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.