Which are the important topics for CSIR NET Mathematical Science.

Hello, I am sharing the important topics of first three units of CSIR NET Mathematical Science Syllabus Unit 1. Real Analysis: Functions of several variables, Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, mean value theorem, metric spaces, compactness, connectedness Linear Algebra: Linear transformations, matrix representations of linear transformations, the rank and nullity theorem, the minimal polynomial, the Jordan canonical form; Inner product spaces, orthonormal bases and spectral theorem Unit 2. Complex analysis: see the previous years question papers and prepare accordingly. Algebra: homomorphisms, cyclic groups, permutation groups, Cayleys theorem, class equations, Slow theorems, Irreducibility criteria. Unit 3 ODE, PDE Numerical Analysis.

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