Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Amritanshu Prasad, Prof. S. Viswanath
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 83
NPTEL Course Size : 4.1 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Permutations
Lecture 2 - Group Axioms
Lecture 3 - Order and Conjugacy
Lecture 4 - Subgroups
Lecture 5 - Problem solving
Lecture 6 - Group Actions
Lecture 7 - Cosets
Lecture 8 - Group Homomorphisms
Lecture 9 - Normal subgroups
Lecture 10 - Qutient Groups
Lecture 11 - Product and Chinese Remainder Theorem
Lecture 12 - Dihedral Groups
Lecture 13 - Semidirect products
Lecture 14 - Problem solving
Lecture 15 - The Orbit Counting Theorem
Lecture 16 - Fixed points of group actions
Lecture 17 - Second application: Fixed points of group actions
Lecture 18 - Sylow Theorem - a preliminary proposition
Lecture 19 - Sylow Theorem - I
Lecture 20 - Problem solving - I
Lecture 21 - Problem solving - II
Lecture 22 - Sylow Theorem - II
Lecture 23 - Sylow Theorem - III
Lecture 24 - Problem solving - I
Lecture 25 - Problem solving - II
Lecture 26 - Free Groups - I
Lecture 27 - Free Groups - IIa
Lecture 28 - Free Groups - IIb
Lecture 29 - Free Groups - III
Lecture 30 - Free Groups - IV
Lecture 31 - Problem Solving/Examples
Lecture 32 - Generators and relations for symmetric groups – I
Lecture 33 - Generators and relations for symmetric groups – II
Lecture 34 - Definition of a Ring
Lecture 35 - Euclidean Domains
Lecture 36 - Gaussian Integers
Lecture 37 - The Fundamental Theorem of Arithmetic
Lecture 38 - Divisibility and Ideals
Lecture 39 - Factorization and the Noetherian Condition
Lecture 40 - Examples of Ideals in Commutative Rings
Lecture 41 - Problem Solving/Examples
Lecture 42 - The Ring of Formal Power Series
Lecture 43 - Fraction Fields
Lecture 44 - Path Algebra of a Quiver
Lecture 45 - Ideals In Non-Commutative Rings
Lecture 46 - Product of Rings
Lecture 47 - Ring Homomorphisms
Lecture 48 - Quotient Rings
Lecture 49 - Problem solving
Lecture 50 - Tensor and Exterior Algebras
Lecture 51 - Modules: definition
Lecture 52 - Modules over polynomial rings $K[x]$
Lecture 53 - Modules: alternative definition
Lecture 54 - Modules: more examples
Lecture 55 - Submodules
Lecture 56 - General constructions of submodules
Lecture 57 - Problem Solving
Lecture 58 - Quotient modules
Lecture 59 - Homomorphisms
Lecture 60 - More examples of homomorphisms
Lecture 61 - First isomorphism theorem
Lecture 62 - Direct sums of modules
Lecture 63 - Complementary submodules
Lecture 64 - Change of ring
Lecture 65 - Problem solving
Lecture 66 - Free Modules (finitely generated)
Lecture 67 - Determinants
Lecture 68 - Primary Decomposition
Lecture 69 - Problem solving
Lecture 70 - Finitely generated modules and the Noetherian condition
Lecture 71 - Counterexamples to the Noetherian condition
Lecture 72 - Generators and relations for Finitely Generated Modules
Lecture 73 - General Linear Group over a Commutative Ring
Lecture 74 - Equivalence of Matrices
Lecture 75 - Smith Canonical Form for a Euclidean domain
Lecture 76 - solved_problems1
Lecture 77 - Smith Canonical Form for PID
Lecture 78 - Structure of finitely generated modules over a PID
Lecture 79 - Structure of a finitely generated abelian group
Lecture 80 - Similarity of Matrices
Lecture 81 - Deciding Similarity
Lecture 82 - Rational Canonical Form
Lecture 83 - Jordan Canonical Form