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A Comprehensive Course in Number Theory

$103.00 (P)

  • Date Published: October 2012
  • availability: Available
  • format: Hardback
  • isbn: 9781107019010

$ 103.00 (P)
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About the Authors
  • Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

    • Carefully blends the author's previous text with more advanced material
    • Based on lecture courses used in the higher parts of the Mathematical Tripos at Cambridge
    • No other work embraces the same range of subjects in number theory
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    Reviews & endorsements

    "Now the idea of a 250-page "comprehensive" introduction to number theory may seem audacious, but among mathematical writers, Baker manifestly possesses the powerful gifts for precision and concision that could even make it possible. Such a book surely demands very careful study, but amazingly never seems rushed or artificially compressed. Highly recommended."
    D.V. Feldman, University of New Hampshire for Choice Magazine

    "Any competent instructor could use this as the starting point of a valuable course."
    Richard T. Bumby, Mathematical Reviews

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    Product details

    • Date Published: October 2012
    • format: Hardback
    • isbn: 9781107019010
    • length: 268 pages
    • dimensions: 229 x 152 x 19 mm
    • weight: 0.57kg
    • contains: 7 b/w illus. 195 exercises
    • availability: Available
  • Table of Contents

    Preface
    Introduction
    1. Divisibility
    2. Arithmetical functions
    3. Congruences
    4. Quadratic residues
    5. Quadratic forms
    6. Diophantine approximation
    7. Quadratic fields
    8. Diophantine equations
    9. Factorization and primality testing
    10. Number fields
    11. Ideals
    12. Units and ideal classes
    13. Analytic number theory
    14. On the zeros of the zeta-function
    15. On the distribution of the primes
    16. The sieve and circle methods
    17. Elliptic curves
    Bibliography
    Index.

  • Author

    Alan Baker, University of Cambridge
    Alan Baker is Emeritus Professor of Pure Mathematics in the University of Cambridge and Fellow of Trinity College, Cambridge. His many distinctions include the Fields Medal (1970) and the Adams Prize (1972).

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