| Sl.No | Chapter Name | MP4 Download |
|---|---|---|
| 1 | Lecture 1 : Historical Perspectives | Download |
| 2 | Lecture 2 : Examples of Fields | Download |
| 3 | Lecture 3 : Polynomials and Basic properties | Download |
| 4 | Lecture 4 : Polynomial Rings | Download |
| 5 | Lecture 5 : Unit and Unit Groups | Download |
| 6 | Lecture 6 : Division with remainder and prime factorization | Download |
| 7 | Lecture 7 : Zeroes of Polynomials | Download |
| 8 | Lecture 8 : Polynomial functions | Download |
| 9 | Lecture 9 : Algebraically closed Fields and statement of FTA | Download |
| 10 | Lecture 10 : Gauss’s Theorem(Uniqueness of factorization) | Download |
| 11 | Lecture 11 : Digression on Rings homomorphism, Algebras | Download |
| 12 | Lecture 12 : Kernel of homomorphisms and ideals in K[X],Z | Download |
| 13 | Lecture 13 : Algebraic elements | Download |
| 14 | Lecture 14 : Examples | Download |
| 15 | Lecture 15 : Minimal Polynomials | Download |
| 16 | Lecture 16 : Characterization of Algebraic elements | Download |
| 17 | Lecture 17 : Theorem of Kronecker | Download |
| 18 | Lecture 18 : Examples | Download |
| 19 | Lecture 19 : Digression on Groups | Download |
| 20 | Lecture 20 : Some examples and Characteristic of a Ring | Download |
| 21 | Lecture 21 : Finite subGroups of the Unit Group of a Field | Download |
| 22 | Lecture 22 : Construction of Finite Fields | Download |
| 23 | Lecture 23 : Digression on Group action-I | Download |
| 24 | Lecture 24 : Automorphism Groups of a Field Extension | Download |
| 25 | Lecture 25 : Dedekind-Artin Theorem | Download |
| 26 | Lecture 26 : Galois Extension | Download |
| 27 | Lecture 27 : Examples of Galois extension | Download |
| 28 | Lecture 28 : Examples of Automorphism Groups | Download |
| 29 | Lecture 29 : Digression on Linear Algebra | Download |
| 30 | Lecture 30 : Minimal and Characteristic Polynomials, Norms, Trace of elements | Download |
| 31 | Lecture 31 : Primitive Element Theorem for Galois Extension | Download |
| 32 | Lecture 32 : Fundamental Theorem of Galois Theory | Download |
| 33 | Lecture 33 : Fundamental Theorem of Galois Theory(Contd) | Download |
| 34 | Lecture 34 : Cyclotomic extensions | Download |
| 35 | Lecture 35 : Cyclotomic Polynomials | Download |
| 36 | Lecture 36 : Irreducibility of Cyclotomic Polynomials over Q | Download |
| 37 | Lecture 37 : Reducibility of Cyclotomic Polynomials over Finite Fields | Download |
| 38 | Lecture 38 : Galois Group of Cyclotomic Polynomials | Download |
| 39 | Lecture 39 : Extension over a fixed Field of a finite subGroup is Galois Extension | Download |
| 40 | Lecture 40 : Digression on Group action II | Download |
| 41 | Lecture 41 : Correspondence of Normal SubGroups and Galois sub-extensions | Download |
| 42 | Lecture 42 : Correspondence of Normal SubGroups and Galois sub-extensions(Contd) | Download |
| 43 | Lecture 43 : Inverse Galois problem for Abelian Groups | Download |
| 44 | Lecture 44 : Elementary Symmetric Polynomials | Download |
| 45 | Lecture 45 : Fundamental Theorem on Symmetric Polynomials | Download |
| 46 | Lecture 46 : Gal (K[X1,X2,…,Xn]/K[S1,S2,...,Sn]) | Download |
| 47 | Lecture 47 : Digression on Symmetric and Alternating Group | Download |
| 48 | Lecture 48 : Discriminant of a Polynomial | Download |
| 49 | Lecture 49 : Zeroes and Embeddings | Download |
| 50 | Lecture 50 : Normal Extensions | Download |
| 51 | Lecture 51 : Existence of Algebraic Closure | Download |
| 52 | Lecture 52 : Uniqueness of Algebraic Closure | Download |
| 53 | Lecture 53 : Proof of The Fundamental Theorem of Algebra | Download |
| 54 | Lecture 54 : Galois Group of a Polynomial | Download |
| 55 | Lecture 55 : Perfect Fields | Download |
| 56 | Lecture 56 : Embeddings | Download |
| 57 | Lecture 57 : Characterization of finite Separable extension | Download |
| 58 | Lecture 58 : Primitive Element Theorem | Download |
| 59 | Lecture 59 : Equivalence of Galois extensions and Normal-Separable extensions | Download |
| 60 | Lecture 60 : Operation of Galois Group of Polynomial on the set of zeroes. | Download |
| 61 | Lecture 61 : Discriminants | Download |
| 62 | Lecture 62 : Examples for further study | Download |
| Sl.No | Chapter Name | English |
|---|---|---|
| 1 | Lecture 1 : Historical Perspectives | Download Verified |
| 2 | Lecture 2 : Examples of Fields | Download Verified |
| 3 | Lecture 3 : Polynomials and Basic properties | Download Verified |
| 4 | Lecture 4 : Polynomial Rings | Download Verified |
| 5 | Lecture 5 : Unit and Unit Groups | Download Verified |
| 6 | Lecture 6 : Division with remainder and prime factorization | Download Verified |
| 7 | Lecture 7 : Zeroes of Polynomials | Download Verified |
| 8 | Lecture 8 : Polynomial functions | Download Verified |
| 9 | Lecture 9 : Algebraically closed Fields and statement of FTA | Download Verified |
| 10 | Lecture 10 : Gauss’s Theorem(Uniqueness of factorization) | Download Verified |
| 11 | Lecture 11 : Digression on Rings homomorphism, Algebras | Download Verified |
| 12 | Lecture 12 : Kernel of homomorphisms and ideals in K[X],Z | Download Verified |
| 13 | Lecture 13 : Algebraic elements | Download Verified |
| 14 | Lecture 14 : Examples | Download Verified |
| 15 | Lecture 15 : Minimal Polynomials | Download Verified |
| 16 | Lecture 16 : Characterization of Algebraic elements | Download Verified |
| 17 | Lecture 17 : Theorem of Kronecker | Download Verified |
| 18 | Lecture 18 : Examples | Download Verified |
| 19 | Lecture 19 : Digression on Groups | Download Verified |
| 20 | Lecture 20 : Some examples and Characteristic of a Ring | Download Verified |
| 21 | Lecture 21 : Finite subGroups of the Unit Group of a Field | Download Verified |
| 22 | Lecture 22 : Construction of Finite Fields | Download Verified |
| 23 | Lecture 23 : Digression on Group action-I | Download Verified |
| 24 | Lecture 24 : Automorphism Groups of a Field Extension | Download Verified |
| 25 | Lecture 25 : Dedekind-Artin Theorem | Download Verified |
| 26 | Lecture 26 : Galois Extension | Download Verified |
| 27 | Lecture 27 : Examples of Galois extension | Download Verified |
| 28 | Lecture 28 : Examples of Automorphism Groups | Download Verified |
| 29 | Lecture 29 : Digression on Linear Algebra | Download Verified |
| 30 | Lecture 30 : Minimal and Characteristic Polynomials, Norms, Trace of elements | Download Verified |
| 31 | Lecture 31 : Primitive Element Theorem for Galois Extension | Download Verified |
| 32 | Lecture 32 : Fundamental Theorem of Galois Theory | Download Verified |
| 33 | Lecture 33 : Fundamental Theorem of Galois Theory(Contd) | Download Verified |
| 34 | Lecture 34 : Cyclotomic extensions | Download Verified |
| 35 | Lecture 35 : Cyclotomic Polynomials | Download Verified |
| 36 | Lecture 36 : Irreducibility of Cyclotomic Polynomials over Q | Download Verified |
| 37 | Lecture 37 : Reducibility of Cyclotomic Polynomials over Finite Fields | Download Verified |
| 38 | Lecture 38 : Galois Group of Cyclotomic Polynomials | Download Verified |
| 39 | Lecture 39 : Extension over a fixed Field of a finite subGroup is Galois Extension | Download Verified |
| 40 | Lecture 40 : Digression on Group action II | Download Verified |
| 41 | Lecture 41 : Correspondence of Normal SubGroups and Galois sub-extensions | Download Verified |
| 42 | Lecture 42 : Correspondence of Normal SubGroups and Galois sub-extensions(Contd) | Download Verified |
| 43 | Lecture 43 : Inverse Galois problem for Abelian Groups | Download Verified |
| 44 | Lecture 44 : Elementary Symmetric Polynomials | Download Verified |
| 45 | Lecture 45 : Fundamental Theorem on Symmetric Polynomials | Download Verified |
| 46 | Lecture 46 : Gal (K[X1,X2,…,Xn]/K[S1,S2,...,Sn]) | Download Verified |
| 47 | Lecture 47 : Digression on Symmetric and Alternating Group | Download Verified |
| 48 | Lecture 48 : Discriminant of a Polynomial | Download Verified |
| 49 | Lecture 49 : Zeroes and Embeddings | Download Verified |
| 50 | Lecture 50 : Normal Extensions | Download Verified |
| 51 | Lecture 51 : Existence of Algebraic Closure | Download Verified |
| 52 | Lecture 52 : Uniqueness of Algebraic Closure | Download Verified |
| 53 | Lecture 53 : Proof of The Fundamental Theorem of Algebra | Download Verified |
| 54 | Lecture 54 : Galois Group of a Polynomial | Download Verified |
| 55 | Lecture 55 : Perfect Fields | Download Verified |
| 56 | Lecture 56 : Embeddings | Download Verified |
| 57 | Lecture 57 : Characterization of finite Separable extension | Download Verified |
| 58 | Lecture 58 : Primitive Element Theorem | Download Verified |
| 59 | Lecture 59 : Equivalence of Galois extensions and Normal-Separable extensions | Download Verified |
| 60 | Lecture 60 : Operation of Galois Group of Polynomial on the set of zeroes. | Download Verified |
| 61 | Lecture 61 : Discriminants | Download Verified |
| 62 | Lecture 62 : Examples for further study | Download Verified |
| Sl.No | Language | Book link |
|---|---|---|
| 1 | English | Download |
| 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 |