Media Storage Type : DVD-ROM
NPTEL Course Name : Algebra II
NPTEL Subject Matter Expert : Prof. Jugal K. Verma
NPTEL Co-ordinating Institute : IIT Bombay
NPTEL Lecture Count : 45
Lecture Titles:
Lecture 1 - Introduction and Overview
Lecture 2 - Algebraic extensions - I
Lecture 3 - Algebraic Extensions - II
Problem Set 1 - Algebraic Extensions
Lecture 4 - Ruler and Compass Constructions - I
Lecture 5 - Ruler and Compass Constructions - II
Problem Set 2 - Ruler and Compass Constructions
Tutorial 1 - Algebraic Extensions and Ruler and Compass Constructions
Lecture 6 - Symmetric Polynomials - I
Lecture 7 - Symmetric Polynomials - II
Problem set 3 - Symmetric Polynomials
Lecture 8 - Algebraic Closure of a Field
Problem set 4 - Splitting Fields
Tutorial 2 - Symmetric Polynomials and Splitting Fields
Lecture 9 - Separable Extensions - I
Lecture 10 - Separable Extensions - II
Problem set 5 - Separable Extensions
Lecture 11 - Finite Fields I
Tutorial 3 - Separable Extensions and Finite Fields
Problem set 6 - Finite Fields
Lecture 12 - The Primitive Element Theorem
Problem set 7 - Primitive elements
Tutorial 4 - Finite Fields and Primitive Elements
Lecture 13 - Normal Extensions
Lecture 14 - Galois group of a Galois Extension - I
Lecture 15 - Galois group of a Galois Extension - II
Problem set 8 - Fundamental Theorem of Galois Theory
Tutorial 5 - Fundamental Theorem of Galois Theory
Lecture 16 - Applications and Illustrations of the FTGT
Lecture 17 - Cyclotomic Extensions - I
Lecture 18 - Cyclotomic Extensions - II
Problem Set 9 - Cyclotomic Extensions
Lecture 19 - Abelian and Cyclic Extensions
Lecture 20 - Cyclic Extensions and Solvable Groups
Tutorial 6 - Cyclotomic Extensions
Lecture 21 - Galois Groups of Composite Extensions
Lecture 22 - Solvability by Radicals
Problem Set 10 - Solvability by Radicals
Lecture 23 - Solutions of Cubic and Quartic Equations
Lecture 24 - Galois Groups of Quartic Polynomials
Problem Set 11 - Galois groups of Quartic Polynomials.
Tutorial 7 - Galois Groups of Quartics and Solvability by Radicals
Lecture 25 - Norm, Trace and Hilbert's Theorem 90
Problem Set 12 - Cyclic Extensions
Lecture 26 - Polynomials with Galois Group Sn: