Advanced Courses in Mathematics - CRM Barcelona
Features a thorough introduction into a new area of research (greedy approximation)
Deals with numerous applications
Recent fundamental results are combined with previous results to build the theory of greedy approximation?
This book systematically presents recent fundamental results on greedy approximation with respect to bases.
Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and does not require a broad background in the field.
Graduate Texts in Mathematics
New edition extensively revised and updated
Covers the core topics of Lie theory from an elementary point of view
Includes many new exercises
This book provides an introduction to Lie groups, Lie algebras, and repre-sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that will make it a useful addition to the literature. First, it treats Lie groups, not just Lie alge-bras, in a way that minimizes the amount of manifold theory needed. Thus, prior knowledge of differentiable manifolds is not assumed. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.
Springer Undergraduate Texts in Mathematics and Technology
First numerical analysis textbook using Sage
Does not require prior knowledge of Python programming
Includes all Sage code for ease of use for students
This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application. Answers may be verified using Sage.
The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as MathematicaR. Sage is open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a plus. Moreover, the code can be written using any web browser and is therefore useful with Laptops, Tablets, iPhones, Smartphones, etc. All Sage code that is presented in the text is openly available on SpringerLink.com.
Understanding Complex Systems
Features state-of-the-art,concrete and real-world applications in various fields of engineering/applied sciences
Contributions written by active and leading research groups
Useful as both a reference and recipe handbook of successful applications
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology?and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role.
This fourth volume concentrates on reviewing further relevant contemporary applications of chaotic and nonlinear dynamics as they apply to the various cuttingedge branches of science and engineering. This encompasses, but is not limited to, topics such as synchronization in complex networks and chaotic circuits, time series analysis, ecological and biological patterns, stochastic control theory and vibrations in mechanical systems.
Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a erecipe bookf full of tried and tested, successful engineering applications.
Universitext
Presents a systematic study that develops the functional model approach for multivariable linear systems.
Provide a bridge between classical frequency response techniques and state space approaches, thereby providing a unified algebraic approach to systems with different kind of system representations.
Contains many examples, exercises and notes and references that complement the main text. Book should thus be suitable for self-study, as well as courses and seminars.
This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems.
Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. gMathematics of Networks of Linear Systemsh contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.
Springer Texts in Statistics
Examples using financial markets and economic data illustrate important concepts
R Labs with real-data exercises give students practice in data analysis
Integration of graphical and analytic methods for model selection and model checking quantify
Helps mitigate risks due to modeling errors and uncertainty
The new edition of this influential textbook, geared towards graduate or advanced undergraduate students, teaches the statistics necessary for financial engineering. In doing so, it illustrates concepts using financial markets and economic data, R Labs with real-data exercises, and graphical and analytic methods for modeling and diagnosing modeling errors. These methods are critical because financial engineers now have access to enormous quantities of data. To make use of this data, the powerful methods in this book for working with quantitative information, particularly about volatility and risks, are essential. Strengths of this fully-revised edition include major additions to the R code and the advanced topics covered. Individual chapters cover, among other topics, multivariate distributions, copulas, Bayesian computations, risk management, and cointegration. Suggested prerequisites are basic knowledge of statistics and probability, matrices and linear algebra, and calculus. There is an appendix on probability, statistics and linear algebra. Practicing financial engineers will also find this book of interest.
Describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods
Provides precise statements regarding different numerical procedures which enables selection of the best method for a given problem
Although it is aimed at a broad audience and presumes only basic mathematical preparation, the book presents the relevant theory of Hamiltonian mechanics and stochastic differential equations
Coverage is provided of symplectic numerical methods, constraints and rigid bodies, Langevin dynamics, thermostats and barostats, multiple time-stepping, and the dissipative particle dynamics method
This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.
Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method.