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How can I apply for CSIR NET exam?

Visit the official website of the CSIR Exam or click here. Click on the link available for filling the online application form, then follow the steps and click on the New Registration button. Download the CSIR NET information brochure before proceeding for filling the application form.

Is CSIR NET 2021 exam conduct online or offline?

The CSIR NET Exam 2021 will be conducted in online mode only i.e. CBT mode.

How many subjects are there for CSIR NET exam?

CSIR NET exam consists of 5 subjects: Life Science, Chemical Science, Mathematical Science, Earth science, and Physical Science.

Can I pay offline for CSIR NET exam fee?

In order to complete the CSIR NET online application process, candidates will have to pay the CSIR NET application fee, in the online mode only by using Credit Card/Debit Card/Net Banking/ PAYTM. The CSIR NET application fee is non-refundable.

CSIR NET Mathematics Sciences Syllabus and Exam Pattern 2021: Check Here! : CSIR NET & SET

CSIR NET Mathematics Sciences Syllabus and Exam Pattern 2021: The Council of Scientific & Industrial Research-National Eligibility Test or CSIR NET is a national level examination that is conducted twice a year across India to select eligible research candidates for awarding Junior Research Fellowship (JRF) and to determine their eligibility for Assistant Professor in various prestigious Indian universities, colleges and institute.

Almost 2.5 lakhs candidates appear for the CSIR NET exam so there is a huge competition among candidates for the CSIR NET exam. Саndidаtes shоuld stаrt рreраring themselves in а systemаtiс mаnner with the helр оf the СSIR NET syllаbus 2021 tо quаlify in the first аttemрt fоr the exаm. Here in this article, aspirants can check the latest CSIR NET Mathematics Sciences Syllabus and Exam Pattern for the academic year 2021. Read on to find out.

This article is specially drafted for those aspiring students who are dreaming to make their career in the field of CSIR NET. This article contains detailed information about the CSIR NET Mathematical Science Syllabus & Exam Pattern and a brief note about the CSIR NET exam highlights, eligibility, important points, etc.

CSIR NET Exam 2021: Highlights

Events	Details
Exam Name	CSIR UGC NET
Conducting Body	National Testing Agency (NTA)
Exam Level	National
Exam Frequency	Twice a year (June and December)
Exam Mode	Online only
Exam Duration	3 hours (180 minutes)
Question Type	MCQ (Multiple Choice Questions)
Exam Purpose	Selection of candidates for the award of JRF and determining the eligibility for Lecturers
Medium	English and Hindi (Both)
Total Marks	200
Exam Helpdesk No.	011-25848155
Official Website	https://csirnet.nta.nic.in/

CSIR NET Mathematical Sciences 2021: Eligibility Criteria

Before getting into the details of the CSIR NET Syllabus, let us have a look at the eligibility criteria for CSIR NET Mathematical Science exam mentioned below:

Eligibility Criteria	Details
Educational Qualification	M.Sc. BS-MS BS-4 Years/B-Tech degree or any other equivalent qualification in the Mathematics field.
Age Limit	The upper age limit is given below: Junior Research Fellowship (JRF) - 28 (Upper Age Limit as on ) Lectureship/ Assistant Professorship - No Upper Age Limit
Age Relaxation	For OBC (Non-Creamy Layer) - 3 Years For SC/ ST/ PwD/ Female Candidate - 5 Years
Nationality	The candidate must be an Indian national.

CSIR NET Mathematical Sciences 2021: Exam Pattern

Candidates desiring to attempt for CSIR NET Mathematical Science 2021 to build their career in the Research or Lecturer profession should clearly be aware of the latest exam pattern and marking scheme. It is important to have extensive knowledge of each section and its marking scheme to get an idea of the questions asked in the exam. Exam pattern always plays a crucial role to crack all competitive exams. So, we have provided the updated exam pattern below for Mathematical Sciences

CSIR NET question paper for Mathematical Sciences consists of 120 Multiple Choice Questions (MCQs), which is a single paper test distributed into 3 parts: Part A, B & C.

Part A: This раrt invоlves questiоns frоm generаl арtitude, generаl sсienсe skills, аnd quаntitаtive reаsоning & аnаlysis, whiсh is the sаme fоr аll the subjeсts.
Раrt B: This раrt invоlves questiоns frоm mаin subjeсt frоm the tорiсs рrоvided in the СSIR NET mаthemаtiсаl sсienсe syllаbus.
Part C: This part contains questions from the analytics based on the application of the theoretical concepts of mathematical science.

Please refer to the table below to know the total number of questions in each section.

Paper Sections	Total Questions Provided	Marks for Each Section	Marks Per Question	Negative Marking for Each Section	Total time
Part A	20	30	2	0.5	3 hours
Part B	40	75	3	0.75
Part C	60	95	4.75	0
Total Marks			200

CSIR NET Mathematical Sciences 2021: Syllabus

CSIR NET mathematical Sciences exam paper consists of 3 sections, A, B and C. Section A is general aptitude and section B & C have subject based questions. As discussed above, a good understanding of the CSIR NET mathematical science exam pattern is essential in cracking any exam.

Part A: General Aptitude

General Aptitude
Graphical Analysis & Data Interpretation	Pie-Chart, Line and bar chart, graph, table, mode, median, mean, and measures of dispersion.
Reasoning	Puzzles, series formation, Clock & calendar, Directions & distance, coding and decoding, Ranking & arrangement, etc.
Numerical Ability	Geometry, proportion & variation, Time & Work, HCF & LCM average, Mensuration, Probability, Permutation & combinations, Sequence & Series, Compound interest, Simple interest, partnership, Mixture & Alligation, Trigonometry, Number & Simplification, Ratio, Time speed & distance, Profit & loss, Percentage, Quadratic equations, Logarithms, Surds & Indices, etc.

Part B & C: Mathematical Sciences

Units	Unit	Topics
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.
1	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
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.
2	Algebra	Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, 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, separation axioms, connectedness and compactness.
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’s 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’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.
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, 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.