Algebra - I GXYT9BP37G

URI	`m2://res/GXYT9BP37G`
Kind	course
Creators	Amritanshu Prasad (instructor), S. Viswanath (instructor)
Date	2020-11-30
Scope	in

Expressions

e1: edition

Language	en
Date	2020-11-30

m1: page, IMSc (record). nptel 111106137
m2: page, 2020-11-30 (record). nptel 111106137

Contents

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

Catalogue records

nptel: 111106137 (manifestation)
nptel_video: 111106137 (manifestation)