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

By Renuka Miglani|Updated : October 6th, 2021

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.

Table of Content

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

EventsDetails
Exam NameCSIR UGC NET
Conducting BodyNational Testing Agency (NTA)
Exam LevelNational
Exam FrequencyTwice a year (June and December)
Exam ModeOnline only
Exam Duration3 hours (180 minutes)
Question TypeMCQ (Multiple Choice Questions)
Exam PurposeSelection of candidates for the award of JRF and determining the eligibility for Lecturers
MediumEnglish and Hindi (Both)
Total Marks200
Exam Helpdesk No.011-25848155
Official Websitehttps://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 CriteriaDetails
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 SectionsTotal Questions ProvidedMarks for Each SectionMarks Per QuestionNegative Marking for Each SectionTotal time
Part A203020.53 hours
Part B407530.75
Part C60954.750
Total Marks200

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 InterpretationPie-Chart, Line and bar chart, graph, table, mode, median, mean, and measures of dispersion.
ReasoningPuzzles, series formation, Clock & calendar, Directions & distance, coding and decoding, Ranking & arrangement, etc.
Numerical AbilityGeometry, 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

UnitsUnit Topics
1Analysis
  • 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
2Complex 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.
  • 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.
3Ordinary 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.
4Descriptive 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.

Download PDF for CSIR NET Mathematical Science Syllabus 2021 Here

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Renuka MiglaniRenuka MiglaniMember since Jan 2021
This article was curated by Renuka Miglani who is an Associate Manager at BYJU'S Exam Prep (CSIR-NET). A PostGrad with an educational background in Nutrition Science, she is an ardent reader & writer. Loves to impart knowledge to students. Being from a Nutrition Science background, she is well aware of the opportunities available and has hared the same in the above article. Stay tuned for more interesting articles from her which will be beneficial for your career.
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  • 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.

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

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

  • 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.

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