A Computational Introduction to Number Theory and Algebra

ISBN-13: 9780521516440 / Angielski / Twarda / 2009 / 600 str.

Victor Shoup

Opis

An introductory graduate-level text emphasizing algorithms and applications. This 2008 second edition includes over 200 new exercises and examples.

Recenzje

'… the book could serve as a course of discrete mathematics for computer science students.' EMS Newsletter

Spis treści

Preface; Preliminaries; 1. Basic properties of the integers; 2. Congruences; 3. Computing with large integers; 4. Euclid's algorithm; 5. The distribution of primes; 6. Abelian groups; 7. Rings; 8. Finite and discrete probability distributions; 9. Probabilistic algorithms; 10. Probabilistic primality testing; 11. Finding generators and discrete logarithms in Z*p; 12. Quadratic reciprocity and computing modular square roots; 13. Modules and vector spaces; 14. Matrices; 15. Subexponential-time discrete logarithms and factoring; 16. More rings; 17. Polynomial arithmetic and applications; 18. Linearly generated sequences and applications; 19. Finite fields; 20. Algorithms for finite fields; 21. Deterministic primality testing; Appendix: some useful facts; Bibliography; Index of notation; Index.