NOC:Algebra - I

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