Introduction to Algebraic Geometry by Brendan Hassett (English) Paperback Book

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Focuses on specific examples and develops only the formalism needed to address these. Introduces the notion of Gröbner bases early and develops algorithms for almost everything covered. Based on courses given over the past five years in a large interdisciplinary programme at Rice University, spanning mathematics, computer science, and bioinformatics.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

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.

Notes

A systematic introduction to the central concepts of algebraic geometry most useful for computation. For advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and develops only the formalism 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 program in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

Author Biography

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

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.

Review

'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.' Sandor Kovacs, University of Washington 'The author accomplished his goals. He created a textbook that will serve as a bridge for many students and researchers to algebraic geometry.' Acta Scientiarum Mathematicarum

Promotional

Central concepts most useful for computation; for undergraduate/graduate students in mathematics, researchers in applications.

Long Description

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 Gr'bner 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.

Review Quote

"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."S'ndor Kov'cs, University of Washington

Promotional "Headline"

Central concepts most useful for computation; for undergraduate/graduate students in mathematics, researchers in applications.

Description for Bookstore

Focuses on specific examples and develops only the formalism needed to address these. Introduces the notion of Gr

Description for Library

Focuses on specific examples and develops only the formalism needed to address these. Introduces the notion of Gr

Details ISBN0521691419 Author Brendan Hassett Publisher Cambridge University Press Language English ISBN-10 0521691419 ISBN-13 9780521691413 Media Book Format Paperback DEWEY 516.35 Year 2007 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Edition 1st Short Title INTRO TO ALGEBRAIC GEOMETRY Affiliation Rice University, Houston DOI 10.1604/9780521691413 UK Release Date 2007-05-03 AU Release Date 2007-05-03 NZ Release Date 2007-05-03 Pages 266 Publication Date 2007-05-03 Alternative 9780511755224 Illustrations Worked examples or Exercises; 10 Line drawings, unspecified Audience Professional & Vocational We've got this

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