty of exercises - most with solutions - and includes background material on matrix algebra and regression
? Thoroughly class-tested over many years at Berkeley, and has extra material for instructors available from www.cambridge.org/0521671051
Contents
1. Observational studies and experiments; 2. The regression line; 3. Matrix algebra; 4. Multiple regression; 5. Path models; 6. Maximum likelihood; 7. The bootstrap; 8. Simultaneous equations; References; Answers to exercises; The computer labs; Appendix: sample MATLAB code; Reprints; Index.
Series: Cambridge Tracts in Mathematics
Hardback (ISBN-10: 0521855357)
available from December 2005 (Stock level updated: 08:00 GMT, 17 May 2005)
This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture.
? Demonstrates how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, and Number Theory, can be applied to the study of unit cubes
? Eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture
? In particular the author demonstrates applications of deep analysis like log concave measure and the Brascamp-Lieb inequality
Contents
Preface; Basic notation; 0. Introduction; 1. Inscribed simplices; 2. Projections; 3. Inscribed simplices; 4. Triangulations; 5. 0/1 polytopes; 6. Minkowski’s conjecture; 7. Furtwangler’s conjecture; 8. Keller’s conjecture; Bibliography; Index.
Hardback (ISBN-10: 0521849039)
available from December 2005 (Stock level updated: 08:00 GMT, 17 May 2005)
Textbook
Lecturers can request inspection copies of this title.
Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. The text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.
? Large collection of stimulating problems associated with each section
? Extensive references to both historical background and further development of subject
? Based extensively on the material used successfully at the University of Michigan, Imperial College London, and Penn State University
Contents
Contributors
Preface; Notation; 1. Dirichlet series-I; 2. The elementary theory of arithmetic functions; 3. Principles and first examples of sieve methods; 4. Primes in arithmetic progressions-I; 5. Dirichlet series-II; 6. The prime number theorem; 7. Applications of the prime number theorem; 8. Further discussion of the prime number theorem; 9. Primitive characters and Gauss sums; 10. Analytic properties of the zeta function and L-functions; 11. Primes in arithmetic progressions-II; 12. Explicit formulae; 13. Conditional estimates; 14. Zeros; 15. Oscillations of error terms; Appendix A. The Riemann-Stieltjes integral; Appendix B. Bernoulli numbers and the Euler-MacLaurin summation formula; Appendix C. The gamma function; Appendix D. Topics in harmonic analysis.