Hilbert S Tenth Problem An Introduction To Logic Number Theory And Computability
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Hilbert S Tenth Problem An Introduction To Logic Number Theory And Computability
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Author : M. Ram Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-05-09
Hilbert S Tenth Problem An Introduction To Logic Number Theory And Computability written by M. Ram Murty and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-09 with Decidability (Mathematical logic) categories.
Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists. This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.
Hilbert S Tenth Problem Relations With Arithmetic And Algebraic Geometry
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Author : Jan Denef
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Hilbert S Tenth Problem Relations With Arithmetic And Algebraic Geometry written by Jan Denef and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bücchi's problem, and results on the complexity of diophantine geometry, highlighting the relation to the theory of computation. The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory
Hilbert S Tenth Problem
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Author : I︠U︡riĭ V. Matii︠a︡sevich
language : en
Publisher: MIT Press
Release Date : 1993
Hilbert S Tenth Problem written by I︠U︡riĭ V. Matii︠a︡sevich and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Computers categories.
This book presents the full, self-contained negative solution of Hilbert's 10th problem.
The Riemann Hypothesis And Hilbert S Tenth Problem
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Author : Sarvadaman Chowla
language : en
Publisher: CRC Press
Release Date : 1987
The Riemann Hypothesis And Hilbert S Tenth Problem written by Sarvadaman Chowla and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Computability Unsolvability
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Author : Martin Davis
language : en
Publisher: Courier Corporation
Release Date : 1982-01-01
Computability Unsolvability written by Martin Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Mathematics categories.
Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.
Hilbert S Tenth Problem
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Author : Alexandra Shlapentokh
language : en
Publisher: Cambridge University Press
Release Date : 2007
Hilbert S Tenth Problem written by Alexandra Shlapentokh and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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Logical Number Theory I
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Author : Craig Smorynski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logical Number Theory I written by Craig Smorynski 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.
Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.
An Introduction To Mathematical Logic
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Author : Richard E. Hodel
language : en
Publisher: Courier Corporation
Release Date : 2013-01-01
An Introduction To Mathematical Logic written by Richard E. Hodel and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
Modern Mathematical Logic
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Author : Joseph Mileti
language : en
Publisher: Cambridge University Press
Release Date : 2022-08-31
Modern Mathematical Logic written by Joseph Mileti and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Mathematics categories.
This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.
Enumerability Decidability Computability
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Author : Hans Hermes
language : en
Publisher: Springer
Release Date : 2013-03-14
Enumerability Decidability Computability written by Hans Hermes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success.