Series: Chapman & Hall/CRC Numerical Analy & Scient Comp. Series
ISBN: 9781420091571
Publication Date: 20/07/2009
Pages: 628 Hardback
Trim Size: 6-1/8 x 9-1/4
An Up-to-Date, Self-Contained Treatment of Topics for a First Graduate Course in Numerical Analysis
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.
The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter.
This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLABｮ code will be available on the CRC Press website to illustrate various concepts.
Mathematical Review and Computer Arithmetic. Numerical Solution of Nonlinear Equations of One Variable. Numerical Linear Algebra. Approximation Theory. Eigenvalue-Eigenvector Computation. Numerical Differentiation and Integration. Initial Value Problems for Ordinary Differential Equations. Numerical Solution of Systems of Nonlinear Equations. Optimization. Boundary Value Problems and Integral Equations. Appendix. References. Index.
Series: Textbooks in Mathematics
ISBN: 9781420089745
Publication Date: 28/07/2009
Pages: 420 Hardback
Trim Size: 6-1/8 x 9-1/4
Brings Readers Up to Speed in This Important and Rapidly Growing Area
Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories.
After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in a number of areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures.
Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.
Fundamentals. Advanced Properties of Topological Spaces. Basic Algebraic Topology. Manifold Theory. Moore亡mith Convergence and Nets. Function Spaces. Knot Theory. Graph Theory. Dynamical Systems. Appendices. Solutions of Selected Exercises. Bibliography. Index.
Series: Textbooks in Mathematics
ISBN: 9781420094527
ISBN-10: 1420094521
Publication Date: 29/07/2009
Pages: 560 Hardback
Trim Size: 6-1/8 x 9-1/4
By integrating the use of GAP and Mathematicaｮ, Abstract Algebra: An Interactive Approach presents a hands-on approach to learning about groups, rings, and fields. Each chapter includes both GAP and Mathematica commands, corresponding Mathematica notebooks, traditional exercises, and several interactive computer problems that utilize GAP and Mathematica to explore groups and rings.
Although the book gives the option to use technology in the classroom, it does not sacrifice mathematical rigor. It covers classical proofs, such as Abel痴 theorem, as well as many graduate-level topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik痴 Cubeｮ-like puzzles, and Wedderburn痴 theorem. He also incorporates problem sequences that allow students to delve into interesting topics in depth, including Fermat痴 two square theorem.
This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.
Understanding the Group Concept. The Structure within a Group. Patterns within the Cosets of Groups. Mappings between Groups. Permutation Groups. Building Larger Groups from Smaller Groups. The Search for Normal Subgroups. Solvable and Insoluble Groups. Introduction to Rings. The Structure within Rings. Integral Domains and Fields. Unique Factorization. Finite Division Rings. The Theory of Fields. Galois Theory. Bibliography. Answers to Odd Problems. Index.
Series: Textbooks in Mathematics
ISBN: 9781420079388
Publication Date: 15/09/2009
Pages: 465 Hardback
Trim Size: 6-1/8 x 9-1/4
Updated to conform to Mathematicaｮ 7.0, Introduction to Probability with Mathematicaｮ, Second Edition continues to show students how to easily create simulations from templates and solve problems using Mathematica. It provides a real understanding of probabilistic modeling and the analysis of data and encourages the application of these ideas to practical problems. The accompanying CD-ROM offers instructors the option of creating class notes, demonstrations, and projects.
Expanded section on Markov chains that includes a study of absorbing chains
New sections on order statistics, transformations of multivariate normal random variables, and Brownian motion
More example data of the normal distribution
More attention on conditional expectation, which has become significant in financial mathematics
Additional problems from Actuarial Exam P
New appendix that gives a basic introduction to Mathematica
New examples, exercises, and data sets, particularly on the bivariate normal distribution
New visualization and animation features from Mathematica 7.0
Updated Mathematica notebooks on the CD-ROM
After covering topics in discrete probability, the text presents a fairly standard treatment of common discrete distributions. It then transitions to continuous probability and continuous distributions, including normal, bivariate normal, gamma, and chi-square distributions. The author goes on to examine the history of probability, the laws of large numbers, and the central limit theorem. The final chapter explores stochastic processes and applications, ideal for students in operations research and finance.
Discrete Probability. Discrete Distributions. Continuous Probability. Continuous Distributions. Asymptotic Theory. Stochastic Processes and Applications. Appendix. References. Index.
Series: Chapman & Hall/CRC Handbooks of Modern Statistical Methods
ISBN: 9781420072877
Publication Date: 26/02/2010
Pages: 904 Hardback
Trim Size: 7 x 10
The past few decades have seen a huge increase in the amount of spatial statistics research. This single volume provides a comprehensive, coherent, and unified summary of the entire field. Divided into broad sections, the text addresses topics in the areas of continuous spatial variation, discrete spatial variation, spatial point patterns, and spatio-temporal analysis. A separate section presents additional topics of interest, such as boundary analysis, ecological bias, and multivariate spatial process models. Leading contributors present balanced coverage of methodology and practical application through the inclusion of worked examples using real data as well as detailed case studies
Continuous Spatial Variation. Discrete Spatial Variation. Spatial Point Patterns. Spatio-Temporal Analysis. Additional Topics.
This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. The main question is whether residues of Feynman integrals always evaluate to periods of mixed Tate motives, as appears to be the case from extensive computations of Feynman integrals carried out by Broadhurst and Kreimer.
Two different approaches to the subject are described. The first, a “bottom-up” approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach grew out of work of Bloch?Esnault?Kreimer and suggests that, while the algebraic varieties associated to the Feynman graphs can be arbitrarily complicated as motives, the part that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, “top-down” approach to the problem, developed in the work of Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization with those formed by mixed Tate motives. The book draws connections between these two approaches and gives an overview of various ongoing directions of research in the field.
The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it cal also be used by graduate students interested in working in this area.
Perturbative Quantum Field Theory and Feynman Diagrams
Motives and Periods
Feynman Integrals and Algebraic Varieties
Feynman Integrals, Singularities, Hodge Structures
Connes-Kreimer Theory in a Nutshell
The Riemann?Hilbert Correspondence
Renormalization and Singularities
Beyond Scalar Theories
Readership: Graduate students and researchers in mathematical physics and theoretical physics.
150pp (approx.) Pub. date: Scheduled Winter 2009
ISBN: 978-981-4271-20-2