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by Hal Schenck

Edition: 03Copyright: 2003

Publisher: Cambridge University Press

Published: 2003

International: No

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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.

Preface

1. Basics of commutative algebra

2. Projective space and graded objects

3. Free resolutions and regular sequences

4. Grobner 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.

Summary

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.

Table of Contents

Preface

1. Basics of commutative algebra

2. Projective space and graded objects

3. Free resolutions and regular sequences

4. Grobner 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.

Publisher Info

Publisher: Cambridge University Press

Published: 2003

International: No

Published: 2003

International: No

1. Basics of commutative algebra

2. Projective space and graded objects

3. Free resolutions and regular sequences

4. Grobner 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.