The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).
Rezensionen / Stimmen
'The book is written in a terse but energetic style - Schenck is clearly in love with the material ... any student who completes this book will be excited about algebraic geometry and well-equipped for further reading.' Bulletin of the American Mathematical Society 'It is a very good introduction to this circle of ideas and it will undoubtedly attract the interest of students to the field.' European Mathematical Society Newsletter 'It is brief, informal and provides many examples - all attributes that many other algebraic geometry books lack! ... its role is to stimulate and outline rather than to give an encyclopedic treatment, and in this it succeeds very well.' Australian Mathematical Society Gazette '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
Reihe
Sprache
Verlagsort
Zielgruppe
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 17 mm
Gewicht
ISBN-13
978-0-521-82964-9 (9780521829649)
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Schweitzer Klassifikation
Preface; 1. Basics of commutative algebra; 2. Projective space and graded objects; 3. Free resolutions and regular sequences; 4. Groebner 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.
