Series: Universitext
2008, Approx. 220 p., Softcover
ISBN: 978-3-540-74117-6
Due: December 4, 2007
About this textbook
Treats the classical one-variable theory of elliptic modular forms
Presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces
Gives an introduction to Siegel modular forms and discusses a conjecture by Harder
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004.
The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture.
Each part treats a number of beautiful applications, and together they form a comprehensive survey for the novice and a useful reference for a broad group of mathematicians.
Table of contents
Part I. Don Zagier - Elliptic Modular Forms and Their Applications.- Part II. Jan Hendrik Bruinier - Hilbert Modular Forms and Their Applications.- Part III: Gerard van der Geer - Siegel Modular Forms.- Part IV: Gunter Harder - A Congruence Between a Siegel and an Elliptic Modular Form.
2008, Approx. 500 p., Hardcover
ISBN: 978-0-387-73183-4
Due: December 2007
About this book
Multilevel analysis is the statistical analysis of hierarchically and non-hierarchically nested data. The simplest example is clustered data, such as a sample of students clustered within schools. Multilevel data are especially prevalent in the social and behavioral sciences and in the bio-medical sciences. The models used for this type of data are linear and nonlinear regression models that account for observed and unobserved heterogeneity at the various levels in the data.
This book presents the state of the art in multilevel analysis, with an emphasis on more advanced topics. These topics are discussed conceptually, analyzed mathematically, and illustrated by empirical examples. The authors of the chapters are the leading experts in the field.
Given the omnipresence of multilevel data in the social, behavioral, and biomedical sciences, this book is useful for empirical researchers in these fields. Prior knowledge of multilevel analysis is not required, but a basic knowledge of regression analysis, (asymptotic) statistics, and matrix algebra is assumed.
Jan de Leeuw is Distinguished Professor of Statistics and Chair of the Department of Statistics, University of California at Los Angeles. He is former president of the Psychometric Society, former editor of the Journal of Educational and Behavioral Statistics, founding editor of the Journal of Statistical Software, and editor of the Journal of Multivariate Analysis. He is coauthor (with Ita Kreft) of Introducing Multilevel Modeling and a member of the Albert Gifi team who wrote Nonlinear Multivariate Analysis.
Erik Meijer is Economist at the RAND Corporation and Assistant Professor of Econometrics at the University of Groningen. He is coauthor (with Tom Wansbeek) of the highly acclaimed Measurement Error and Latent Variables in Econometrics.
Table of contents
Introduction to multilevel analysis, Jan de Leeuw, Erik Meijer.- Bayesian multilevel analysis and MCMC, David Draper.- Diagnostic checks for multilevel models, Tom A.B. Snijders, Johannes Berkhof.- Optimal designs for multilevel studies, Mirjam Moerbeek, Gerard J.P. VAn Breukelen, Martijn P.F. Berger.- Many small groups, Donald Hedeker.- Multilevel and related models for longitudinal data, Anders Skrondol, Sophia Rabe-Hesketh.- Non-hierarchical multilevel models, German Rodriguez.- Missing Data, Nicholas T. Longford.- Resampling multilevel models, Rien van der Leeden, Erik Meijer, Frank M.T.A. Busing.- Multilevel structural equation modeling, Stephen H.C. du Toit, Mathilda du Toit.
Series: Stochastic Modelling and Applied Probability , Vol. 58
2008, Approx. 480 p., Hardcover
ISBN: 978-0-387-74316-5
Due: November 2007
About this book
This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles.
A detailed analysis of the SODEaE?s and (quasi-linear) SPDEaE?s is presented. Semi-linear (parabolic) SPDEaE?s are represented as first order stochastic transport equations driven by Stratonovich differentials. The time evolution of correlated Brownian motions is shown to be consistent with the depletion phenomena experimentally observed in colloids. A covariance analysis of the random processes and random fields as well as a review section of various approaches to SPDEa??s are also provided.
The intended audience consists of scientists and graduate students in probability theory (stochastic analysis) and mathematical/theoretical physics.
Peter Kotelenez is a professor of mathematics at Case Western Reserve University in Cleveland, Ohio.
Table of contents
Introduction.- From Microscopic Dynamics to Mesoscopic Kinematics.- Mesoscopic A- Stochastic Ordinary Differential Equations.-Mesoscopic B-Stochastic Partial Differential Equations.- Macroscopic: Deterministic Partial Differential Equations.- General Appendix.- Subject Index.- List of Symbols.- References
Series: Universitext
2008, Approx. 625 p., Softcover
ISBN: 978-1-84800-047-6
Due: December 2007
About this textbook
Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer sciences. They help us understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms.
This text book is a comprehensive introduction to modern probability theory and its measure theoretical foundation. It contains a great variety of topics that cannot be found in many introductory textbooks (e.g. percolation, large deviations, stochastic differential equations, point processes, electrical networks and exchangeability). The theory is developed rigorously and in a self-contained way and still the examples are not missing.
This book is written for graduate students and researchers. The main topics are
measure and integration theory
limit theorems for sums of random variables (law of large numbers, central limit theorems, ergodic theorems, law of the iterated logarithm, invariance principles, infinite divisibility)
Table of contents
Basic Measure Theory.- Independence.- Generating Functions.- The Integral.- Moments and Laws of Large Numbers.- Convergence Theorems.- Lp-Spaces and Radon-Nikodym Theorem.- Conditional Expectations.- Martingales.- Optional Sampling Theorems.- Martingale Convergence Theorems and their Applications.- Backwards Martingales and Exchangeability.- Convergence of Measures.- Probability Measures on Product Spaces.- Characteristics Functions and Central Limit Theorem.- Infinitely Divisible Distributions.- Markov Chains.- Convergence of Markov Chains.- Markov Chains and Electrical Networks.- Ergodic Theory.- Brownian Motion.- Law of the Iterated Logarithm.- Large Deviations.- The Poisson Point Process.- The Ito Integral.- Stochastic Differential Equations.- References.- Notation Index.- Name Index.- Subject Index
Series: Modern Birkhauser Classics
2008, XII, 342 p. 307 illus., Softcover
ISBN: 978-0-8176-4718-6
Due: October 2007
About this textbook
Includes fundamental mathematical concepts as well as applications in physics, biology, and chemistry
Offers illuminating historical background and notes
Clarifies theoretical discussions with more than 300 illustrations
Covers developments over the past ten years, such as the study of Jones polynomials and the Vassiliev invariants
Avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory
Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these fields.
The book contains most of the fundamental classical facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials; also included are key newer developments and special topics such as chord diagrams and covering spaces. The work introduces the fascinating study of knots and provides insight into applications to such studies as DNA research and graph theory. In addition, each chapter includes a supplement that consists of interesting historical as well as mathematical comments.
The author clearly outlines what is known and what is not known about knots. He has been careful to avoid advanced mathematical terminology or intricate techniques in algebraic topology or group theory. There are numerous diagrams and exercises relating the material. The study of Jones polynomials and the Vassiliev invariants are closely examined.
"The book ...develops knot theory from an intuitive geometric-combinatorial point of view, avoiding completely more advanced concepts and techniques from algebraic topology...Thus the emphasis is on a lucid and intuitive exposition accessible to a broader audience... The book, written in a stimulating and original style, will serve as a first approach to this interesting field for readers with various backgrounds in mathematics, physics, etc. It is the first text developing recent topics as the Jones polynomial and Vassiliev invariants on a level accessible also for non-specialists in the field." -Zentralblatt Math
Table of contents
Introduction.- Fundamental Concepts of Knot Theory.- Knot Tables.- Fundamental Problems of Knot Theory.- Classical Knot Invariants.- Seifert Matrices.- Invariants from the Seifert matrix.- Torus Knots.- Creating Manifolds from Knots.- Tangles and 2-Bridge Knots.- The Theory of Braids.- The Jones Revolution.- Knots via Statistical Mechanics.- Knot Theory in Molecular Biology.- Graph Theory Applied to Chemistry.- Vassiliev Invariants.- Appendix.- Notes.- Bibliograph.- Index.