"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
The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Recent advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. Suitable for graduate students, the objective of this book is to bring advanced algebra to life with lots of examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book then focuses on three active areas of contemporary algebra:* Homological Algebra--the snake lemma, long exact sequence in homology, 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.* Algebraic Geometry--points and curves in projective space, Riemann-Roch, Cech cohomology,regularity.