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Computational Commutative Algebra - Intro video
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mod01lec01 - Definitions
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mod01lec02 - Homomorphisms
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mod01lec03 - Quotient rings
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mod01lec04 - Noetherian rings
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mod01lec05 - Monomials
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mod02lec06 - Initial ideals
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mod02lec07 - Division algorithm
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mod02lec08 - Grobner basis
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mod02lec09 - Solving Polynomial Equations
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mod02lec10 - Nullstellensatz - Part 1
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mod03lec11 - Nullstellensatz - Part 2
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mod03lec12 - Buchberger criterion
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mod03lec13 - Monomial basis
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mod03lec14 - Elimination
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mod03lec15 - Modules - Part 1
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mod04lec16 - Modules - Part 2
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mod04lec17 - Localisation
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mod04lec18 - Nakayama Lemma
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mod04lec19 - Spectrum - Part 1
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mod04lec20 - Spectrum - Part 2
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mod05lec21 - Associated primes
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mod05lec22 - Primary Decomposition
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mod05lec23 - Support of a module
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mod05lec24 - Associated primes
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mod05lec25 - Prime avoidance
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mod06lec26 - Saturation - Part 1
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mod06lec27 - saturation - Part 2
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mod06lec28 - saturation - Part 3
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mod06lec29 - Morphisms - Part 1
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mod06lec30 - Morphisms - Part 2
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mod07lec31 - Integral extensions
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mod07lec32 - Noether normalisation lemma
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mod07lec33 - Noether normalisation lemma
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mod07lec34 - Polynomial rings
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mod07lec35 - Going up theorem
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mod08lec36 - Artinian rings
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mod08lec37 - Graded modules
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mod08lec38 - Hilbert polynomial
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mod08lec39 - Hilbert-Samuel polynomial
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mod08lec40 - Artin Rees Lemma
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mod09lec41 - Degree of Hilbert-Samuel polynomial
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mod09lec42 - Dimension of noetherian local rings - Part 1
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mod09lec43 - Dimension of noetherian local rings - Part 2
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mod09lec44 - Dimension of polynomial rings
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mod09lec45 - Algebras over a field
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mod10lec46 - Graded rings - Part 1
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mod10lec47 - Graded rings - Part 2
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mod10lec48 - Polynomial rings over fields
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mod10lec49 - Hilbert series - Part 1
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mod10lec50 - Hilbert Series - Part 2
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mod11lec51 - Proj of a graded ring
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mod11lec52 - Homogenization - Part 1
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mod11lec53 - Homogenization - Part 2
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mod11lec54 - More on graded rings
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mod11lec55 - Free resolutions
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mod12lec56 - Computing syzygies
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mod12lec57 - Koszul complex
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mod12lec58 - More on Koszul complexes
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mod12lec59 - Castelnuovo Mumford regularity - Part 1
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mod12lec60 - Castelnuovo Mumford regularity - Part 2
Description:
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. INTENDED AUDIENCE: Advanced undergraduate / post-graduate studentsPREREQUISITES: Introduction to the basic theory of rings, modulesINDUSTRIES SUPPORT: None

Computational Commutative Algebra

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#Mathematics #Algebra #Computational Mathematics #Commutative Algebra #Abstract Algebra #Homomorphisms
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Computational Commutative Algebra - Intro video