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Hilbert's Tenth Problem

Hilbert's Tenth Problem

Wydawnictwo American Mathematical Society
Data wydania 01/06/2019
Wydanie Pierwsze
Liczba stron 242
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9781470443993
Kategorie Podstawy matematyki, Logika matematyczna, Teoria liczb
284.41 PLN (z VAT)
$74.05 / €66.46 / £57.23 /
Produkt na zamówienie
Przesyłka w 3-4 tygodnie
Do schowka

Opis książki

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 Godel'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

Spis treści

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

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