Brendan HassettCambridge University Press, 5/3/2007EAN 9780521691413, ISBN10: 0521691419Paperback, 264 pages, 24.7 x 17.4 x 1.4 cmLanguage: EnglishAlgebraic 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.Introduction1. Guiding problems2. Division algorithm and Gröbner bases3. Affine varieties4. Elimination5. Resultants6. Irreducible varieties7. Nullstellensatz8. Primary decomposition9. Projective geometry10. Projective elimination theory11. Parametrizing linear subspaces12. Hilbert polynomials and BezoutAppendix. Notions from abstract algebraReferencesIndex.'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
