Victor Shoup

A Computational Introduction to Number Theory and Algebra

• Gebundenes Buch

Produktbeschreibung

This introductory book emphasizes algorithms and applications, and is accessible to a broad audience. The author alternates between theory and applications in order to illustrate the mathematics. This second edition includes many new exercises and worked examples, and has been reorganized to improve presentation and clarity of exposition.

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Produktdetails

• Verlag: Cambridge University Press
• 2. Auflage
• Seitenzahl: 600
• Erscheinungstermin: 12. März 2012
• Englisch
• Abmessung: 250mm x 175mm x 36mm
• Gewicht: 1200g
• ISBN-13: 9780521516440
• ISBN-10: 0521516447
• Artikelnr.: 25614479

Autorenporträt

Victor Shoup is a Professor in the Department of Computer Science at the Courant Institute of Mathematical Sciences, New York University.

Inhaltsangabe

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.