CSIR NET MATHEMATICS || IIT JAM || GATE || NBHM PRACTICE QUESTION
PRACTICE QUESTION FOR CSIR NET MATHEMATICS
The tests are conducted twice in a year generally in the months of June and December. It is conducted both in English and the Vernacular Language. The Council of Scientific and Industrial Research - CSIR has assigned the responsibility of conducting CSIR-UGC NET in CBT mode to NTA for science subjects namely Life Sciences, Chemical Sciences, Physical Sciences Mathematical Sciences and Earth Sciences jointly with the UGC.
Syllabus of Mathematics
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, Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, Differentiability, Mean value theorem, Sequences, and series. Functions of several variables, Metric spaces, compactness, connectedness. Normed Linear Spaces.
Linear Algebra: Vector spaces, algebra of linear transformations. Algebra of matrices, 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.Quadratic forms, reduction, and classification of quadratic forms
Unit 2 Complex Analysis: Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric, and hyperbolic functions. Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.
Algebra:
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