CSIR NET 2023 – Get to know the complete Structure

CSIR NET 2023 – Get to know the complete Structure

 

In this blog, we have provided you with complete details about CSIR NET 2023 including paper pattern, syllabus, marking scheme, cutoffs and many more.

 

What is the CSIR NET Exam 

CSIR NET stands for Council of Scientific & Industrial Research – National Eligibility Test. It is a national-level exam conducted by the National Testing Agency (NTA) for the candidates who want to choose Junior Research Fellowship (JRF) or Lectureship (LS) as their career.

NTA CSIR UGC NET  is conducted in 5 subjects: Life Sciences, Physical Sciences, Chemical Sciences, Earth Sciences, and Mathematical Sciences, twice a year.

Candidates who qualify for CSIR NET JRF are eligible to become lecturers in the Science & Technology subjects only.

Eligibility

To appear for the exam, candidates are required to prove their eligibility, such as educational qualification and age limit.

 

Educational Qualification	Mathematical Sciences – Must have M.Sc./BS-MS/BS-4 Years/B-Tech degree or any other equivalent qualification in the Mathematics field. For General and OBC Candidates – 55% Marks For ST/SC/PWD Candidates – 50% Marks
Age Limit and Relaxation	Maximum Age – candidates should not exceed the age of 28 years(General), 33 years(SC/ST/OBC/ PwD/Female Applicants) & 31 years (OBC (non-creamy layer))  for JRF posts. There is no age limit to appear for Assistant Professor. Age Relaxation – Up to 5 Years for SC/ST/OBC/ PwD/Female Applicants & 3 years in case of OBC (non-creamy layer)

 

Exam Pattern

 

Number of questions	120
Maximum Marks	200
Mode of exam	Computer based
Duration of the exam	3 hours
Sections	Part A – General Aptitude (Common for all subjects) Part B – Subject- Specific Questions Part C – Subject- Specific Questions
Types of questions	Multiple Choice Questions (MCQ)
Number of Subjects	5
Number of attempts	There is no limit on the number of attempts for the CSIR NET Exam for the Assistant Professor post. For the JRF posts, there is an age limit of 28 years in the CSIR NET Exam.

 

Marking Scheme for CSIR NET (for Mathematical Sciences)

 

Mathematical Sciences	Total Questions	Maximum number of questions  to attempt	Marks for each correct answer	Negative Marking
Part A	20	15	2	– 0.5
Part B	40	25	3	-0.75
Part C	60	20	4.75	0
Total	120	60	200	–

 

Syllabus for CSIR NET Exam

There are four units in the CSIR NET for Mathematics common syllabus (Part B &C). Each chapter has many subtopics. The complete syllabus of Mathematics paper is given below.

 

Unit – 1 

• Analysis

1. 1. Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. 
   2. Sequences and series, convergence, limsup, liminf. 
   3. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem. 
   4. Sequences and series of functions, uniform convergence. 
   5. Riemann sums and Riemann integral, Improper Integrals. 
   6. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. 
   7. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. 
   8. Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples. 

 

• Linear Algebra

1. 1. Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations. 
   2. Algebra of matrices, rank and determinant of matrices, linear equations. 
   3. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. 
   4. Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. 
   5. Inner product spaces, orthonormal basis. 
   6. Quadratic forms, reduction and classification of quadratic forms 

 

UNIT – 2 

• Complex Analysis

1. 1. Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric and hyperbolic functions. Analytic functions, Cauchy-Riemann equations. 
   2. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. 
   3. Taylor series, Laurent series, calculus of residues. 
   4. Conformal mappings, Mobius transformations. 

 

• Algebra 

1. 1. Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. 
   2. Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots. 
   3. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems. 
   4. Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain. 
   5. Polynomial rings and irreducibility criteria. 
   6. Fields, finite fields, field extensions, Galois Theory. 

 

• Topology

1. 1. Basis, dense sets, subspace and product topology, separation axioms, connectedness and compactness. 

 

UNIT – 3 

• Ordinary Differential Equations (ODEs)

1. 1. 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. 
   2. General theory of homogeneous and non-homogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, Green’s function. 

 

• Partial Differential Equations (PDEs)

1. 1. Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. 
   2. 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

1. 1. 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

1. 1. 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

1. 1. 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

1. 1. Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and principle of least action, Two-dimensional motion of rigid bodies, Euler’s 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 behavior of n-step transition probabilities, stationary distribution, Poisson and birth-and-death processes. 

 

• 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, confidence intervals, tests for linear hypotheses. 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 designs, randomized block designs and Latin-square designs. Connectedness and orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction.

 

• Hazard function and failure rates, censoring and life testing, series and parallel systems. 

 

• 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. 

 

All students are expected to answer questions from Unit I. Students in mathematics are expected to answer additional questions from Unit II and III. Students within statistics are expected to answer additional question from Unit IV.

 

Cutoffs (in %)

The CSIR NET cut-off is decided after considering the total number of applicants who appeared in the CSIR NET examination, maximum availability of seats, the difficulty level of the exam and performance of candidates.

 

Subject	General	EWS	OBC	SC	PwD	ST
Mathematical Sciences (JRF)	47 – 53	48 – 52	46 – 50	35 – 37	25 – 26	27 – 28
Mathematical Sciences (Lectureship)	48 – 51	43 – 46	41 – 44	31 – 33	23 – 25	25 – 26