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Week
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Topics
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Study Metarials
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1
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Ideals and varieties, Noetherian rings and the Hilbert basis theorem
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2
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Associated primes and primary decomposition, the Nullstellensatz and Zariski topology
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3
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Projective space and projective varieties,
Hilbert function and series
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4
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Hilbert polynomial
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5
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Free modules and projective modules, free resolutions
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6
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Regular sequences, mapping cone
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7
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Gröbner bases, monomial ideals and applications
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8
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Syzygies and Gröbner bases for modules, projection and elimination
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9
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Simplicial complexes and simplicial homology
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10
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The Stanley-Reisner ring
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11
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Localization, the Hom functor
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12
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Tensor product
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13
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Hilbert functions of points, regularity, the theorems of Macaulay and Gotzmann
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14
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Artinian reduction and hypersurfaces
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