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Please provide me syllabus for MSC mathematics entrance examination of Cochin University of Science and Technology ?
Here I am giving you syllabus for MSC mathematics entrance examination of Cochin University of Science and Technology below .. Algebra & Linear Algebra Group – Automorphism, inner automorphisms, automorphism groups, Congjugacy relation and centraliser, Normaliser, Counting principle and the class equation of a finite group, Cauchy’s theorem and Sylow’s theorems for finite abelian groups and non abelian groups. Ring theory – Ring homonorphism, Ideals and Quotient Rings, Field of Quotients of an Integral Domain. Euclidean Rings, polynomial Rings, Polynomials over the Rational Field, Polynomial Rings over Commutaive Rings, Unique factorization domain. Definition and examples of vector spaces. Subspaces. Sum and direct sum of subspaces. Linear span. Linear dependence, independence and their basic properties. Finite dimensional vector spaces. Existence theorem for bases. Invariance of the number of elements of a basis set. Dimension. Existence of complementary subspace of a subs pace of a finite dimensional vector space. Dimension of sums of subspaces. Quotient space and its dimension. Linear transformations and their representation as matrices. The algebra of linear transformations. The rank nullity theorem. Change of basis. Dual space. Bidual space and natural isomorphism. Adjoint of a linear transformation. Eigenvalues and eigenvector of a linear transformation. Diagonalisation. Bilinear, Quadratic and Hermitian forms. Inner Product Spaces, CauchySchwarz inequality Orthogonal vectors. Orthogonal Complements. Orthonormal sets and bases. Bessel’s inequality for finite dimensional spaces. Gram – Schmidt Orthogonalization process. Last edited by Anuj Bhola; October 18th, 2019 at 11:29 AM. 
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