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Using Algebraic Geometry

  • Textbook
  • © 1998

Overview

Authors:
  1. David Cox

    1. Department of Mathematics and Computer Science, Amherst College, Amherst, USA

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    You can also search for this author in PubMed   Google Scholar

  2. John Little

    1. Department of Mathematics, College of the Holy Cross, Worcester, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Donal O’Shea

    1. Department of Mathematics, Statistics and Computer Science, Mount Holyoke College, South Hadley, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Graduate Texts in Mathematics (GTM, volume 185)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • David Cox, John Little, Donal O’Shea
    Pages 1-23

  3. Solving Polynomial Equations

    • David Cox, John Little, Donal O’Shea
    Pages 24-70

  4. Resultants

    • David Cox, John Little, Donal O’Shea
    Pages 71-129

  5. Computation in Local Rings

    • David Cox, John Little, Donal O’Shea
    Pages 130-178

  6. Modules

    • David Cox, John Little, Donal O’Shea
    Pages 179-233

  7. Free Resolutions

    • David Cox, John Little, Donal O’Shea
    Pages 234-289

  8. Polytopes, Resultants, and Equations

    • David Cox, John Little, Donal O’Shea
    Pages 290-358

  9. Integer Programming, Combinatorics, and Splines

    • David Cox, John Little, Donal O’Shea
    Pages 359-406

  10. Algebraic Coding Theory

    • David Cox, John Little, Donal O’Shea
    Pages 407-467

  11. Back Matter

    Pages 468-503
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Keywords

About this book

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gr"obner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

Authors and Affiliations

  • Department of Mathematics and Computer Science, Amherst College, Amherst, USA

    David Cox

  • Department of Mathematics, College of the Holy Cross, Worcester, USA

    John Little

  • Department of Mathematics, Statistics and Computer Science, Mount Holyoke College, South Hadley, USA

    Donal O’Shea

Bibliographic Information

  • Book Title: Using Algebraic Geometry

  • Authors: David Cox, John Little, Donal O’Shea

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-6911-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • eBook ISBN: 978-1-4757-6911-1Published: 17 April 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 503

  • Topics: Algebraic Geometry, Combinatorics

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