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B.Sc. MATHEMATICS, SEMESTER - VI, CORE XII - MODERN ALGEBRA - II, UNITI: Vector Spaces and Modules, , Elementary Basic concepts and Linear Independence & Bases - definition - lemmas -theorems examples.- Dual spaces- Inner Product Spaces - definition - lemmas -theorems - examples.- Modules, (Sections 4.1 to 4.5), , , , UNIT I: Fields, , Extension fields - The Trancedence of e — roots of polynomials — constructions with straightedge and, compass — more about roots — the elements of Galois theory. (Sections 5.1 to 5.6), , UNIT HI: Linear Transformations., , The Algebra of linear transformations, Characteristic roots and Matrices - definition - lemmas-theorems, - examples. (Sections 6.1 to 6.3), , UNIT IV: Linear Transformations, , Canonical forms: Triangular form and Nilpotent Transformations - definition - lemmas —theorems, examples. (Sections 6.4 & 6.5), , UNIT V: Linear Transformations(continuation), , Trace and Transpose and Determinants - Definitions - Properties - Theorems - Cramer's Rule -Problems., (Sections6.8 & 6.9), , TEXT BOOK, , 1. LN. Herstein, Topics in Algebra-2nd Edition, John Wiely, New York, 1975., REFERENCE BOOKS, , 1. Dr. US Rana, Mathematics for Degree Students (B.Sc 3" Years), S.Chand, 2012., , 2. A.R.Vasistha, A first course in modern algebra, Krishna Prekasan Mandhir, 9, Shivaji Road, Meerut, (UP), 1983., , 3. K.Viswanatha Naik, Modern Algebra, Emerald Publishers, 135, Anna Salai, Chennai -2, 2001., , , , 4. K.Viswanatha Naik, Modern Algebra, Emerald Publishers, 135, Anna Salai, Chennai -2, 1988.