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Author : Ronald A. DeVore,Arieh Iserles,Endre Süli
Publisher : Cambridge University Press
Page : 418 pages
File Size : 48,8 Mb
Release : 2001-05-17
Category : Mathematics
ISBN : 0521003490
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
Author : Carol Critchlow,David Eck
Publisher : Unknown
Page : 128 pages
File Size : 55,5 Mb
Release : 2011
Category : Computer science
ISBN : OCLC:1148175537
Author : Society for the Foundation of Computational Mathematics
Publisher : Cambridge University Press
Page : 249 pages
File Size : 49,7 Mb
Release : 2013
Category : Computers
ISBN : 9781107604070
A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.
Author : Xin-She Yang
Publisher : World Scientific Publishing Company
Page : 344 pages
File Size : 54,6 Mb
Release : 2014-11-26
Category : Mathematics
ISBN : 9789814635806
This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.
Author : Kamran Dadkhah
Publisher : Springer Science & Business Media
Page : 547 pages
File Size : 40,7 Mb
Release : 2011-01-11
Category : Business & Economics
ISBN : 9783642137488
This is a book on the basics of mathematics and computation and their uses in economics for modern day students and practitioners. The reader is introduced to the basics of numerical analysis as well as the use of computer programs such as Matlab and Excel in carrying out involved computations. Sections are devoted to the use of Maple in mathematical analysis. Examples drawn from recent contributions to economic theory and econometrics as well as a variety of end of chapter exercises help to illustrate and apply the presented concepts.
Author : Franck Assous,Patrick Ciarlet,Simon Labrunie
Publisher : Springer
Page : 458 pages
File Size : 45,6 Mb
Release : 2018-06-09
Category : Mathematics
ISBN : 9783319708423
This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
Author : Pavel Pudlák
Publisher : Springer Science & Business Media
Page : 699 pages
File Size : 52,8 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9783319001197
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Author : Anonim
Publisher : Unknown
Page : 519 pages
File Size : 42,8 Mb
Release : 2003
Category : Mathematics
ISBN : OCLC:795928574
Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 45,9 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130
An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author : Peter J. Pahl,Rudolf Damrath
Publisher : Springer Science & Business Media
Page : 1007 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642568930
Computational engineering is the treatment of engineering tasks with computers. It is based on computational mathematics, which is presented here in a comprehensive handbook. From the existing rich repertoire of mathematical theories and methods, the fundamentals of engineering computation are here presented in a coherent fashion. They are brought into a suitable order for specific engineering purposes, and their significance for typical applications shown. The relevant definitions, notations and theories are presented in a durable form which is independent of the fast development of information and communication technology.
Author : Felipe Cucker,Michael Shub
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642605390
This book contains a collection of articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics conference held at IMPA in Rio de Janeiro in January 1997. Some ofthe others are published in the December 1996 issue of the Journal of Complexity. Both of these publications were available and distributed at the meeting. Even in this aspect we hope to have achieved a synthesis of the mathematics and computer science cultures as well as of the disciplines. The reaction to the Park City meeting on Mathematics of Numerical Analy sis: Real Number Algorithms which was chaired by Steve Smale and had around 275 participants, was very enthusiastic. At the suggestion of Narendra Karmar mar a lunch time meeting of Felipe Cucker, Arieh Iserles, Narendra Karmarkar, Jim Renegar, Mike Shub and Steve Smale decided to try to hold a periodic meeting entitled "Foundations of Computational Mathematics" and to form an organization with the same name whose primary purpose will be to hold the meeting. This is then the first edition of FoCM as such. It has been organized around a small collection of workshops, namely - Systems of algebraic equations and computational algebraic geometry - Homotopy methods and real machines - Information-based complexity - Numerical linear algebra - Approximation and PDEs - Optimization - Differential equations and dynamical systems - Relations to computer science - Vision and related computational tools There were also twelve plenary speakers.
Author : Felipe Cucker,Joseph Maurice Rojas
Publisher : World Scientific
Page : 488 pages
File Size : 52,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9812778039
This invaluable book contains 19 papers selected from those submitted to a conference held in Hong Kong in July 2000 to celebrate the 70th birthday of Professor Steve Smale. It may be regarded as a continuation of the proceedings of SMALEFEST 1990 ("From Topology to Computation") held in Berkeley, USA, 10 years before, but with the focus on the area in which Smale worked more intensively during the '90's, namely the foundations of computational mathematics.
Author : B. J. C. Baxter,A. Iserles,University of Cambridge. Department of Applied Mathematics and Theoretical Physics
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 2002
Category : Applied mathematics
ISBN : OCLC:59325365
Author : Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
Publisher : SIAM
Page : 710 pages
File Size : 49,9 Mb
Release : 2017-07-07
Category : Mathematics
ISBN : 9781611974898
This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?
Author : Felipe Cucker
Publisher : Cambridge University Press
Page : 218 pages
File Size : 53,5 Mb
Release : 2004-03-25
Category : Mathematics
ISBN : 0521542537
This volume, first published in 2004, contains the plenary invited talks given at main conference in the subject.