الصفحة 14
الصفحة 14
Measure, Integration & Real Analysis
This book welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results.
Measure Theory and Probability Theory
The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics.Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms.
Measure Theory
This book gives a systematic presentation of modern measure theory as it has developed over the past century and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises. Bibliographical and historical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Meaning in Mathematics Education
This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education.
Mean Oscillations and Equimeasurable Rearrangements of Functions
Various applications of equimeasurable function rearrangements to the ''best constant"-type problems are considered in this volume. Several classical theorems are presented along with some very recent results. In particular, the text includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation (BMO) functions with sharp exponent, a refinement of the Gurov-Reshetnyak lemma, sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, reverse Hölder, and Gehring classes, etc. This volume is interesting for graduate students and mathematicians involved with these topics.
Max-Plus Methods for Nonlinear Control and Estimation
The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality.. The max-plus-based methods examined in this monograph belong to an entirely new class of numerical methods for the solution of nonlinear control problems.The potential advantages of the max-plus-based approaches lie in the fact that solution operators for nonlinear HJB problems are linear over the max-plus algebra, and this linearity is exploited in the construction of algorithms.
Matrix-Based Multigrid : Theory and Applications
Multigrid methods are often used for solving partial differential equations. This book introduces and analyzes the multigrid approach. The approach used here applies to both test problems on rectangular grids and to more realistic applications with complicated grids and domains.
Matrix Convolution Operators on Groups
In the last decade, convolution operators of matrix functions have received unusual attention due to their diverse applications. This monograph presents some new developments in the spectral theory of these operators. The setting is the Lp spaces of matrix-valued functions on locally compact groups. The focus is on the spectra and eigenspaces of convolution operators on these spaces, defined by matrix-valued measures. Among various spectral results, the L2-spectrum of such an operator is completely determined and as an application, the spectrum of a discrete Laplacian on a homogeneous graph is computed using this result. The contractivity properties of matrix convolution semigroups are studied and applications to harmonic functions on Lie groups and Riemannian symmetric spaces are discussed. An interesting feature is the presence of Jordan algebraic structures in matrix-harmonic functions.
Matrix Algebra From a Statistician`s Perspective
This book presents matrix algebra in a way that is well-suited for those with an interest in statistics or a related discipline. It provides thorough and unified coverage of the fundamental concepts along with the specialized topics encountered in areas of statistics such as linear statistical models and multivariate analysis. It includes a number of very useful results that have only been available from relatively obscure sources. Detailed proofs are provided for all results. The style and level of presentation are designed to make the contents accessible to a broad audience. The book is essentially self-contained, though it is best-suited for a reader who has had some previous exposure to matrices (of the kind that might be acquired in a beginning course on linear or matrix algebra).
Matrix Algebra : Theory, Computations, and Applications in Statistics
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained.
Mathématiques, informatique, physique. Au fil des TIPE = Mathematics, computer science, physics : Throughout the TIPE projects
Presents nine cases in mathematics, physics, or computer science used in the competition. Each case study is accompanied by general remarks, commentary, a suggested outline, questions a jury might ask, and an explanation placing the case study's theme within its scientific context. The authors hope not only to assist CPGE students in their preparation but also to provide valuable support to teachers who have embraced this new pedagogical approach. Laurent Decreusefond and Alain Maruani, the pedagogical coordinators for the mathematics, computer science, and physics component of the TIPE, have made significant contributions to its design and implementation.
Mathématiques de base pour économistes = Basic Mathematics for Economists
This book contains fundamental elements of mathematics and includes the following elements: notion of logic, propositions, theorems, sets, relations and functions; graphical representations of functions, economic applications of lines and functions, sequences, limits and first derivative, differential economic applications of derivatives; integrals: undefined and defined with economic applications; mathematical series; functions of several variables, partial derivatives, Lagrange multiplier with economic applications; linear algebra: matrix calculus, system of linear equations, vectors, differential calculus in matrix form.
Mathematics teacher preparation in Central America and the Caribbean : The cases of Colombia, Costa Rica, the Dominican Republic and Venezuela
This book brings to the international Educational Community an important collection of experiences and ideas in the Mathematics Education of four countries of a region within the heart of the American continent, a region that has been many times forgotten. The dissemination of these results can promote the search for international collaborative actions in a wider scale.
Mathematics teacher education in the Andean region and Paraguay : A comparative analysis of issues and challenges
This Open Access book is an excellent synthesis of the initial and continuing preparation for Mathematics Teaching in Bolivia, Ecuador, Paraguay and Peru, from which comparative analyses can be made that show similarities and differences, and highlight various perspectives. This book brings to the international Educational Community an important collection of experiences and ideas in the Mathematics Education of four Latin-American countries in the developing Andean region and Paraguay. The dissemination of these results can promote the search for international collaborative actions in a wider scale.
Mathematics of Uncertainty : Ideas, Methods, Application Problems
Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variability, imprecision and fuzziness of data are of importance. This introductory book describes the basic ideas of the mathematical fields of uncertainty from simple interpolation to wavelets, from error propagation to fuzzy sets and neural networks. The book presents the treatment of problems of interpolation and approximation, as well as observation fuzziness which can essentially influence the preciseness and reliability of statements on functional relationships.
Mathematics of Surfaces XII ; 12th IMA International Conference, Sheffield, UK, September 4-6, 2007, Proceedings
This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces.
Mathematics of Surfaces XI ; 11th IMA International Conference, Loughborough, UK, September 5-7, 2005, Proceedings
Constitutes the refereed proceedings of the 11th IMA International Conference on the Mathematics of Surfaces, held in Loughborough, UK in September 2005. Among the topics addressed are Voronoi diagrams, linear systems, curvatures on meshes, approximate parameterization, condition numbers, pythagorean hodographs, and more.
Mathematics of Program Construction ; 9th International Conference, MPC 2008, Marseille, France, July 15-18, 2008. Proceedings
This book constitutes the refereed proceedings of the 9th International Conference on Mathematics of Program Construction, MPC 2008, held in Marseille, France in July 2008.The 18 revised full papers presented together with 1 invited talk were carefully reviewed and selected from 41 submissions. Issues addressed range from algorithmics to support for program construction in programming languages and systems. Topics of special interest are type systems, program analysis and transformation, programming language semantics, program logics.
Mathematics of Program Construction ; 8th International Conference, MPC 2006, Kuressaare, Estonia, July 3-5, 2006, Proceedings
This volume contains the proceedings of the 8th International Conference on Mathematics of ProgramConstruction, MPC 2006,held at Kuressaare, Estonia, July 3-5, 2006, colocated with the 11th International Conference on Algebraic Methodology and Software Technology, AMAST 2006, July 5-8, 2006. TheMPCconferencesaimtopromotethedevelopmentofmathematicalpr- ciples and techniques that are demonstrably useful and usable in the process of constructing computer programs. Topics of interest range from algorithmics to support for program construction in programming languages and systems.
Mathematics of Large Eddy Simulation of Turbulent Flows
Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations.
