A Computational Introduction to Number Theory and Algebra

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

Victor Shoup (Author)

9780521516440, Cambridge University Press

Hardback, published 4 December 2008

600 pages, 650 exercises
24.4 x 17 x 3.3 cm, 1.2 kg

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

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.

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.

Subject Areas: Maths for computer scientists [UYAM], Number theory [PBH], Algebra [PBF]