CSIR MATHEMATICAL SCIENCES

CSIR

NET (National Eligibility Test) is a national level test, held for five major science subjects (Chemical Sciences, Earth Sciences, Life Sciences, Mathematical Sciences, Physical Sciences). It is called CSIR-UGC NET as the exam is held in association with UGC (University Grant Commission).UGC on its own also conducts another exam called UGC NET, which is held for 93 other applied science/humanities subjects. CSIR-UGC NET is conducted twice a year (in mid June and mid December). On qualifying CSIR-NET, you become eligible to apply for the post of lecturer in all Indian universities/Institutes/Colleges as well as to receive junior Research Fellowship (UGC/CSIR) under various schemes, subjects to you finding placement in the universities/IITs/other national organizations.

CSIR Eligibility Criteria

Educational Qualification

M.Sc. or Equivalent degree under the subjects mentioned, with minimum 55% marks for General & OBC candidates; 50% for SC/ST candidates, Physically and Visually Handicapped candidates and Ph.D. degree holders who had passed Master's degree prior to 19th September 1991.
A candidate can also apply for the Test under RA (Result Awaited) category, if he/she is appearing or has appeared in his/her final year (Last Semester where Semester system is there) of M.Sc. OR equivalent Degree Examination in the subjects. Such candidates will have to submit the attestation format (given at the reverse of the application form) duly certified by the Head of the Deptt./Institute over his/her signature and rubber stamp (with address and name) from where the candidate is appearing or has appeared in the final year(Last Semester where Semester system is there) M.Sc. or equivalent degree examination. However, such candidates shall be admitted to the Test provisionally. They shall only be considered eligible for JRF-(NET)/LS-(NET), if they are able to produce the proof of having passed the Master’s Degree examination in the relevant or related subject with the requisite percentage of marks and within the stipulated time frame.

Age limit and relaxation

For JRF (NET): Minimum 19 Years and maximum 28 years (upper age limit may be relaxed up to 5 years as in case of candidates belonging to SC/ST/OBC(Non Creamy Layer), Physically handicapped/Visually handicapped and female applicants). For LS (NET): Minimum 19 years. No upper age limit.

General Guidelines for CSIR Admission


The Selection for award of JRF shall be made on the basis of a competitive written test called the National Eligibility Test (NET), conducted by CSIR at national level twice a year in the following areas (1) Chemical Sciences (2) Earth, Atmosphere, Ocean and Planetary Sciences (3) Life Sciences, (4) Mathematical Sciences and (5) Physical Sciences. From June 2011, CSIR has introduced a Single Paper MCQ (Multiple Choice Question) based test comprising of three parts. Part-A shall be common to all subjects comprising question on General Science and Research Aptitude. Part-B shall contain subject-related conventional MCQ and Part-C shall contain higher value questions that may test the candidate’s knowledge of scientific concepts and/or application of the scientific concepts. Negative marking for wrong answers shall be done. The candidates who qualify the test are informed individually. The Fellowship is awarded on receipt of necessary details of the qualifying degree examination, proposed place of research work, research topic, the name of supervisor and the concurrence of the Institution to provide all the necessary facilities. The validity of the offer of this award will be one year, which will not be extendable.

Application Fees


By Cash

Candidates applying for the Test may obtain the Information Bulletin and Application forms (inclusive of fee payable) through the branches of the Bank notified in UGC CSIR NET 2012 Information Bulletin (within the prescribed dates) by paying the following fee in cash General 400/- Other Backward Classes (OBC) (Non Creamy Layer) 200/- SC / ST / Physically Handicapped (PH) or Visually Handicapped (VH) 100/-

By Post


CSIR UGC NET Information Bulletin and Application form may also be obtained through Value Payable Post (V.P.P) by sending a crossed Demand draft for 400/-, 200/- or 100/- (as the case may be) drawn in favor of “Indian Bank, West Patel Nagar, New Delhi†payable at New Delhi from the following address :
Indian Bank,
3 / 1, West Patel Nagar,
New Delhi – 110008.

For this purpose, the candidate should send a request to the Bank with Two self – addressed slips clearly mentioning the address at which he / she desires CSIR UGC NET Information Bulletin & Application Form to be sent by Value Payable Post (V.P.P.) to Indian Bank, West Patel Nagar, New Delhi will entertain the request for forms through post. Candidates are advised to send well in advance so as to reach their request within the period.

The candidate should write his / her name, Date of Birth, address, date of Examination and subject code on the back of the Demand Draft. However, before attaching the draft with letter of request, the candidates should check that it bears the code number of the issuing bank and drawee bank and also amount and signatures of issuing authority.

Apply through Online CSIR UGC NET Application

Interested & eligible candidates may apply for CSIR UGC NET Test Online through a link available at CSIR, HRDG website : www.csirhrdg.res.in. In order to apply Online the candidates are required to download Bank challan Performa from www.csirhrdg.res. in and then deposit the requisite examination fee in any of the Indian Bank branches throughout the country.
The examination fee for the Online application is same as mentioned. Candidates after successfully submitting application online are required to take print out of the Application Form, paste his / her recent black & white photograph, put his / her signature at the required space, attach requisite certificates and send alongwith CSIR marked copy of fee deposited Bank Challan in an envelope to the following address so as to reach on or before the prescrided date. Sr. Controller of Examinations, Human Resource Development Group, Examination Unit, CSIR Complex, Library Avenue, Pusa, New Delhi 110012.
Online applications without hard copy or bank challan receipt or incomplete in an respect will be summarily rejected. Before applying Online, candidates are advised to go through detailed notification available at CSIR, HRDG website www.csirhrdg.res.in.
Examination fee paid along with CSIR UGC NET 2012 Information Bulletin or through Bank Challan for a particular examination will neither be adjusted for any subsequent examination nor refunded under any circumstances. Candidates should also check all the columns of Bank Challan, online application, which are to be filled in properly to avoid cancellation of application, Please note that Fee submitted by any other mode like money order, demand draft, IPO etc. will be summarily rejected.
Note : In order to avoid last minutes rush, the candidates are advised to apply early enough. CSIR will not be responsible for network problem or any other such type of problem.

Examination Center

The test will be held at 26 centres spread all over India, as specified below:
Bangalore, Bhavnagar, Bhopal, Bhubaneshwar, Chandigarh, Chennai, Cochin, Delhi, Guntur, Guwahati, Hyderabad, Imphal, Jammu, Jamshedpur, Karaikudi, Kolkata, Lucknow, Nagpur, Pilani, Pune, Raipur Roorkee, Srinagar, Thiruvananthapuram, Udaipur and Varanasi.
Syllabus The Joint CSIR-UGC JRF/LS (NET) Examination shall comprise 2 papers:
PART A This paper shall be of 2 hours and 30 minutes duration and shall have a maximum of 200 marks. Part of Paper I shall contain 40 General Science questions. These questions shall be common to all subject areas of NET Examination. A candidate shall be required to answer a maximum of 25 questions from Part. In case, a candidate answers more than 25 questions, only the first 25 answered questions will be taken up for evaluation. Part of Paper I shall have 75 questions. A candidate shall be required to answer a maximum of 50 questions. If more than 50 questions are answered from part only first 50 answered questions will be taken up for evaluation. All questions in Part carry two marks each. Questions in Part shall be of 3 marks each. There will be negative marking for wrong answers.
PART B & C (Common Syllabus) This paper shall be of 2 hours and 30 minutes duration and shall have a maximum of 200 marks This Paper shall consist of 39-46 short answer type questions requiring descriptive answers. A candidate is required to answer a maximum of 10 questions either in Hindi or in English. If more than 10 questions are answered, only first 10 will be evaluated. To answer a question, a candidate will be provided one page. Each questions shall be of analytical nature where a candidate is expected to apply the scientific knowledge to arrive at the solution to the given scientific problem.

Mathematics

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, lineardependence, basis, dimension, algebra of linear transformations.Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem.Matrix representationof 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 theorem, Cauchy integral formula, Liouville 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.Fundamental theorem of arithmetic, divisibility in Z,congruences, Chinese Remainder Theorem, Euler function, primitive roots. Groups, subgroups, normal subgroups, quotient groups, homeomorphisms, cyclic groups, permutation groups, Cayley theorem, classequations, Sylow theorems.Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain.Polynomial rings and irreducibility criteria.Fields, finite fields, field extensions, Galois Theory.

Topology


Basis, Dense Sets, Subspace and Product Topology, Seperation Axiomx, Connectedness & Compectness.

UNIT 3
Ordinary Differential Equations (ODEs)


Existence and Uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ODEs, system of first order ODEs.General theory of homogenous and non-homogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, Green function.

Partial Differential Equations (PDEs)


Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. Classification of second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations.

Numerical Analysis

Numerical solutions of algebraic equations, Method of iteration and Newton-Raphson method, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline interpolation, Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods.

Calculus of Variations

Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations.

Linear Integral Equations

Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel.

Classical Mechanics

Generalized coordinates, Lagrange equations, Hamilton canonical equations, Hamilton principle and principle of least action, Two-dimensional motion of rigid bodies, Euler dynamical equations for the motion of a rigid body about an axis, theory of small oscillations.

UNIT 4

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 designes , randomized blocks and Latin-square designs. Connectedness, 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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