Lecture 1 - Algebraic and Transcendental Numbers

Lecture 2 - Extensions Generated by Elements

Lecture 3 - Isomorphic Extensions

Lecture 4 - Degree of an Extension

Lecture 5 - Constructible Numbers

Lecture 6 - The Field of Constructible Numbers

Lecture 7 - Characterization of Constructible Numbers

Lecture 8 - Solved Problems (Week 1)

Lecture 9 - Some Things can't be Constructed

Lecture 10 - Symbolic Adjunction

Lecture 11 - Repeated Roots

Lecture 12 - Gauss Lemma

Lecture 13 - Eisenstein’s criterion

Lecture 14 - Existence Theorem for Finite Fields

Lecture 15 - Subfields of a Finite Field

Lecture 16 - Multiplicative Group of a Finite Field

Lecture 17 - Uniqueness Theorem for Finite Fields

Lecture 18 - Solved Problems (Week 2)

Lecture 19 - Algebraic Extensions and Algebraic Closures

Lecture 20 - Existence of Algebraic Closures

Lecture 21 - Uniqueness of Algebraic Closure

Lecture 22 - Solved Problems - Part 1 (Week 3)

Lecture 23 - Existence of splitting fields, bound on degree

Lecture 24 - Uniqueness of splitting fields

Lecture 25 - Solved problems - Part 2 (Week 3)

Lecture 26 - Normal Extensions

Lecture 27 - Separable polynomials

Lecture 28 - Perfect fields, separable extensions

Lecture 29 - Definition and examples, fixed fields

Lecture 30 - Characterization of Galois extensions

Lecture 31 - Linear Independence of Characters

Lecture 32 - Solved problems (Week 4)

Lecture 33 - Artin’s Theorem - Part 1

Lecture 34 - Artin’s Theorem - Part 2

Lecture 35 - Finite Galois Extensions

Lecture 36 - The fundamental theorem of Galois Theory - 1

Lecture 37 - The fundamental theorem of Galois Theory - 2

Lecture 38 - Solved problems (Week 5)

Lecture 39 - Cyclotomic extensions

Lecture 40 - Irreducibility of the cyclotomic polynomial

Lecture 41 - Application: Constructibility of regular n-gons.

Lecture 42 - Insolvability of the general quintic - Part 1

Lecture 43 - Insolvability of the general quintic - Part 2

Lecture 44 - Insolvability of the general quintic - Part 3

Lecture 45 - What is category theory (and why is it important)?

Lecture 46 - Definition of a category

Lecture 47 - Monomorphisms, epimorphisms, and isomorphisms

Lecture 48 - Categories: First Problem Session

Lecture 49 - Initial and Terminal Objects

Lecture 50 - Products and Coproducts

Lecture 51 - Categories: Second Problem Session

Lecture 52 - Functors

Lecture 53 - The Category of Categories

Lecture 54 - Natural Transformations

Lecture 55 - Functor Categories

Lecture 56 - Categories: Third Problem Session

Lecture 57 - Adjunction

Lecture 58 - Categories: Fourth Problem Session

Lecture 59 - Tensor products of Z-modules

Lecture 60 - Free abelian groups and quotient groups

Lecture 61 - Construction of the tensor product

Lecture 62 - Problem session

Lecture 63 - Tensor product of R-modules

Lecture 64 - Functoriality of the tensor product

Lecture 65 - Bimodules

Lecture 66 - Tensor products of bimodules

Lecture 67 - Tensor products of modules over commutative rings

Lecture 68 - Extension of scalars

Lecture 69 - Problem session - tensor products of vector spaces

Lecture 70 - Some Properties of the tensor product

Lecture 71 - F-algebras

Lecture 72 - Composition Series

Lecture 73 - Schreier’s Theorem

Lecture 74 - Ascending and Descending Chain Conditions

Lecture 75 - Existence of Jordan-Holder Series

Lecture 76 - The Jordan-Holder Theorem

Lecture 77 - Examples related to the Jordan-Holder Theorem

Lecture 78 - The Jordan-Holder Theorem for Groups

Lecture 79 - Indecomposable Modules

Lecture 80 - Direct Sum Decompositions

Lecture 81 - Decomposition as a sum of Indecomposables

Lecture 82 - The Endomorphism Ring of an Indecomposable Module

Lecture 83 - Krull-Schmidt Theorem

Lecture 84 - Krull-Schmidt Examples