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Council of Scientific and Industrial Research conducts Joint CSIRUGC NET exams at various centers in India every year. Joint CSIRUGC NET exam is conducted for Junior Research Fellowship and Eligibility for lectureship in core sciences subjects. Here I am providing CSIRUGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturership Common syllabus for part ‘B’ and ‘C’ Mathematical Sciences CSIR NET Exam Mathematical Sciences Syllabus 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. Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, CayleyHamilton 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 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, CauchyRiemann 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: Permutations, combinations, pigeonhole principle, inclusionexclusion principle, derangements. Here I am sharing Suggestion for books for exam preparation : Ace The Race  CSIR UGC NET Life Sciences (JRF & LS) (360 Prep Tool) Paperback – 2014 by Nitin Sharma (Author), S.K. Singla (Editor), Raman Soni (Editor), & 4 More CSIRUGC  Mathematics Sciences Paperback – 2014 by Dr. V.N. Jha (Author) Trueman's UGC CSIRNET Mathematical Sciences Paperback – 2014 by A.M. Tripathi (Author), Sunil Kushwaha (Author) Here I am uploading a pdf file which having Complete Detailed CSIR NET Exam Mathematical Sciences Syllabus Last edited by Aakashd; July 1st, 2019 at 01:57 PM. 
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Re: Study material for CSIR NET Exam Statistics Preparation
As you are looking for the Study material for preparation for CSIR NET exam in Statistics, so here I am giving you its detail
CSIR NET exam in Mathematical Sciences cover this Statistics topic and here is its syllabus Descriptive Statistics, Exploratory Data Analysis— Sample space, discrete probability, independent events, Bayes theorem. Random variables and distribution functions (univariate and multivariate); expectation and moments. Independent random variables, marginal and conditional distributions. Characteristic functions. Probability inequalities (Tchebyshef, Markov, Jensen). Modes of convergence, weak and strong laws of large numbers, Central Limit theorems (i.i.d. case). Markov chains with finite and countable state space, classification of states, limiting behaviour of nstep transition probabilities, stationary distribution. Standard discrete and continuous univariate distributions. Sampling distributions. Standard errors and asymptotic distributions, distribution of order statistics and range. Methods of estimation. Properties of estimators. Confidence intervals. Tests of hypotheses: most powerful and uniformly most powerful tests, Likelihood ratio tests. Analysis of discrete data and chisquare test of goodness of fit. Large sample tests. Simple nonparametric tests for one and two sample problems, rank correlation and test for independence. Elementary Bayesian inference. GaussMarkov models, estimability of parameters, Best linear unbiased estimators, tests for linear hypotheses and confidence intervals. Analysis of variance and covariance. Fixed, random and mixed effects models. Simple and multiple linear regression. Elementary regression diagnostics. Logistic regression. Multivariate normal distribution, Wishart distribution and their properties. Distribution of quadratic forms. Inference for parameters, partial and multiple correlation coefficients and related tests. Data reduction techniques: Principle component analysis, Discriminant analysis, Cluster analysis, Canonical correlation. Simple random sampling, stratified sampling and systematic sampling. Probability proportional to size sampling. Ratio and regression methods. Completely randomized, randomized blocks and Latinsquare designs. Connected, complete and orthogonal block designs, BIBD. 2K factorial experiments: confounding and construction. Series and parallel systems, hazard function and failure rates, censoring and life testing. Linear programming problem. Simplex methods, duality. Elementary queuing and inventory models. Steadystate solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.
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