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  #1  
Old January 17th, 2014, 10:32 AM
Rahul Parik
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Posts: 14,224
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Will you please provide me the Study material for preparation of CSIR NET exam in Statistics???

Council of Scientific and Industrial Research conducts Joint CSIR-UGC NET exams at various centers in India every year. Joint CSIR-UGC NET exam is conducted for Junior Research Fellowship and Eligibility for lectureship in core sciences subjects.

Here I am providing CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer-ship 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, 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

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: Permutations, combinations, pigeon-hole principle, inclusion-exclusion 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



CSIR-UGC - Mathematics Sciences Paperback – 2014
by Dr. V.N. Jha (Author)



Trueman's UGC CSIR-NET 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
Attached Files
File Type: pdf CSIR NET Exam Mathematical Sciences Syllabus.pdf (75.8 KB, 22 views)

Last edited by Aakashd; July 1st, 2019 at 01:57 PM.
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  #2  
Old January 17th, 2014, 11:29 AM
Aakashd
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Join Date: Jun 2013
Posts: 42,978
Default 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 n-step 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 chi-square 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.
Gauss-Markov 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 Latin-square 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. Steady-state 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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  #3  
Old September 17th, 2015, 01:55 PM
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Default Re: Study material for CSIR NET Exam Statistics Preparation

Hello friend , I want to qualify CSIR National Eligibility Test , for it will you please provide me Mathematical Sciences Syllabus ?? Can you please tell me suggestion for books ??
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