TY  - GEN
AU  - Murty,M.Ram
AU  - Fodden,Brandon
TI  - Hilbert's tenth problem: : an introduction to logic number theory and computability
T2  - Student Mathematical Library
SN  - 9781470443993
U1  - 512.74 23
PY  - 2019///
CY  - Providence
PB  - AMS
KW  - Number Theory-Problems, Exercises
KW  - Mathematical Recreations-Problems, Exercises
KW  - Hilbert
KW  - AMS: Number Theory
KW  - Field Theory and Polynomials
N1  - Includes Bibliographical References and Index; Preface -- Acknowledgement -- Introduction -- Chapter 1. Cantor and Infinity -- Chapter 2. Axiomatic Set Theory -- Chapter 3. Elementary Number Theory -- Chapter 4. Computability and Provability -- Chapter 5. Hilbert's Tenth Problem -- Chapter 6. Applications of Hilbert's Tenth Problem -- Chapter 7. Hilbert's Tenth Problem over Number Fields -- Appendix A. Background Material -- Biliography -- Index
N2  - 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

ER  -