Series: Lecture Notes in Logic
Hardback (ISBN-13: 9780521899512)
Page extent: 464 pages
Size: 228 x 152 mm
The proceedings of the Los Angeles Caltech-UCLA gCabal Seminarh were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Focusing on the subjects of gGames and Scalesh (Part 1) and gSuslin Cardinals, Partition Properties, and Homogeneityh (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context.
Includes updated/revised material from original volume of Cabal Seminars.
Part I. Games and Scales: 1. Games and scales. introduction to part I John R. Steel; 2. Notes on the theory of scales Alexander S. Kechris and Yiannis N. Moschovakis; 3. Propagation of the scale property using games Itay Neeman; 4. Scales on E-sets John R. Steel; 5. Inductive scales on inductive sets Yiannis N. Moschovakis; 6. The extent of scales in L(R) Donald A. Martin and John R. Steel; 7. The largest countable this, that, and the other Donald A. Martin; 8. Scales in L(R) John R. Steel; 9. Scales in K(R) John R. Steel; 10. The real game quantifier propagates scales Donald A. Martin; 11. Long games John R. Steel; 12. The length-w1 open game quantifier propagates scales John R. Steel; Part II. Suslin Cardinals, Partition Properties, Homogeneity: 13. Suslin cardinals, partition properties, homogeneity. introduction to part II Steve Jackson; 14. Suslin cardinals, K-suslin sets and the scale property in the hyperprojective hierarchy Alexander S. Kechris; 15. The axiom of determinacy, strong partition properties and nonsingular measures Alexander S. Kechris, Eugene M. Kleinberg, Yiannis N. Moschovakis, and W. Hugh Woodin; 16. The equivalence of partition properties and determinacy Alexander S. Kechris; 17. Generic codes for uncountable ordinals, partition properties, and elementary embeddings Alexander S. Kechris and W. Hugh Woodin; 18. A coding theorem for measures Alexander S. Kechris; 19. The tree of a Moschovakis scale is homogeneous Donald A. Martin and John R. Steel; 20. Weakly homogeneous trees Donald A. Martin and W. Hugh Woodin.
Series: Cambridge Tracts in Mathematics (No. 177)
Hardback (ISBN-13: 9780521894876)
5 halftones 15 tables 10 worked examples
Page extent: 290 pages
Size: 228 x 152 mm
Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A MathematicaR software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of MathematicaR which aid in the computation of such functions.
* Fully explains the theory of higher dimensional sieves using many examples
* Modern and reliable guide for researchers needing to solve combinatorial
problems with sieving arguments * Computational methods are explained in
detail in an appendix and on the accompanying website
List of tables; List of illustrations; Preface; Notation; Part I. Sieves:
1. Introduction; 2. Selbergfs sieve method; 3. Combinatorial foundations;
4. The fundamental Lemma; 5. Selbergfs sieve method (continued); 6. Combinatorial
foundations (continued); 7. The case È = 1: the linear sieve; 8. An application
of the linear sieve; 9. A sieve method for È > 1; 10. Some applications
of Theorem 9.1; 11. A weighted sieve method; Part II. Proof of the Main
Analytic Theorem: 12. Dramatis personae and preliminaries; 13. Strategy
and a necessary condition; 14. Estimates of ÐÈ (u) = jÈ (u/2); 15. The
pÈ and qÈ functions; 16. The zeros of ®*2 and ¬; 17. The parameters
ÐÈ and ÀÈ; 18. Properties of FÈ and fÈ; Appendix 1. Methods for computing
sieve functions; Bibliography; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 115)
Hardback (ISBN-13: 9780521888615)
56 exercises 25 worked examples
Page extent: 208 pages
Size: 228 x 152 mm
Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmuller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.
* Includes complete proofs of major tools used in real and complex one-dimensional
dynamics, some of which have never before appeared in book format * Numerous
exercises aid understanding and provide a glimpse of further developments
in real and complex one-dimensional dynamics * Appendix on Riemann surfaces
and Teichmuller theory includes proofs of some key results in this theory,
such as the Bers embedding
Preface; 1. Introduction; 2. Preliminaries in complex analysis; 3. Uniformization and conformal distortion; 4. The measurable Riemann mapping theorem; 5. Holomorphic motions; 6. The Schwarzian derivative and cross-ratio distortion; 7. Appendix: Riemann Surfaces and Teichmuller spaces; Bibliography; Index.
Hardback (ISBN-13: 9780521898065)
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
* Comprehensive: generous notes, appendices, examples and exercises, as
well as the inclusion of proofs of fundamental results * Unified: ties
together classical mathematics and modern applications * Cutting edge:
first book with extensive coverage of analytic methods needed to analyse
large combinatorial configurations
Preface; An invitation to analytic combinatorics; Part A. Symbolic Methods: 1. Combinatorial structures and ordinary generating functions; 2. Labelled structures and exponential generating functions; 3. Combinatorial parameters and multivariate generating functions; Part B. Complex Asymptotics: 4. Complex analysis, rational and meromorphic asymptotics; 5. Applications of rational and meromorphic asymptotics; 6. Singularity analysis of generating functions; 7. Applications of singularity analysis; 8. Saddle-Point asymptotics; Part C. Random Structures: 9. Multivariate asymptotics and limit laws; Part D. Appendices: Appendix A. Auxiliary elementary notions; Appendix B. Basic complex analysis; Appendix C. Concepts of probability theory; Bibliography; Index.