# A Computational Introduction to Number Theory and Algebra (World Trade Organization)

Cambridge University Press

Edition: 2, 12/4/2008

EAN 9780521516440, ISBN10: 0521516447

Hardcover, 600 pages, 24.4 x 17 x 3.3 cm

Language: English

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.

'The subject matter is presented in a very thorough way ... The material is very well organized: definitions, results and their interrelations fit together perfectly ... The book is especially attractive to students with a background or interest in computer science ... The suitability of the book for self-study is greatly enhanced by a wealth of exercises and examples that are provided ... the book is very well-written, and it is a pleasure to read.' Mathematics of Computation