Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Manoj Kummini
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 60
NPTEL Course Size : 4.9 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Definitions
Lecture 2 - Homomorphisms
Lecture 3 - Quotient rings
Lecture 4 - Noetherian rings
Lecture 5 - Monomials
Lecture 6 - Initial ideals
Lecture 7 - Division algorithm
Lecture 8 - Grobner basis
Lecture 9 - Solving Polynomial Equations
Lecture 10 - Nullstellensatz - Part 1
Lecture 11 - Nullstellensatz - Part 2
Lecture 12 - Buchberger criterion
Lecture 13 - Monomial basis
Lecture 14 - Elimination
Lecture 15 - Modules - Part 1
Lecture 16 - Modules - Part 2
Lecture 17 - Localisation
Lecture 18 - Nakayama Lemma
Lecture 19 - Spectrum - Part 1
Lecture 20 - Spectrum - Part 2
Lecture 21 - Associated primes
Lecture 22 - Primary Decomposition
Lecture 23 - Support of a module
Lecture 24 - Associated primes
Lecture 25 - Prime avoidance
Lecture 26 - Saturation - Part 1
Lecture 27 - Saturation - Part 2
Lecture 28 - Saturation - Part 3
Lecture 29 - Morphisms - Part 1
Lecture 30 - Morphisms - Part 2
Lecture 31 - Integral extensions
Lecture 32 - Noether normalisation lemma
Lecture 33 - Noether normalisation lemma
Lecture 34 - Polynomial rings
Lecture 35 - Going up theorem
Lecture 36 - Artinian rings
Lecture 37 - Graded modules
Lecture 38 - Hilbert polynomial
Lecture 39 - Hilbert-Samuel polynomial
Lecture 40 - Artin Rees Lemma
Lecture 41 - Degree of Hilbert-Samuel polynomial
Lecture 42 - Dimension of noetherian local rings - Part 1
Lecture 43 - Dimension of noetherian local rings - Part 2
Lecture 44 - Dimension of polynomial rings
Lecture 45 - Algebras over a field
Lecture 46 - Graded rings - Part 1
Lecture 47 - Graded rings - Part 2
Lecture 48 - Polynomial rings over fields
Lecture 49 - Hilbert series - Part 1
Lecture 50 - Hilbert series - Part 2
Lecture 51 - Proj of a graded ring
Lecture 52 - Homogenization - Part 1
Lecture 53 - Homogenization - Part 2
Lecture 54 - More on graded rings
Lecture 55 - Free resolutions
Lecture 56 - Computing syzygies
Lecture 57 - Koszul complex
Lecture 58 - More on Koszul complexes
Lecture 59 - Castelnuovo Mumford regularity
Lecture 60 - Castelnuovo Mumford regularity