Description

Book Synopsis

Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900. It asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. This book is an exposition of their achievement.

Table of Contents

  • Introduction
  • Cantor and infinity
  • Axiomatic set theory
  • Elementary number theory
  • Computability and provability
  • Hilbert's tenth problem
  • Applications of Hilbert's tenth problem
  • Hilbert's tenth problem over number fields
  • Background material
  • Bibliography
  • Index

    Hilberts Tenth Problem

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      A Paperback by M. Ram Murty, Brandon Fodden

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        Book details

        Publisher American Mathematical Society
        Published 30 June 2019
        ISBN-13 9781470443993
        978-1470443993
        ISBN-10 1470443996
        Also in:
        Mathematical logic

        Description

        Book Synopsis

        Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900. It asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. This book is an exposition of their achievement.

        Table of Contents

        • Introduction
        • Cantor and infinity
        • Axiomatic set theory
        • Elementary number theory
        • Computability and provability
        • Hilbert's tenth problem
        • Applications of Hilbert's tenth problem
        • Hilbert's tenth problem over number fields
        • Background material
        • Bibliography
        • Index

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