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CSIR Syllabus

 Mathematical Sciences

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PAPER 1 – SECTION A

1. General information on science and its interface with society to test the candidate’s awareness of science, aptitude of scientific and quantitative reasonsing.

2. COMMON ELEMENTRY COMPUTER SCIENCE ( Applicable to all candidates offering subject areas ).

3. History of development of computers, Mainframe, Mini, Micro’s and Super Computer Systems.

4. General awareness of computer Hardware i..e. CPU and other peripheral devices       ( input / output and auxiliary storage devices ).

5. Basic knowledge of computer systems, software and programming languages i.e. Machine language, Assembly language and higher level language.

6. General awareness of popular commercial software packages like LOTUS, DBASE, WORDSTAR, other Scientific application packages.

PAPER I – SECTION B

General information  :  Units 1, 2, 3 and 4 are compulsory for all candidates.  Candidates with Mathematics background may omit units 10 – 14 and units 17, 18.  Candidates with Statistics background may omit units 6, 7, 9, 15 and 16. Adequate alternatives would be given for candidates with O. R. background

1. Basic concepts of Real and Complex analysis :  Sequences and series, continuity, uniform continuity, Differentiability, Mean Value Theorem, sequences and series of functions, uniform convergence, Riemann integral – definition and simple properties.  Algebra of Complex numbers, Analytic functions.  Cauchy’s Theorem and integral formula, Power series, Taylor’s and Laurent’s series, Residues, Contour integration.

2. Basic Concepts of Linear Algebra  :  Space of n – vectors, Linear dependence, Basis, Linear transformation, Algebra of matrices, Rank of a matrix, Determinants, Linear equations, Quadratic forms, Characteristic roots and vectors.

3. Basic concepts of probability  :  Sample space, discrete probability, simple theorems on probability, independence of events, Bayes Theorem.  Discrete and continuous random variables, Binomial, Paisson and Normal distributions ;  Expectation and moments, independence of random variables, Chebyshev’s inequality.

4. Linear Programming Basic Concepts  :  Convex sets.  Linear Programming Problem ( LPP ).  Examples of LPP, Hyperplane, open and closed half – spaces.  Feasible, basic feasible and optimal solutions.  Extreme point and graphical method.
5. Real Analysis  :  Finite, countable and uncountable sets, Bounded and unbounded sets.  Archimedean property, ordered field, completeness of R, Extended real number system, liens up and limits of a sequence, the epsilon – delta definition of continuity and convergence, the algebra of continuous functions, monotonic functions, types of discontinuities, infinite limits and limits at infinity, functions of bounded variation, elements of metric spaces.

• Mathematics Paper I Cont.
• Mathematics Paper I cont.
• Mathematics Part II
• Mathematics Paper II Cont.
• Mathematics Paper II cont.
• Mathematics con.