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September 20th, 2016, 12:18 PM
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Join Date: Mar 2012
Re: Syllabus For CSIR UGC NET Mathematics

Well below I have given you the syllabus for the CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer-ship so you can have a look

CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship
and Lecturer-ship



COMMON SYLLABUS FOR PART ‘B’ AND ‘C’ MATHEMATICAL SCIENCES UNIT – 1
Analysis: Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum.
Sequences and series, convergence, limsup, liminf.
Bolzano Weierstrass theorem, Heine Borel theorem.
Continuity, uniform continuity, differentiability, mean value theorem.
Sequences and series of functions, uniform convergence.
Riemann sums and Riemann integral, Improper Integrals.
Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral.
Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems.
Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.
Linear Algebra: Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations.
Algebra of matrices, rank and determinant of matrices, linear equations.
Eigenvalues and eigenvectors, Cayley-Hamilton theorem.
Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms.
Inner product spaces, orthonormal basis.
Quadratic forms, reduction and classification of quadratic forms


CSIR-UGC National Eligibility Test (NET) syllabus for Junior Research Fellowship and Lecturer-ship in Mathematics








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