Modules / Lectures

Sl.No | Chapter Name | English |
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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 |