Transcription of PROPOSED SYLLABUS FOR ‘Mathematical Science'
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PROPOSED SYLLABUS FOR ‘Mathematical Science'
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, countabl e and uncountabl e sets, Real number s ystem as a complete ordere d field, Arc himede an propert y, s upremum, inf imum. Sequenc es and series, converg ence, limsup, liminf. Bolzano Weiers trass theor em, Heine Borel theorem. Continu ity, uniform continuity, differe ntiabi lity, mean value the or em. Sequenc es and series of func tions, uniform converg ence. Riemann sums and Riemann integra l, I mproper I ntegra ls. Monotonic functions, types of discontinuity, f unctions of bounded variation, Lebe sgue measure, Lebesgue integra l.
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.
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