# Computational Commutative Algebra

This is an introductory course in computational commutative algebra. Topics in a typical first course in commutative algebra are developed along with computations in Macaulay2. The emphasis will be on concrete computations, more than on giving complete proofs of theorems.

**COURSE LAYOUT**

Week 1:Introduction: rings and ideals, ring homomorphisms, Hilbert basis theorem, Hilbert Nullstellensatz, introduction to Macaulay2

Week 2:Groebner bases, ideal membership, solving systems of polynomial rings

Week 3:Modules.

Week 4:Associated primes and primary decomposition

Week 5:Associated primes and primary decomposition, ctd.

Week 6:Integral extensions, integral closure, Noether normalization

Week 7:Integral extensions, integral closure, Noether normalization, ctd.

Week 8:Hilbert functions, dimension theory

Week 9:Hilbert functions, dimension theory ctd.

Week 10:Applications to geometry.

Week 11:Homological algebra: depth, Koszul complex

Week 12:Homological algebra: free resolutions, Auslander-Buchsbaum formula.

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