Computation
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Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
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
Projects In Scientific Computation
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Author : Richard E. Crandall
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-06-22
Projects In Scientific Computation written by Richard E. Crandall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-22 with Computers categories.
This interdisciplinary book provides a compendium of projects, plus numerous example programs for readers to study and explore. Designed for advanced undergraduates or graduates of science, mathematics and engineering who will deal with scientific computation in their future studies and research, it also contains new and useful reference materials for researchers. The problem sets range from the tutorial to exploratory and, at times, to "the impossible". The projects were collected from research results and computational dilemmas during the authors tenure as Chief Scientist at NeXT Computer, and from his lectures at Reed College. The content assumes familiarity with such college topics as calculus, differential equations, and at least elementary programming. Each project focuses on computation, theory, graphics, or a combination of these, and is designed with an estimated level of difficulty. The support code for each takes the form of either C or Mathematica, and is included in the appendix and on the bundled diskette. The algorithms are clearly laid out within the projects, such that the book may be used with other symbolic numerical and algebraic manipulation products
Mathematics For Computation M4c
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Author : Marco Benini
language : en
Publisher: World Scientific
Release Date : 2023-03-21
Mathematics For Computation M4c written by Marco Benini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-21 with Mathematics categories.
The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.
Perspectives In Computation
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Author : Robert Geroch
language : en
Publisher: University of Chicago Press
Release Date : 2009-09-15
Perspectives In Computation written by Robert Geroch and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-15 with Science categories.
Computation is the process of applying a procedure or algorithm to the solution of a mathematical problem. Mathematicians and physicists have been occupied for many decades pondering which problems can be solved by which procedures, and, for those that can be solved, how this can most efficiently be done. In recent years, quantum mechanics has augmented our understanding of the process of computation and of its limitations. Perspectives in Computation covers three broad topics: the computation process and its limitations, the search for computational efficiency, and the role of quantum mechanics in computation. The emphasis is theoretical; Robert Geroch asks what can be done, and what, in principle, are the limitations on what can be done? Geroch guides readers through these topics by combining general discussions of broader issues with precise mathematical formulations—as well as through examples of how computation works. Requiring little technical knowledge of mathematics or physics, Perspectives in Computation will serve both advanced undergraduates and graduate students in mathematics and physics, as well as other scientists working in adjacent fields.
Demystifying Computation
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Author : Apostolos Syropoulos
language : en
Publisher: Wspc (Europe)
Release Date : 2017
Demystifying Computation written by Apostolos Syropoulos and has been published by Wspc (Europe) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Computers categories.
Problem solving in computing is referred to as computational thinking. The theory behind this concept is challenging in its technicalities, yet simple in its ideas. This book introduces the theory of computation from its inception to current form of complexity; from explanations of how the field of computer science was formed using classical ideas in mathematics by GOdel, to conceptualization of the Turing Machine, to its more recent innovations in quantum computation, hypercomputation, vague computing and natural computing. It describes the impact of these in relation to academia, business and wider society, providing a sound theoretical basis for its practical application. Written for accessibility, Demystifying Computation provides the basic knowledge needed for non-experts in the field, undergraduate computer scientists and students of information and communication technology and software development.
Numerical Computation 1
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Author : Christoph W. Ueberhuber
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Computation 1 written by Christoph W. Ueberhuber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book deals with various aspects of scientific numerical computing. No at tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.
Understanding Computation
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Author : Tom Stuart
language : en
Publisher: "O'Reilly Media, Inc."
Release Date : 2013-05-15
Understanding Computation written by Tom Stuart and has been published by "O'Reilly Media, Inc." this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-15 with Computers categories.
Finally, you can learn computation theory and programming language design in an engaging, practical way. Understanding Computation explains theoretical computer science in a context you’ll recognize, helping you appreciate why these ideas matter and how they can inform your day-to-day programming. Rather than use mathematical notation or an unfamiliar academic programming language like Haskell or Lisp, this book uses Ruby in a reductionist manner to present formal semantics, automata theory, and functional programming with the lambda calculus. It’s ideal for programmers versed in modern languages, with little or no formal training in computer science. Understand fundamental computing concepts, such as Turing completeness in languages Discover how programs use dynamic semantics to communicate ideas to machines Explore what a computer can do when reduced to its bare essentials Learn how universal Turing machines led to today’s general-purpose computers Perform complex calculations, using simple languages and cellular automata Determine which programming language features are essential for computation Examine how halting and self-referencing make some computing problems unsolvable Analyze programs by using abstract interpretation and type systems
Computation And Applied Mathematics
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Author :
language : en
Publisher:
Release Date : 2002
Computation And Applied Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Evolutionary Computation
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Author : Kenneth A. De Jong
language : en
Publisher: MIT Press
Release Date : 2006-02-03
Evolutionary Computation written by Kenneth A. De Jong and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-03 with Computers categories.
This text is an introduction to the field of evolutionary computation. It approaches evolution strategies and genetic programming, as instances of a more general class of evolutionary algorithms.
Computation And Applied Mathematics
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Author :
language : en
Publisher:
Release Date : 1985
Computation And Applied Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.