Part of Lecture Notes in Logic
DATE PUBLISHED: November 2020 AVAILABILITY: Not yet published - available from February 2021
FORMAT: Multiple copy pack SBN: 9781108920223
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. This series of four books collects the seminal papers from those proceedings, together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Volume I focuses on the subjects of 'Games and Scales' and 'Suslin Cardinals, Partition Properties, and Homogeneity', Volume II on 'Wadge Degrees and Pointclasses' and 'Projective Ordinals', Volume III on 'HOD and its Local Versions' and 'Recursion Theory', and Volume IV on 'Extensions of AD, models with choice', along with material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of every set theorist's library.
Includes updated/revised material from the original Cabal Seminars volume
New, unpublished survey articles put the historical papers into context
Now includes uniform and modern notation to make the material more accessible to the reader
Part of London Mathematical Society Lecture Note Series
PUBLICATION PLANNED FOR: May 2021AVAILABILITY: Not yet published - available from May 2021
FORMAT: Paperback ISBN: 9781108949538
The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.
The first book on the theory of modules invariant under automorphisms of their envelopes and covers
Begins with the basics of ring and module theory, making it self-contained and suitable for graduate students
Contains plentiful examples and a whole chapter of open problems to which researchers can apply the theory
1. Preliminaries
2. Modules invariant under automorphisms of envelopes
3. Structure and properties of modules invariant under automorphisms
4. Automorphism-invariant modules
5. Modules coinvariant under automorphisms of their covers
6. Schroder?Bernstein problem
7. Automorphism-extendable modules
8. Automorphism-liftable modules
9. Open problems
References
Index.
PUBLICATION PLANNED FOR: July 2021AVAILABILITY: Not yet published - available from July 2021
FORMAT: PaperbackISBN: 9781108798853
String matching is one of the oldest algorithmic techniques, yet still one of the most pervasive in computer science. The past 20 years have seen technological leaps in applications as diverse as information retrieval and compression. This copiously illustrated collection of puzzles and exercises in key areas of text algorithms and combinatorics on words offers graduate students and researchers a pleasant and direct way to learn and practice with advanced concepts. The problems are drawn from a large range of scientific publications, both classic and new. Building up from the basics, the book goes on to showcase problems in combinatorics on words (including Fibonacci or Thue-Morse words), pattern matching (including Knuth-Morris-Pratt and Boyer-Moore like algorithms), efficient text data structures (including suffix trees and suffix arrays), regularities in words (including periods and runs) and text compression (including Huffman, Lempel-Ziv and Burrows-Wheeler based methods).
150 illustrations and 125 exercises support understanding of proofs
All self-contained problems come with worked solutions
A wide-ranging bibliography points to applications and research directions
1. The Very Basics of Stringology
2. Combinatorial Puzzles
3. Pattern Matching
4. Efficient Data Structures
5. Regularities in Words
6. Text Compression
7. Miscellaneous.
Part of Cambridge Studies in Advanced Mathematics
PUBLICATION PLANNED FOR: April 2021AVAILABILITY: Not yet published - available from April 2021
FORMAT: HardbackISBN: 9781108840965
Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
Provides an introduction to probabilistic number theory from scratch at a level suitable for beginning graduate students
Contains the most up-to-date developments in probabilistic number theory that are not available in any other book
Emphasizes the probabilistic aspects of the proofs, and probability theory language, highlighting how ideas from probability are useful to understand even arithmetic arguments
Contains appendices reviewing the basic results in analysis, probability and number theory most commonly used in the text
1. Introduction
2. Classical probabilistic number theory
3. The distribution of values of the Riemann zeta function, I
4. The distribution of values of the Riemann zeta function, II
5. The Chebychev bias
6. The shape of exponential sums
7. Further topics
Appendix A. Analysis
Appendix B. Probability
Appendix C. Number theory
References
Index
Part of Encyclopedia of Mathematics and its Applications
PUBLICATION PLANNED FOR: July 2021AVAILABILITY: Not yet published - available from July 2021
FORMAT: HardbackISBN: 9781108492607
Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on algorithms as connected with graph theory.
Timely coverage of the rapidly expanding area of algorithmic graph theory
Written by world leaders in the field, with authors from eleven countries and five continents
Provides extensive background material and gives detailed references for each chapter
Covers the main areas of the subject, using a consistent chapter structure, terminology and notation throughout
Foreword Martin Charles Golumbic
Preface Lowell W. Beineke and Robin J. Wilson
Preliminaries Lowell W. Beineke, Martin Charles Golumbic and Robin J. Wilson
1. Graph Algorithms Martin Charles Golumbic
2. Graph Colouring Variations Alain Hertz and Bernard Ries
3. Total Colouring Celina M. H. de Figueiredo
4. Testing of Graph Properties Ilan Newman
5. Cliques, Colouring and Satisfiability: From Structure to Algorithms Vadim Lozin
6. Chordal Graphs Martin Charles Golumbic
7. Dually and Strongly Chordal Graphs Andreas Brandstadt and Martin Charles Golumbic
8. Leaf Powers Christian Rosenke, Van Bang Le and Andreas Brandstadt
9. Split Graphs Karen L. Collins and Ann N. Trenk
10. Strong Cliques and Stable Sets Martin Milani?
11. Restricted Matchings Maximilian Furst and Dieter Rautenbach
12. Covering Geometric Domains Gila Morgenstern
13. Graph Homomorphisms Pavol Hell and Jaroslav Ne?et?il
14. Sparsity and Model Theory Patrice Ossona de Mendez
15. Extremal Vertex-sets Serge Gaspers
Notes on Contributors
Index.
PUBLICATION PLANNED FOR: August 2021AVAILABILITY: Not yet published - available from August 2021
FORMAT: PaperbackISBN: 9781108969086
Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.
The revised second edition, with more examples and additional background material
Contains a wealth of new exercises to challenge the reader
Gives a direct and straightforward account of the mathematical theory
'Garling's book presents Galois theory in a style which is at once readable and compact. The necessary prerequisites are developed in the early chapters only to the extent that they are needed later. The proofs of the lemmas and main theorems are presented in as concrete a manner as possible, without unnecessary abstraction. Yet they seem remarkably short, without the difficulties being glossed over. In fact the approach throughout the book is down-to-earth and concrete … I can heartily recommend this book as an undergraduate text.' Bulletin of the London Mathematical Society
Part I. The Algebraic Background:
1. Groups
2. Integral domains
3. Vector spaces and determinants
Part II. The Theory of Fields, and Galois Theory:
4. Field extensions
5. Ruler and compass constructions
6. Splitting fields
7. Normal extensions
8. Separability
9. The fundamental theorem of Galois theory
10. The discriminant
11. Cyclotomic polynomials and cyclic extensions
12. Solution by radicals
13. Regular polygons
14. Polynomials of low degree
15. Finite fields
16. Quintic polynomials
17. Further theory
18. The algebraic closure of a field
19. Transcendental elements and algebraic independence
20. Generic and symmetric polynomials
Appendix: the axiom of choice
Index.
PUBLICATION PLANNED FOR: August 2021AVAILABILITY: Not yet published - available from August 2021
FORMAT: HardbackISBN: 9781107151642FORMAT: PaperbackISBN: 9781316606216
Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided.
Builds up the mathematical background for a new approach to the foundations of bifurcation theory
The first two parts are of independent interest and can be the basis for an advanced undergraduate or graduate course
Contains many colour figures and exercises, with some solutions included and a manual for selected others available for teachers