Computational Algebraic Geometry
Computational Algebraic Geometry
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.
- Concise snapshots of several different areas of advanced algebra - algebraic combinatorics, algebraic topology, commutative algebra and algebraic geometry
- Introduction to homological algebra in a concrete setting
- Lots of examples and exercises to help reader develop facility for computation by hand and by computer
- Appendices on abstract algebra and complex analysis to provide quick refreshers to the reader
- Code interspersed with text to encourage the reader to experiment as progressing through the book
Reviews & endorsements
"Schenck's book offers an interesting path into this wonderful subject...Any student who completes this book will be excited about algebraic geometry and well-equipped for further reading."
Bulletin of the American Mathematical Society
Product details
October 2003Paperback
9780521536509
208 pages
229 × 153 × 13 mm
0.278kg
Available
Table of Contents
- 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.
