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In this course, you will learn
- 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
