Computable Analysis
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Computable Analysis
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Author : Klaus Weihrauch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computable Analysis written by Klaus Weihrauch 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 Computers categories.
Is the exponential function computable? Are union and intersection of closed subsets of the real plane computable? Are differentiation and integration computable operators? Is zero finding for complex polynomials computable? Is the Mandelbrot set decidable? And in case of computability, what is the computational complexity? Computable analysis supplies exact definitions for these and many other similar questions and tries to solve them. - Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid basis for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.
Handbook Of Computability And Complexity In Analysis
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Author : Vasco Brattka
language : en
Publisher: Springer Nature
Release Date : 2021-06-04
Handbook Of Computability And Complexity In Analysis written by Vasco Brattka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-04 with Computers categories.
Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
Computable Analysis
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Author : Oliver Aberth
language : en
Publisher: McGraw-Hill Companies
Release Date : 1980
Computable Analysis written by Oliver Aberth and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Theory And Applications Of Models Of Computation
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Author : Jin-Yi Cai
language : en
Publisher: Springer
Release Date : 2006-05-05
Theory And Applications Of Models Of Computation written by Jin-Yi Cai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-05 with Computers categories.
This book constitutes the refereed proceedings of the Third International Conference on Theory and Applications of Models of Computation, TAMC 2006, held in Beijing, China, in May 2006. The 75 revised full papers presented together with 7 plenary talks were carefully reviewed and selected from 319 submissions. All major areas in computer science, mathematics (especially logic) and the physical sciences particularly with regard to computation and computability theory are addressed.
Computability And Models
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Author : Barry S. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computability And Models written by Barry S. Cooper 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.
Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.
Pi 0 1 Classes In Computable Analysis And Topology
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Author : Joseph Stephen Miller
language : en
Publisher:
Release Date : 2002
Pi 0 1 Classes In Computable Analysis And Topology written by Joseph Stephen Miller 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.
Computable Calculus
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Author : Oliver Aberth
language : en
Publisher: Academic Press
Release Date : 2001-06-04
Computable Calculus written by Oliver Aberth and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-04 with Mathematics categories.
Computable Calculus treats the fundamental topic of calculus in a novel way that is more in tune with today's computer age. Comprising 11 chapters and an accompanying CD-ROM, the book presents mathematical analysis that has been created to deal with constructively defined concepts. The book's "show your work" approach makes it easier to understand the pitfalls of various computations and, more importantly, how to avoid these pitfalls. The accompanying CD-ROM has self-contained programs that interact with the text, providing for easy grasp of the new concepts and enabling readers to write their own demonstration programs. Contains software on CD ROM: The accompanying software demonstrates, through simulation and exercises, how each concept of calculus can be associated with a program for the 'ideal computer' Using this software readers will be able to write their own demonstration programs
Theory And Applications Of Models Of Computation
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Author : T-H. Hubert Chan
language : en
Publisher: Springer
Release Date : 2013-04-15
Theory And Applications Of Models Of Computation written by T-H. Hubert Chan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Computers categories.
This book constitutes the refereed proceedings of the 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013, held in Hong Kong, China, in May 2013. The 31 revised full papers presented were carefully reviewed and selected from 70 submissions. Bringing together a wide range of researchers with interests in computational theory and applications, the papers address the three main themes of the conference which were computability, complexity, and algorithms and present current research in these fields with aspects to theoretical computer science, algorithmic mathematics, and applications to the physical sciences.
Algorithms Main Ideas And Applications
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Author : Vladimir Uspensky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algorithms Main Ideas And Applications written by Vladimir Uspensky 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 2013-03-14 with Mathematics categories.
Today the notion of the algorithm is familiar not only to mathematicians. It forms a conceptual base for information processing; the existence of a corresponding algorithm makes automatic information processing possible. The theory of algorithms (together with mathematical logic ) forms the the oretical basis for modern computer science (see [Sem Us 86]; this article is called "Mathematical Logic in Computer Science and Computing Practice" and in its title mathematical logic is understood in a broad sense including the theory of algorithms). However, not everyone realizes that the word "algorithm" includes a transformed toponym Khorezm. Algorithms were named after a great sci entist of medieval East, is al-Khwarizmi (where al-Khwarizmi means "from Khorezm"). He lived between c. 783 and 850 B.C. and the year 1983 was chosen to celebrate his 1200th birthday. A short biography of al-Khwarizmi compiled in the tenth century starts as follows: "al-Khwarizmi. His name is Muhammad ibn Musa, he is from Khoresm" (cited according to [Bul Rozen Ah 83, p.8]).
Logical Approaches To Computational Barriers
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Author : Arnold Beckmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-26
Logical Approaches To Computational Barriers written by Arnold Beckmann 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 2006-06-26 with Computers categories.
This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.