Modules / Lectures

Sl.No Chapter Name English
1Algebraic and Transcendental NumbersDownload
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2Extensions Generated by ElementsDownload
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3Isomorphic ExtensionsDownload
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4Degree of an ExtensionDownload
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5Constructible NumbersDownload
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6The Field of Constructible NumbersDownload
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7Characterization of Constructible NumbersDownload
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8Solved Problems (Week 1)Download
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9Some Things can't be ConstructedDownload
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10Symbolic AdjunctionDownload
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11Repeated RootsDownload
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12Gauss LemmaDownload
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13Eisenstein’s criterionDownload
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14Existence Theorem for Finite FieldsDownload
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15Subfields of a Finite FieldDownload
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16Multiplicative Group of a Finite FieldDownload
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17Uniqueness Theorem for Finite FieldsDownload
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18Solved Problems (week 2)Download
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19Algebraic Extensions and Algebraic ClosuresDownload
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20Existence of Algebraic ClosuresDownload
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21Uniqueness of Algebraic ClosureDownload
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22Solved Problems, part 1 (Week 3)Download
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23Existence of splitting fields, bound on degreeDownload
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24Uniqueness of splitting fieldsDownload
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25Solved problems , part 2 (Week 3)Download
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26Normal ExtensionsDownload
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27Separable polynomialsDownload
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28Perfect fields, separable extensionsDownload
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29Definition and examples, fixed fieldsDownload
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30Characterization of Galois extensionsDownload
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31Linear Independence of CharactersDownload
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32Solved problems (Week 4)Download
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33Artin’s Theorem – part 1Download
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34Artin’s Theorem – part 2Download
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35Finite Galois ExtensionsDownload
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36The fundamental theorem of Galois Theory - 1Download
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37The fundamental theorem of Galois Theory – 2Download
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38Solved problems (Week 5)Download
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39Cyclotomic extensionsDownload
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40Irreducibility of the cyclotomic polynomialDownload
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41Application: Constructibility of regular n-gons.Download
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42Insolvability of the general quintic – part 1Download
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43Insolvability of the general quintic – part 2Download
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44Insolvability of the general quintic – part 3Download
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45What is category theory (and why is it important)?PDF unavailable
46Definition of a categoryPDF unavailable
47Monomorphisms, epimorphisms, and isomorphismsPDF unavailable
48Categories: First Problem SessionPDF unavailable
49Initial and Terminal ObjectsPDF unavailable
50Products and CoproductsPDF unavailable
51Categories: Second Problem SessionPDF unavailable
52FunctorsPDF unavailable
53The Category of CategoriesPDF unavailable
54Natural TransformationsPDF unavailable
55Functor CategoriesPDF unavailable
56Categories: Third Problem SessionPDF unavailable
57Adjunction PDF unavailable
58Categories: Fourth Problem SessionPDF unavailable
59Tensor products of Z-modulesPDF unavailable
60Free abelian groups and quotient groupsPDF unavailable
61Construction of the tensor productPDF unavailable
62Problem session PDF unavailable
63Tensor product of R-modulesPDF unavailable
64Functoriality of the tensor productPDF unavailable
65BimodulesPDF unavailable
66Tensor products of bimodulesPDF unavailable
67Tensor products of modules over commutative ringsPDF unavailable
68Extension of scalarsPDF unavailable
69Problem session – tensor products of vector spacesPDF unavailable
70Some Properties of the tensor productPDF unavailable
71F-algebrasPDF unavailable
72Composition SeriesPDF unavailable
73Schreier’s TheoremPDF unavailable
74Ascending and Descending Chain ConditionsPDF unavailable
75Existence of Jordan-Holder SeriesPDF unavailable
76The Jordan-Holder TheoremPDF unavailable
77Examples related to the Jordan-Holder TheoremPDF unavailable
78The Jordan-Holder Theorem for GroupsPDF unavailable
79Indecomposable ModulesPDF unavailable
80Direct Sum DecompositionsPDF unavailable
81Decomposition as a sum of IndecomposablesPDF unavailable
82The Endomorphism Ring of an Indecomposable ModulePDF unavailable
83Krull-Schmidt TheoremPDF unavailable
84Krull-Schmidt ExamplesPDF unavailable


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1EnglishNot Available
2BengaliNot Available
3GujaratiNot Available
4HindiNot Available
5KannadaNot Available
6MalayalamNot Available
7MarathiNot Available
8TamilNot Available
9TeluguNot Available