Galois Theory 9R34HCJY7C

URI	`m2://res/9R34HCJY7C`
Kind	course
Creators	Dilip Patil (instructor)
Date	2018-12-13
Scope	in
Ids	course 02qyf5152:111101117

Expressions

e1: edition

Language	en
Date	2018-12-13

m1: page, IIT Bombay (record). nptel 111101117
m2: page, 2018-12-13 (record). nptel 111101117

Contents

part 1: Week 1
session 1: Lecture 1 : Historical Perspectives
session 2: Lecture 2 : Examples of Fields
session 3: Lecture 3 : Polynomials and Basic properties
session 4: Lecture 4 : Polynomial Rings
session 5: Lecture 5 : Unit and Unit Groups
part 2: Week 2
session 6: Lecture 6 : Division with remainder and prime factorization
session 7: Lecture 7 : Zeroes of Polynomials
session 8: Lecture 8 : Polynomial functions
session 9: Lecture 9 : Algebraically closed Fields and statement of FTA
session 10: Lecture 10 : Gauss’s Theorem(Uniqueness of factorization)
part 3: Week 3
session 11: Lecture 11 : Digression on Rings homomorphism, Algebras
session 12: Lecture 12 : Kernel of homomorphisms and ideals in K[X],Z
session 13: Lecture 13 : Algebraic elements
session 14: Lecture 14 : Examples
session 15: Lecture 15 : Minimal Polynomials
part 4: Week 4
session 16: Lecture 16 : Characterization of Algebraic elements
session 17: Lecture 17 : Theorem of Kronecker
session 18: Lecture 18 : Examples
session 19: Lecture 19 : Digression on Groups
session 20: Lecture 20 : Some examples and Characteristic of a Ring
part 5: Week 5
session 21: Lecture 21 : Finite subGroups of the Unit Group of a Field
session 22: Lecture 22 : Construction of Finite Fields
session 23: Lecture 23 : Digression on Group action-I
session 24: Lecture 24 : Automorphism Groups of a Field Extension
session 25: Lecture 25 : Dedekind-Artin Theorem
session 26: Lecture 26 : Galois Extension
part 6: Week 6
session 27: Lecture 27 : Examples of Galois extension
session 28: Lecture 28 : Examples of Automorphism Groups
session 29: Lecture 29 : Digression on Linear Algebra
session 30: Lecture 30 : Minimal and Characteristic Polynomials, Norms, Trace of elements
session 31: Lecture 31 : Primitive Element Theorem for Galois Extension
part 7: Week 7
session 32: Lecture 32 : Fundamental Theorem of Galois Theory
session 33: Lecture 33 : Fundamental Theorem of Galois Theory(Contd)
session 34: Lecture 34 : Cyclotomic extensions
session 35: Lecture 35 : Cyclotomic Polynomials
session 36: Lecture 36 : Irreducibility of Cyclotomic Polynomials over Q
session 37: Lecture 37 : Reducibility of Cyclotomic Polynomials over Finite Fields
part 8: Week 8
session 38: Lecture 38 : Galois Group of Cyclotomic Polynomials
session 39: Lecture 39 : Extension over a fixed Field of a finite subGroup is Galois Extension
session 40: Lecture 40 : Digression on Group action II
session 41: Lecture 41 : Correspondence of Normal SubGroups and Galois sub-extensions
session 42: Lecture 42 : Correspondence of Normal SubGroups and Galois sub-extensions(Contd)
part 9: Week 9
session 43: Lecture 43 : Inverse Galois problem for Abelian Groups
session 44: Lecture 44 : Elementary Symmetric Polynomials
session 45: Lecture 45 : Fundamental Theorem on Symmetric Polynomials
session 46: Lecture 46 : Gal (K[X1,X2,…,Xn]/K[S1,S2,...,Sn])
session 47: Lecture 47 : Digression on Symmetric and Alternating Group
part 10: Week 10
session 48: Lecture 48 : Discriminant of a Polynomial
session 49: Lecture 49 : Zeroes and Embeddings
session 50: Lecture 50 : Normal Extensions
session 51: Lecture 51 : Existence of Algebraic Closure
session 52: Lecture 52 : Uniqueness of Algebraic Closure
part 11: Week 11
session 53: Lecture 53 : Proof of The Fundamental Theorem of Algebra
session 54: Lecture 54 : Galois Group of a Polynomial
session 55: Lecture 55 : Perfect Fields
session 56: Lecture 56 : Embeddings
session 57: Lecture 57 : Characterization of finite Separable extension
part 12: Week 12
session 58: Lecture 58 : Primitive Element Theorem
session 59: Lecture 59 : Equivalence of Galois extensions and Normal-Separable extensions
session 60: Lecture 60 : Operation of Galois Group of Polynomial on the set of zeroes.
session 61: Lecture 61 : Discriminants
session 62: Lecture 62 : Examples for further study

Catalogue records

nptel: 111101117 (manifestation)
nptel_video: 111101117 (manifestation)