CSIR UGC Net Syllabus of Mathematics - 2014-2015 StudyChaCha

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Old June 7th, 2013, 05:59 PM
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Default CSIR UGC Net Syllabus of Mathematics

Can you provide me syllabus of Mathematics CSIR-UGC National Ability Tests.
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Old June 8th, 2013, 05:06 PM
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Default Re: CSIR UGC Net Syllabus of Mathematics

Here I am providing you syllabus of Mathematics CSIR-UGC National Ability Tests.

Some content of the file has been given here:


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. 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.

The syllabus includes:

Unit 1- Analysis
Unit -2 - Algebra
Unit -3- Differential equations
Unit -4- Descriptive statistics

For further details I am providing you pdf file of the syllabus.

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Can you provide me syllabus of Mathematics CSIR-UGC National Ability Tests.
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