| Module Name | Download |
|---|
| Sl.No | Chapter Name | MP4 Download |
|---|---|---|
| 1 | Algebraic and Transcendental Numbers | Download |
| 2 | Extensions Generated by Elements | Download |
| 3 | Isomorphic Extensions | Download |
| 4 | Degree of an Extension | Download |
| 5 | Constructible Numbers | Download |
| 6 | The Field of Constructible Numbers | Download |
| 7 | Characterization of Constructible Numbers | Download |
| 8 | Solved Problems (Week 1) | Download |
| 9 | Some Things can't be Constructed | Download |
| 10 | Symbolic Adjunction | Download |
| 11 | Repeated Roots | Download |
| 12 | Gauss Lemma | Download |
| 13 | Eisenstein’s criterion | Download |
| 14 | Existence Theorem for Finite Fields | Download |
| 15 | Subfields of a Finite Field | Download |
| 16 | Multiplicative Group of a Finite Field | Download |
| 17 | Uniqueness Theorem for Finite Fields | Download |
| 18 | Solved Problems (week 2) | Download |
| 19 | Algebraic Extensions and Algebraic Closures | Download |
| 20 | Existence of Algebraic Closures | Download |
| 21 | Uniqueness of Algebraic Closure | Download |
| 22 | Solved Problems, part 1 (Week 3) | Download |
| 23 | Existence of splitting fields, bound on degree | Download |
| 24 | Uniqueness of splitting fields | Download |
| 25 | Solved problems , part 2 (Week 3) | Download |
| 26 | Normal Extensions | Download |
| 27 | Separable polynomials | Download |
| 28 | Perfect fields, separable extensions | Download |
| 29 | Definition and examples, fixed fields | Download |
| 30 | Characterization of Galois extensions | Download |
| 31 | Linear Independence of Characters | Download |
| 32 | Solved problems (Week 4) | Download |
| 33 | Artin’s Theorem – part 1 | Download |
| 34 | Artin’s Theorem – part 2 | Download |
| 35 | Finite Galois Extensions | Download |
| 36 | The fundamental theorem of Galois Theory - 1 | Download |
| 37 | The fundamental theorem of Galois Theory – 2 | Download |
| 38 | Solved problems (Week 5) | Download |
| 39 | Cyclotomic extensions | Download |
| 40 | Irreducibility of the cyclotomic polynomial | Download |
| 41 | Application: Constructibility of regular n-gons. | Download |
| 42 | Insolvability of the general quintic – part 1 | Download |
| 43 | Insolvability of the general quintic – part 2 | Download |
| 44 | Insolvability of the general quintic – part 3 | Download |
| 45 | What is category theory (and why is it important)? | Download |
| 46 | Definition of a category | Download |
| 47 | Monomorphisms, epimorphisms, and isomorphisms | Download |
| 48 | Categories: First Problem Session | Download |
| 49 | Initial and Terminal Objects | Download |
| 50 | Products and Coproducts | Download |
| 51 | Categories: Second Problem Session | Download |
| 52 | Functors | Download |
| 53 | The Category of Categories | Download |
| 54 | Natural Transformations | Download |
| 55 | Functor Categories | Download |
| 56 | Categories: Third Problem Session | Download |
| 57 | Adjunction | Download |
| 58 | Categories: Fourth Problem Session | Download |
| 59 | Tensor products of Z-modules | Download |
| 60 | Free abelian groups and quotient groups | Download |
| 61 | Construction of the tensor product | Download |
| 62 | Problem session | Download |
| 63 | Tensor product of R-modules | Download |
| 64 | Functoriality of the tensor product | Download |
| 65 | Bimodules | Download |
| 66 | Tensor products of bimodules | Download |
| 67 | Tensor products of modules over commutative rings | Download |
| 68 | Extension of scalars | Download |
| 69 | Problem session – tensor products of vector spaces | Download |
| 70 | Some Properties of the tensor product | Download |
| 71 | F-algebras | Download |
| 72 | Composition Series | Download |
| 73 | Schreier’s Theorem | Download |
| 74 | Ascending and Descending Chain Conditions | Download |
| 75 | Existence of Jordan-Holder Series | Download |
| 76 | The Jordan-Holder Theorem | Download |
| 77 | Examples related to the Jordan-Holder Theorem | Download |
| 78 | The Jordan-Holder Theorem for Groups | Download |
| 79 | Indecomposable Modules | Download |
| 80 | Direct Sum Decompositions | Download |
| 81 | Decomposition as a sum of Indecomposables | Download |
| 82 | The Endomorphism Ring of an Indecomposable Module | Download |
| 83 | Krull-Schmidt Theorem | Download |
| 84 | Krull-Schmidt Examples | Download |
| Sl.No | Chapter Name | English |
|---|---|---|
| 1 | Algebraic and Transcendental Numbers | Download To be verified |
| 2 | Extensions Generated by Elements | Download To be verified |
| 3 | Isomorphic Extensions | Download To be verified |
| 4 | Degree of an Extension | Download To be verified |
| 5 | Constructible Numbers | Download To be verified |
| 6 | The Field of Constructible Numbers | Download To be verified |
| 7 | Characterization of Constructible Numbers | Download To be verified |
| 8 | Solved Problems (Week 1) | Download To be verified |
| 9 | Some Things can't be Constructed | Download To be verified |
| 10 | Symbolic Adjunction | Download To be verified |
| 11 | Repeated Roots | Download To be verified |
| 12 | Gauss Lemma | Download To be verified |
| 13 | Eisenstein’s criterion | Download To be verified |
| 14 | Existence Theorem for Finite Fields | Download To be verified |
| 15 | Subfields of a Finite Field | Download To be verified |
| 16 | Multiplicative Group of a Finite Field | Download To be verified |
| 17 | Uniqueness Theorem for Finite Fields | Download To be verified |
| 18 | Solved Problems (week 2) | Download To be verified |
| 19 | Algebraic Extensions and Algebraic Closures | Download To be verified |
| 20 | Existence of Algebraic Closures | Download To be verified |
| 21 | Uniqueness of Algebraic Closure | Download To be verified |
| 22 | Solved Problems, part 1 (Week 3) | Download To be verified |
| 23 | Existence of splitting fields, bound on degree | Download To be verified |
| 24 | Uniqueness of splitting fields | Download To be verified |
| 25 | Solved problems , part 2 (Week 3) | Download To be verified |
| 26 | Normal Extensions | Download To be verified |
| 27 | Separable polynomials | Download To be verified |
| 28 | Perfect fields, separable extensions | Download To be verified |
| 29 | Definition and examples, fixed fields | Download To be verified |
| 30 | Characterization of Galois extensions | Download To be verified |
| 31 | Linear Independence of Characters | Download To be verified |
| 32 | Solved problems (Week 4) | Download To be verified |
| 33 | Artin’s Theorem – part 1 | Download To be verified |
| 34 | Artin’s Theorem – part 2 | Download To be verified |
| 35 | Finite Galois Extensions | Download To be verified |
| 36 | The fundamental theorem of Galois Theory - 1 | Download To be verified |
| 37 | The fundamental theorem of Galois Theory – 2 | Download To be verified |
| 38 | Solved problems (Week 5) | Download To be verified |
| 39 | Cyclotomic extensions | Download To be verified |
| 40 | Irreducibility of the cyclotomic polynomial | Download To be verified |
| 41 | Application: Constructibility of regular n-gons. | Download To be verified |
| 42 | Insolvability of the general quintic – part 1 | Download To be verified |
| 43 | Insolvability of the general quintic – part 2 | Download To be verified |
| 44 | Insolvability of the general quintic – part 3 | Download To be verified |
| 45 | What is category theory (and why is it important)? | PDF unavailable |
| 46 | Definition of a category | PDF unavailable |
| 47 | Monomorphisms, epimorphisms, and isomorphisms | PDF unavailable |
| 48 | Categories: First Problem Session | PDF unavailable |
| 49 | Initial and Terminal Objects | PDF unavailable |
| 50 | Products and Coproducts | PDF unavailable |
| 51 | Categories: Second Problem Session | PDF unavailable |
| 52 | Functors | PDF unavailable |
| 53 | The Category of Categories | PDF unavailable |
| 54 | Natural Transformations | PDF unavailable |
| 55 | Functor Categories | PDF unavailable |
| 56 | Categories: Third Problem Session | PDF unavailable |
| 57 | Adjunction | PDF unavailable |
| 58 | Categories: Fourth Problem Session | PDF unavailable |
| 59 | Tensor products of Z-modules | PDF unavailable |
| 60 | Free abelian groups and quotient groups | PDF unavailable |
| 61 | Construction of the tensor product | PDF unavailable |
| 62 | Problem session | PDF unavailable |
| 63 | Tensor product of R-modules | PDF unavailable |
| 64 | Functoriality of the tensor product | PDF unavailable |
| 65 | Bimodules | PDF unavailable |
| 66 | Tensor products of bimodules | PDF unavailable |
| 67 | Tensor products of modules over commutative rings | PDF unavailable |
| 68 | Extension of scalars | PDF unavailable |
| 69 | Problem session – tensor products of vector spaces | PDF unavailable |
| 70 | Some Properties of the tensor product | PDF unavailable |
| 71 | F-algebras | PDF unavailable |
| 72 | Composition Series | PDF unavailable |
| 73 | Schreier’s Theorem | PDF unavailable |
| 74 | Ascending and Descending Chain Conditions | PDF unavailable |
| 75 | Existence of Jordan-Holder Series | PDF unavailable |
| 76 | The Jordan-Holder Theorem | PDF unavailable |
| 77 | Examples related to the Jordan-Holder Theorem | PDF unavailable |
| 78 | The Jordan-Holder Theorem for Groups | PDF unavailable |
| 79 | Indecomposable Modules | PDF unavailable |
| 80 | Direct Sum Decompositions | PDF unavailable |
| 81 | Decomposition as a sum of Indecomposables | PDF unavailable |
| 82 | The Endomorphism Ring of an Indecomposable Module | PDF unavailable |
| 83 | Krull-Schmidt Theorem | PDF unavailable |
| 84 | Krull-Schmidt Examples | PDF unavailable |
| Sl.No | Language | Book link |
|---|---|---|
| 1 | English | Not Available |
| 2 | Bengali | Not Available |
| 3 | Gujarati | Not Available |
| 4 | Hindi | Not Available |
| 5 | Kannada | Not Available |
| 6 | Malayalam | Not Available |
| 7 | Marathi | Not Available |
| 8 | Tamil | Not Available |
| 9 | Telugu | Not Available |