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A Computational Introduction to Number Theory and Algebra

$50.00 USD

  • Date Published: January 2007
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511112126

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About the Authors
  • 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.

    • Contains over 450 exercises, which present new applications to number theory and algebra
    • Minimal mathematics prerequisites
    • Presents complete and self-contained proofs of Chebyshev's theorem on the distribution of primes, Bertand's postulate, Mertens' theorem and the leftover hash lemma
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    Reviews & endorsements

    '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 Reviews

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    Product details

    • Date Published: January 2007
    • format: Adobe eBook Reader
    • isbn: 9780511112126
    • contains: 450 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    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
    Index of notation

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    A Computational Introduction to Number Theory and Algebra

    Victor Shoup

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  • Author

    Victor Shoup, New York University
    Victor Shoup is Associate Professor at The Courant Institute of Mathematical Sciences at New York University.

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