Series: Cornerstones
2011, 2012, XVII, 560 p. 42 illus.
ISBN 978-0-8176-4692-9
Presents a unified and competitive approach to compact and noncompact Riemann surfaces
Includes continuing exercises that run throughout the book and lead to generalizations of the main theorems
Will help expand and reinforce a studentfs knowledge of analysis, geometry, and topology
This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L2 -method, a powerful technique used in the theory of several complex variables. The work features a simple construction of a strictly subharmonic exhaustion function and a related construction of a positive-curvature Hermitian metric in a holomorphic line bundle, topics which serve as starting points for proofs of standard results such as the Mittag-Leffler, Weierstrass, and Runge theorems; the Riemann?Roch theorem; the Serre duality and Hodge decomposition theorems; and the uniformization theorem. The book also contains treatments of other facts concerning the holomorphic, smooth, and topological structure of a Riemann surface, such as the biholomorphic classification of Riemann surfaces, the embedding theorems, the integrability of almost complex structures, the Schonflies theorem (and the Jordan curve theorem), and the existence of smooth structures on second countable surfaces.
Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises?many of which lead to further development of the theory?and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course.
Series: Springer Monographs in Mathematics
2012, 2012, XIV, 738 p.
Hardcover, ISBN 978-0-387-84793-1
Due: December 28, 2011
This text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students. Building on the authors' Lie-Gruppen und Lie-Algebren textbook from 1991, it presents the fundamental principles of Lie groups while incorporating the past 20 years of the authors' teaching and research, and giving due emphasis to the role played by differential geometry in the field. The text is entirely self contained, and provides ample guidance to students with the presence of many exercises and selected hints.
The work begins with a study of matrix groups, which serve as examples to concretely and directly illustrate the correspondence between groups and their Lie algebras. In the second part of the book, the authors investigate the basic structure and representation theory of finite dimensional Lie algebras, such as the rough structure theory relevant to the theorems of Levi and Malcev, the fine structure of semisimple Lie algebras (root decompositions), and questions related to representation theory. In the third part of the book, the authors turn to global issues, most notably the interplay between differential geometry and Lie theory. Finally, the fourth part of the book deals with the structure theory of Lie groups, including some refined applications of the exponential function, various classes of Lie groups, and structural issues for general Lie groups. To round out the book's content, several appendices appear at the end of this last part.
Containing a wealth of useful information, including new results, Structure and Geometry of Lie Groups provides a unique perspective on the study of Lie groups and is a valuable addition to the literature. Prerequisites are generally kept to a minimum, and various pedagogical features make it an excellent supplemental text for graduate students. However, the work also contains much that will be of interest to more advanced audiences, and can serve as a useful research reference in the field.
Matrix Groups.- Concrete Matrix Groups. The Matrix Exponential Function. Linear Lie Groups. Lie Algebras.- Elementary Structure Theory of Lie Algebras. Root Decomposition. Representation Theory of Lie Algebras.
Series: Springer Monographs in Mathematics
2012, 2012, X, 176 p.
Hardcover, ISBN 978-1-4614-2124-5
Due: December 28, 2011
This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable.
One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes:
(I) The correspondence between the forms of half-integral weight and those of integral weight.
(II) The arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight.
Goro Shimura is currently a professor emeritus of mathematics at Princeton University.
Preface.- Notation and Terminology.- Chapter I. Preliminaries.- Chapter II. Theta Functions and Factors of Automorphy.- Chapter III. The Rationality and Eisenstein Series.- Chapter IV. The Correspondence between Forms of Integral and Half-integral Weight.- Chapter V. The Arithmeticity of Critical Values of Dirichlet Series.- Appendix.- References.- Index.
Series: Universitext
2012, 2012, XII, 247 p. 26 illus.
Hardcover, ISBN 978-1-4614-1938-9
Due: February 28, 2012
This book provides an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. It covers standard topics such as bounds on the sizes of cliques and cocliques, chromatic number and Shannon capacity, the connection between randomness and the 'eigenvalue gap', and applications. It continues with a presentation of some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text.
Spectra of Graphs is written for researchers, teachers and students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
Graph spectrum.- Linear algebra.- Eigenvalues and eigenvectors of graphs.- The second largest eigenvalue.- Trees.- Groups and graphs.- Topology.- Euclidean representations.- Strongly regular graphs.- Regular two-graphs.- Association schemes.- Distance regular graphs. - p-ranks.- Spectral characterizations.- Graphs with few eigenvalues.- References.- Author Index.- Subject Index.
To Be Published 24th October 2011 by 564 pages
Series: Statistics: A Series of Textbooks and Monographs
Hardback: 978-1-4398183-7-4:
Virtually any random process developing chronologically can be viewed as a time series. In economics, closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis includes examples across a variety of fields, develops theory, and provides software to address time series problems in a broad spectrum of fields. The authors organize the information in such a format that graduate students in Applied Science, Statistics, and Economics can satisfactorily navigate their way through the book while maintaining mathematical rigor.
One of the unique features of Applied Time Series Analysis is the associated software, GW-WINKS, designed to help students easily generate realizations from models and explore the associated model and data characteristics. The text explores many important new methodologies that have developed in time series, such as ARCH and GARCH processes, time varying frequencies (TVF), wavelets, and more. Other programs (some written in R and some requiring S-plus) are available on an associated website for performing computations related to the material in the final four chapters.
Monographs in Number Theory - Vol. 6
184pp Pub. date: Sep 2011
ISBN: 978-981-4366-45-8
981-4366-45-5
This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter.
The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.
The Basic Identity
The Differential Equations of P, Q and R
The Jordan-Kronecker Function
The Weierstrassian Invariants
The Weierstrassian Invariants, II
Development of Elliptic Functions
The Modular Function É
Readership: Graduate students and researchers in Number Theory and Classical Analysis, as well as scholars and aficionados of Ramanujan's work.
Series on Knots and Everything - Vol. 48
300pp (approx.) Pub. date: Dec 2011
ISBN: 978-981-4374-49-1
981-4374-49-0
The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations.
The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.
A Sphere
Surfaces, Folds, and Cusps
The Inside and Outside
Dimensions
Immersed Surfaces
Movies
Movie Moves
Taxonomic Summary
How Not to Turn the Sphere Inside-Out
A Physical Metaphor
Sarah's Thesis
The Eversion
The Double Point and Fold Surfaces