VINOBA BHAVE UNIVERSITY, HAZARIBAG UNIVERSITY DEPARTMENT OF MATHEMATICS LECTURE PLAN Name : Dr. P. K. Manjhi Designation : Asstt. Professor Semester/Paper : I/I FOUNDATION COURSE IN MODERN ALGEBRA(CBCS) Sl. Topic/Chapter No. of Classes in Remark Classes a Week No. Groups : Normal and Subnormal series, 1 12 6 Isomorphism theorems, Jordan-Holder theorem, Solvable groups, Nilpotent groups. Group action, orbit -stabilizer theorem, orbit 2 12 6 decomposition, Sylow’s theorems (proofs using group actions). Canonical Forms Similarity of linear – 3 12 6 transformations. Invariant subspaces. Eigen values and Eigen vectors, Reduction to diagonal and triangular forms. Nilpotent transformations index of nilpotency. Invariants of nilpotent transformation. The primary decomposition theorem. Field theory-Extension fields, finite extention, 4 12 6 Algebraic and transcendental extensions, splitting Separable and fields- existence and uniqueness, inseparable extension, Normal extensions. Finite fields. Primitive elements. Algebraically 5 12 6 closed fields. Automorphism of extensions. Galois extension. Fundamental theorem of Galois theory.
VINOBA BHAVE UNIVERSITY, HAZARIBAG UNIVERSITY DEPARTMENT OF MATHEMATICS LECTURE PLAN Name : Dr. P. K. Manjhi Designation : Asstt. Professor Semester/Paper : I/I FOUNDATION COURSE IN MODERN ALGEBRA(CBCS) Sl. No. Topic/Chapter No. of Classes Classes in a Week Remark 1 Groups : Normal and Subnormal series, Isomorphism theorems, Jordan-Holder theorem, Solvable groups, Nilpotent groups. 12 6 2 Group action, orbit -stabilizer theorem, orbit decomposition, Sylow’s theorems (proofs using group actions). 12 6 3 Canonical Forms – Similarity of linear transformations. Invariant subspaces. Eigen values and Eigen vectors, Reduction to diagonal and triangular forms. Nilpotent transformations index of nilpotency. Invariants of nilpotent transformation. The primary decomposition theorem. 12 6 4 Field theory-Extension fields, finite extention, Algebraic and transcendental extensions, splitting fields- existence and uniqueness, Separable and inseparable extension, Normal extensions. 12 6 5 Finite fields. Primitive elements. Algebraically closed fields. Automorphism of extensions. Galois extension. Fundamental theorem of Galois theory. 12 6