| 000 | 02435 a2200253 4500 | ||
|---|---|---|---|
| 008 | 240423b 2019|||||||| |||| 00| 0 eng d | ||
| 020 | _a9781470443993 (PB) | ||
| 041 | _aeng | ||
| 080 |
_a512 _bMUR |
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| 100 | _aMurty, M. Ram | ||
| 245 |
_aHilbert's Tenth Problem _b: An Introduction to Logic, Number Theory, and Computability, |
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| 260 |
_bAmerican Mathematical Society _c2019 _aRhode Island |
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| 300 | _axiii, 237p. | ||
| 490 |
_aStudent Mathematical Library _v88 |
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| 504 | _aIncludes Bibliography (229- 232) and Index | ||
| 505 | _a1. Introduction 2. Cantor and infinity 3. Axiomatic set theory 4. Elementary number theory 5. Computability and provability 6. Hilbert’s tenth problem 7. Applications of Hilbert’s tenth problem 8. Hilbert’s tenth problem over number fields 9. Background material | ||
| 520 | _aHilbert'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. | ||
| 650 | _aNumber theory | ||
| 650 | _aMathematical recreations and problems | ||
| 650 | _aField theory and polynomials | ||
| 690 | _aMathematics | ||
| 700 | _aFodden, Brandon | ||
| 942 | _cBK | ||
| 999 |
_c60042 _d60042 |
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