Hilbert S Tenth Problem
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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.
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
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.
Extensions And Corollaries Of Recent Work On Hilbert S Tenth Problem
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Author : Martin Davis
language : en
Publisher:
Release Date : 1961
Extensions And Corollaries Of Recent Work On Hilbert S Tenth Problem written by Martin Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Functions categories.
The theorem that every recursively enumerable set is expon ntial Diophantine is improve ; a sharp form is given of Kleene's (Introduction to Metamathematics, D. Van Nostrand Company, Inc., 1952) normal form theorem, a problem of Quine (Synthese, VII; 441-46, 1948-9) is proved recursively unsolvable. (Author).
Hilbert S Tenth Problem
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Author :
language : en
Publisher:
Release Date : 2006
Hilbert S Tenth Problem written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Algebraic number theory categories.
Hilbert's Tenth Problem - to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions - was shown to be unsolvable in the late sixties. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields.
Extensions And Corollaries Of Recent Work On Hilbert S Tenth Problem
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Author : Martin Davis
language : en
Publisher:
Release Date : 2015-08-04
Extensions And Corollaries Of Recent Work On Hilbert S Tenth Problem written by Martin Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-04 with Reference categories.
Excerpt from Extensions and Corollaries of Recent Work on Hilbert's Tenth Problem: June 1961 Abstract: The theorem that every recursively enumerable set is exponential Diophantine is improved; a sharp for is a given of Kleen's normal form theorem, a problem of Quine is proved recursively unsolvable. "Qualified requestors may obtain copies of this report from the Astia Document Service Center, Arlingtong Hall Station, Arlingtong 12, Virginia. Department of Defence contractors must be established for Astia service, or have their "need-to-know" certified by the cognizant military agency of their project or contract." About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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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The Heritage Of Thales
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Author : W.S. Anglin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Heritage Of Thales written by W.S. Anglin 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 Science categories.
The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting. Although primarily intended for mathematics undergraduates, the book will also appeal to students in the sciences, humanities and education with a strong interest in this subject. The first part proceeds from about 1800 BC to 1800 AD, discussing, for example, the Renaissance method for solving cubic and quartic equations and providing rigorous elementary proof that certain geometrical problems posed by the ancient Greeks cannot be solved by ruler and compass alone. The second part presents some fundamental topics of interest from the past two centuries, including proof of G del's incompleteness theorem, together with a discussion of its implications.
Mathematical Developments Arising From Hilbert Problems
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Author : Felix E. Browder
language : en
Publisher:
Release Date : 1976
Mathematical Developments Arising From Hilbert Problems written by Felix E. Browder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.