Series: London Mathematical Society Lecture Note Series (No. 360)
Paperback (ISBN-13: 9780521735605)
50 exercises
Page extent: 230 pages
Size: 228 x 152 mm
This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Its logical approach helps us understand why algebraic geometry is so fundamental throughout mathematics and why the extension to noncommutative geometry, which has been forced by recent developments in quantum physics, is both natural and necessary. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.
* Contains survey material as well as detailed mathematical proofs * Assumes no specialist background in logic * Over 50 exercises help the reader test their understanding of the material
1. Introduction; 2. Topological structures; 3. Noetherian Zariski structures; 4. Classification results; 5. Non-classical Zariski geometries; 6. Analytic Zariski geometries; A. Basic model theory; B. Geometric stability theory; References; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 122)
Hardback (ISBN-13: 9780521194402)
305 exercises
Page extent: 160 pages
Size: 228 x 152 mm
This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure theory, proofs of fundamental ergodic theorems, and material on entropy, martingales, Bernoulli processes, and various varieties of mixing. Original proofs of classic theorems - including the Shannon*McMillan*Breiman theorem, the Krieger finite generator theorem, and the Ornstein isomorphism theorem - are presented by degrees, together with helpful hints that encourage the reader to develop the proofs on their own. Hundreds of exercises and open problems are also included, making this an ideal text for graduate courses. Professionals needing a quick review, or seeking a different perspective on the subject, will also value this book.
* Encourages readers to actively participate in the development of proofs * Contains original proofs of classic theorems in ergodic theory * Easily navigable for experts requiring only a quick review
Preface; Introduction; 1. Measure-theoretic preliminaries; 2. Measure preserving systems, stationary processes; 3. Martingales and coupling; 4. Entropy; 5. Bernoulli transformations; 6. Ornstein isomorphism theorem; 7. Varieties of mixing; Appendix; References; Index.
Series: London Mathematical Society Lecture Note Series (No. 372)
Paperback (ISBN-13: 9780521106641)
1 b/w illus.
Page extent: 400 pages
Size: 228 x 152 mm
In 1979, John Conway and Simon Norton’s famous paper, ‘Monstrous Moonshine’, outlined the remarkable connection between the monster group M and the theory of modular functions. The search for an explanation of this phenomenon involved the development and application of diverse areas of mathematics, including (generalized) Kac*Moody algebras, vertex (operator) algebras, automorphic forms and elliptic cohomology, together with string and conformal field theory from theoretical physics. This volume consists of seventeen papers based on talks presented at a workshop held to mark the anniversary of ‘Monstrous Moonshine’. Containing a mixture of expository and current research material, they illustrate its extensive impact and reflect the broad range of research activity that has stemmed from the Moonshine conjectures. Potential directions for future development are also discussed.
* Authors include leading experts in the field * Highlights possible directions for future research * Provides a broad snapshot of current research in the area
Preface; Schedule of talks; 1. Characters of crossed modules and premodular categories Peter Bantay; 2. On the injectivity of the Kudla*Millson lift and surjectivity of the Borcherds lift Jan Hendrik Bruinier and Jens Funke; 3. Ordered spanning sets for vertex operator algebras and their modules Geoffrey Buhl; 4. Friendly giant meets pointlike instantons* On a new conjecture by John McKay Anda Degeratu and Katrin Wendland; 5. Modularity of trace functions in orbifold theory for Z-graded vertex operator superalgebras Chongying Dong and Zhongping Zhao; 6. Twisted modules for vertex operator algebras Benjamin Doyon; 7. Vertex operators and sporadic groups John F. Duncan; 8. The algebraic meaning of being a Hauptmodul Terry Gannon; 9. Borcherds' proof of the Conway*Norton conjecture Elizabeth Jurisich; 10. On the connection of certain Lie algebras with vertex algebras Haisheng Li; 11. Vertex operators and arithmetic: how a single photon illuminates number theory Geoffrey Mason; 12. Rational vertex operator algebras and their orbifolds Geoffrey Mason; 13. Quasi-finite algebras graded by Hamiltonian and vertex operator algebras Atushi Matsuo, Kiyokazu Nagatomo and Akihiro Tsuchiya; 14. On certain automorphic forms associated to rational vertex operator algebras Antun Milas; 15. Moonshine and group cohomology Charles B. Thomas; 16. Monstrous and generalized Moonshine and permutation orbifolds Michael P. Tuite; 17. New computations in the Monster Robert A. Wilson.
Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 10)
Hardback (ISBN-13: 9780521762939)
150 b/w illus. 12 colour illus. 40 tables
Page extent: 560 pages
Size: 247 x 174 mm
Discover what you can do with R! Introducing the R system, covering standard regression methods, then tackling more advanced topics, this book guides users through the practical, powerful tools that the R system provides. The emphasis is on hands-on analysis, graphical display, and interpretation of data. The many worked examples, from real-world research, are accompanied by commentary on what is done and why. The companion website has code and datasets, allowing readers to reproduce all analyses, along with solutions to selected exercises and updates. Assuming basic statistical knowledge and some experience with data analysis (but not R), the book is ideal for research scientists, final-year undergraduate or graduate-level students of applied statistics, and practising statisticians. It is both for learning and for reference. This third edition expands upon topics such as Bayesian inference for regression, errors in variables, generalized linear mixed models, and random forests.
* Practical, hands-on, example-based approach deals with real-world issues * Extensive use of graphs for exploration of data and interpretation of analyses * R code, data sets, updates and exercise solutions, all provided on companion website
Preface; Content - how the chapters fit together; 1. A brief introduction to R; 2. Styles of data analysis; 3. Statistical models; 4. A review of inference concepts; 5. Regression with a single predictor; 6. Multiple linear regression; 7. Exploiting the linear model framework; 8. Generalized linear models and survival analysis; 9. Time series models; 10. Multi-level models, and repeated measures; 11. Tree-based classification and regression; 12. Multivariate data exploration and discrimination; 13. Regression on principal component or discriminant scores; 14. The R system - additional topics; 15. Graphs in R; Epilogue; Index of R symbols and functions; Index of authors.
Series: Encyclopedia of Mathematics and its Applications (No. 87)
Paperback (ISBN-13: 9780521106580)
Page extent: 690 pages
Size: 234 x 156 mm
This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.
* A self-contained exposition of the main theorems of classical algebraic K-theory * Accessible to anyone with a good first semester introduction to algebra * The methods are entirely algebraic, unlike other treatments which require some advanced knowledge of topology, geometry, or functional analysis
1. Groups of modules: Ko; 2. Sources of Ko; 3. Groups of matrices: K1; 4. Relations among matrices: K2; 5. Sources of K2.