Council of Scientific and
Human Resource Development Group
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.