A Computational Introduction to Number Theory and Algebra
A Computational Introduction to Number Theory and Algebra
$69.99
USDNumber 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.
- Now contains over 650 exercises, which present new applications to number theory and algebra
- Minimal mathematics needed
- An ideal textbook for an introductory graduate or advanced undergraduate course, geared towards computer science students
Reviews & endorsements
'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
'… the book could serve as a course of discrete mathematics for computer science students.' EMS Newsletter
Product details
December 2008Hardback
9780521516440
600 pages
244 × 170 × 33 mm
1.2kg
650 exercises
Available
Table of Contents
- 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.
