Maths Lesson -1

Title         : TRB Study Material

Exam       : TRB Exam

Category  : Maths Lesson - 1 (Algebra - Study Material)

Language : English

Content    : Groups – Examples – Cyclic Groups- Permulation Groups – Lagrange’s theorem- Cosets – Normal groups - Homomorphism – Theorems – Cayley’s theorem - Cauchy’s Theorem - Sylow’s theorem - Finitely Generated Abelian Groups – Rings- Euclidian Rings- Polynomial Rings- U.F.D. - Quotient - Fields of integral domains- Ideals- Maximal ideals - Vector Spaces - Linear independence and Bases - Dual spaces - Inner product spaces - Linear transformation – rank - Characteristic roots of matrices - Cayley Hamilton Theorem - Canonical form under equivalence – Fields - Characteristics of a field - Algebraic extensions - Roots of Polynomials - Splitting fields - Simple extensions Elements of Galois theory- Finite fields.

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