A Computational Introduction to Number Theory and Algebra

A Computational Introduction to Number Theory and Algebra

3.6 (15 ratings by Goodreads)
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Description

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 emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 1139165461
  • 9781139165464

Review quote

'It's a pleasure to find a book that is so masterful and so well written that it has all tha hallmarks of a classic. This is such a book. Shoup set himself the difficult task of bringing readers upt o speed with number theory and algebra, starting 'from scratch' - he is quite successful... This is a truly magnificent text, deserving a place on the shelves of any mathematician or computer scientist working in these areas.' Computing Reviewsshow more

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. Finite and discrete probability distributions; 7. Probabilistic algorithms; 8. Abelian groups; 9. Rings; 10. Probabilistic primality testing; 11. Finding generators and discrete logarithms in Zp*; 12. Quadratic residues and quadratic reciprocity; 13. Computational problems related to quadratic residues; 14. Modules and vector spaces; 15. Matrices; 16. Subexponential-time discrete logarithms and factoring; 17. More rings; 18. Polynomial arithmetic and applications; 19. Linearly generated sequences and applications; 20. Finite fields; 21. Algorithms for finite fields; 22. Deterministic primality testing; Appendix: some useful facts; Bibliography; Index of notation; Index.show more

Rating details

15 ratings
3.6 out of 5 stars
5 7% (1)
4 53% (8)
3 33% (5)
2 7% (1)
1 0% (0)
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