Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

NPTEL

Computational Commutative Algebra

NPTEL and Chennai Mathematical Institute via YouTube

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!

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 students
PREREQUISITES: Introduction to the basic theory of rings, modules
INDUSTRIES SUPPORT: None

Syllabus

Computational Commutative Algebra - Intro video.
mod01lec01 - Definitions.
mod01lec02 - Homomorphisms.
mod01lec03 - Quotient rings.
mod01lec04 - Noetherian rings.
mod01lec05 - Monomials.
mod02lec06 - Initial ideals.
mod02lec07 - Division algorithm.
mod02lec08 - Grobner basis.
mod02lec09 - Solving Polynomial Equations.
mod02lec10 - Nullstellensatz - Part 1.
mod03lec11 - Nullstellensatz - Part 2.
mod03lec12 - Buchberger criterion.
mod03lec13 - Monomial basis.
mod03lec14 - Elimination.
mod03lec15 - Modules - Part 1.
mod04lec16 - Modules - Part 2.
mod04lec17 - Localisation.
mod04lec18 - Nakayama Lemma.
mod04lec19 - Spectrum - Part 1.
mod04lec20 - Spectrum - Part 2.
mod05lec21 - Associated primes.
mod05lec22 - Primary Decomposition.
mod05lec23 - Support of a module.
mod05lec24 - Associated primes.
mod05lec25 - Prime avoidance.
mod06lec26 - Saturation - Part 1.
mod06lec27 - saturation - Part 2.
mod06lec28 - saturation - Part 3.
mod06lec29 - Morphisms - Part 1.
mod06lec30 - Morphisms - Part 2.
mod07lec31 - Integral extensions.
mod07lec32 - Noether normalisation lemma.
mod07lec33 - Noether normalisation lemma.
mod07lec34 - Polynomial rings.
mod07lec35 - Going up theorem.
mod08lec36 - Artinian rings.
mod08lec37 - Graded modules.
mod08lec38 - Hilbert polynomial.
mod08lec39 - Hilbert-Samuel polynomial.
mod08lec40 - Artin Rees Lemma.
mod09lec41 - Degree of Hilbert-Samuel polynomial.
mod09lec42 - Dimension of noetherian local rings - Part 1.
mod09lec43 - Dimension of noetherian local rings - Part 2.
mod09lec44 - Dimension of polynomial rings.
mod09lec45 - Algebras over a field.
mod10lec46 - Graded rings - Part 1.
mod10lec47 - Graded rings - Part 2.
mod10lec48 - Polynomial rings over fields.
mod10lec49 - Hilbert series - Part 1.
mod10lec50 - Hilbert Series - Part 2.
mod11lec51 - Proj of a graded ring.
mod11lec52 - Homogenization - Part 1.
mod11lec53 - Homogenization - Part 2.
mod11lec54 - More on graded rings.
mod11lec55 - Free resolutions.
mod12lec56 - Computing syzygies.
mod12lec57 - Koszul complex.
mod12lec58 - More on Koszul complexes.
mod12lec59 - Castelnuovo Mumford regularity - Part 1.
mod12lec60 - Castelnuovo Mumford regularity - Part 2.

Taught by

NPTEL-NOC IITM

Tags

Reviews

Start your review of Computational Commutative Algebra

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.