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Introduction to Algebraic Geometry

$45.99 (X)

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  • Date Published: May 2007
  • availability: Available
  • format: Paperback
  • isbn: 9780521691413

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  • Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

    • Exposition of theory motivated by computational applications
    • Lots of carefully chosen problems and exercises; many with hints and morals that build intuition and facility
    • Solutions to a significant number of exercises available at author's website
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    Reviews & endorsements

    "Yet another introduction to algebraic geometry? No! This is a book that has been missing from our textbook arsenal and that belongs on the bookshelf of anyone who plans to either teach or study algebraic geometry."
    Sándor Kovács, University of Washington

    "This is a commonsense introduction with examples and relations to computational algebra. Hassett is in touch with current thinking in algebraic geometry itself, and has a light touch with the computational aspects."
    Miles Reid, University of Warwick

    "... A nice introduction to algebraic geometry. The book is clearly written and should be an important reference for elementary courses in algebraic geometry and commutative algebra."
    D.-M. Popescu, Mathematical Reviews

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    Product details

    • Date Published: May 2007
    • format: Paperback
    • isbn: 9780521691413
    • length: 266 pages
    • dimensions: 244 x 170 x 14 mm
    • weight: 0.43kg
    • contains: 10 b/w illus. 203 exercises
    • availability: Available
  • Table of Contents

    Introduction
    1. Guiding problems
    2. Division algorithm and Gröbner bases
    3. Affine varieties
    4. Elimination
    5. Resultants
    6. Irreducible varieties
    7. Nullstellensatz
    8. Primary decomposition
    9. Projective geometry
    10. Projective elimination theory
    11. Parametrizing linear subspaces
    12. Hilbert polynomials and Bezout
    Appendix. Notions from abstract algebra
    References
    Index.

  • Resources for

    Introduction to Algebraic Geometry

    Brendan Hassett

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    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

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  • Instructors have used or reviewed this title for the following courses

    • Algebra ll
    • Algebraic Geometry
  • Author

    Brendan Hassett, Rice University, Houston
    Brendan Hassett is Professor of Mathematics at Rice University, Houston.

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