Computational Algebraic Geometry

ISBN-13: 9780521536509 / Angielski / Miękka / 2003 / 208 str.

Hal Schenck

Opis

Recent advances in computing and algorithms make it easier to do many classical problems in algebra. Suitable for graduate students, this book brings advanced algebra to life with many examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The remainder of the book focuses on three active areas of contemporary algebra: homological algebra; algebraic combinatorics and algebraic topology; and algebraic geometry.

Recenzje

'It is a very good introduction to this circle of ideas and it will undoubtedly attract the interest of students to the field.' EMS Newsletter

Spis treści

Preface; 1. Basics of commutative algebra; 2. Projective space and graded objects; 3. Free resolutions and regular sequences; 4. Gröbner bases; 5. Combinatorics and topology; 6. Functors: localization, hom, and tensor; 7. Geometry of points; 8. Homological algebra, derived functors; 9. Curves, sheaves and cohomology; 10. Projective dimension; A. Abstract algebra primer; B. Complex analysis primer; Bibliography.