CSIR NET Maths Syllabus - Download Unit-wise Syllabus PDF
CSIR NET Maths Syllabus - National Testing agency (NTA) prescribes the syllabus of NET Maths for all the candidates willing to take Maths. NET Maths syllabus has been prescribed in the form of PDF. Candidates should go through NET Maths syllabus to know all important topics from which questions will be asked in the exam. By going through the CSIR NET syllabus, candidates will be able to make a schedule to study. NTA conducts CSIR NET exam to determine the eligibility of the candidates as Assistant Professors and award Junior Research Fellowship (JRF) in Maths and Science. As per the exam pattern of CSIR NET, the test is held for 5 subjects - Physical Science, Chemical Sciences, Earth Sciences, Life Sciences and Mathematical Sciences. Here in this article, candidates will be able to know all topics and chapters for NET Maths.
CSIR UGC NET 2020 exam has been postponed this year due to the COVID-19 outbreak. The new exam dates will be announced by the authorities later on the website. Candidates can fill the CSIR NET application form in online mode tillJune 30, 2020. To know more about the NET Maths syllabus, go through the article below
NET Maths Syllabus - Important Dates
The table below contains CSIR NET exam dates and other event related dates:
CSIR NET Important Dates
Dates for June 2020
Start date of application form
March 16, 2020
Last date of fill application form
June 30, 2020 (5:00 pm)
Application form edit dates
To be notified
Admit card download date
To be notified
CSIR NET 2020 exam date
To be notified
Result declaration date
To be notified
CSIR NET Maths Syllabus - Units-wise
The table below contains the units from where the topics and the chapters will be mentioned in the syllabus.
NET syllabus For Maths
Details mentioned below in article
UNIT I - CSIR NET Maths Syllabus
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,
Functions of several variables, derivative as a linear transformation, directional derivative, partial derivative, inverse and implicit function theorems.
Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.
Vector spaces, subspaces, dimension, linear dependence, basis, algebra of linear
Algebra of matrices, linear equations, rank and determinant of matrices.
Eigenvalues and eigenvectors, Cayley-Hamilton theorem.
Matrix representation of linear transformations. Change of basis, Jordan forms, canonical forms, diagonal forms, triangular forms.
Inner product spaces, orthonormal basis.
Quadratic forms, reduction and classification of quadratic forms
UNIT II - CSIR NET Syllabus For Maths
1) Algebra of complex numbers, power series, the complex plane, trigonometric and hyperbolic functions, polynomials, transcendental functions such as exponential.
2) Analytic functions, Cauchy-Riemann equations. Cauchy’s integral formula, Contour integral, Cauchy’s theorem, Schwarz lemma, Liouville’s theorem, Maximum modulus principle, Open mapping theorem.
3) Taylor series, calculus of residues, Laurent series, Mobius transformations, Conformal mappings.
4) Algebra: Permutations, inclusion-exclusion principle, combinations, pigeon-hole principle, derangements.
5) Fundamental theorem of arithmetic, congruences, divisibility in Z, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots. normal subgroups, Groups, subgroups, homomorphisms, quotient groups, cyclic groups, class equations, permutation groups, Cayley’s theorem, Sylow theorems.
6) Rings, quotient rings, ideals, principal ideal domain, prime and maximal ideals, unique factorization domain, Euclidean domain.
7) 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.
UNIT III - CSIR NET Maths Syllabus
Ordinary Differential Equations (ODEs)
Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, system of first order ODEs, singular solutions of first order ODEs. General theory of homogeneous and non-homogeneous linear ODEs, Sturm-Liouville boundary value problem, variation of parameters, Green’s function.
Partial Differential Equations (PDEs)
Cauchy problem for first order PDEs, Lagrange and Charpit methods for solving first order PDEs, General solution of higher order PDEs with constant coefficients, Classification of second order PDEs, Method of separation of variables for Laplace, Heat and Wave equations.
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
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, Necessary and sufficient conditions for extrema, Euler-Lagrange equation. Variational methods for boundary value problems in ordinary and partial differential equations.
Linear Integral Equations
Solutions with separable kernels, Linear integral equation of the first and second kind of Fredholm and Volterra type. Characteristic numbers and eigenfunctions, resolvent kernel.
Hamilton’s canonical equations, Lagrange’s equations, Generalized coordinates, Hamilton’s principle and principle of least action, Euler’s dynamical equations for the motion of a rigid body about an axis, Two-dimensional motion of rigid bodies, theory of small oscillations.
UNIT IV - CSIR Maths Syllabus For NET
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, limiting behaviour of n-step transition probabilities, classification of states, stationary distribution, Poisson and birth-and-death processes.
Standard discrete and continuous univariate distributions. sampling distributions, distribution of order statistics and range, standard errors and asymptotic distributions.
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, tests for linear hypotheses, estimability of parameters, best linear unbiased estimators, confidence intervals, Analysis of variance and covariance. Fixed, random and mixed effects models.
Elementary regression diagnostics, Simple and multiple linear regression, 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: Principal component analysis, Discriminant analysis, Cluster analysis,
CSIR NET Maths Paper Pattern
According to the CSIR NET exam pattern, the test will be held for five subjects - Physical Science, Chemical Sciences, Earth Sciences, Life Sciences and Mathematical Sciences. Candidates will have to select one of their desired subjects. The test will be held for a total of 200 marks for which the candidates will be given a total of 3 hours. The test is held in online mode. The table below contains the NET Exam pattern for all five subjects for which the test is held.
CSIR NET Exam Pattern 2020
Total Number of questions
Earth, Atmospheric, Ocean and Planetary Sciences
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Questions related to CSIR UGC NET
when will be CSIR net 2020 exam conducted??
CSIR UGC NET June 2020 Exam will be conducted by the National Testing Agency (NTA) on 21st June 2020 for determining the eligibility of Indian Nationals for the award of Junior Research Fellowships (JRF) and for determining eligibility for Lectureship (LS)/Assistant Professorship in certain subject areas falling under the faculty of Science & Technology like Chemical Sciences, Earth, Atmospheric, Ocean and Planetary Sciences, Life Sciences, Mathematical Sciences and Physical Sciences.
Can I be eligible for CSIR UGC NET LIFE SCIENCE after completing MBA IN BIOTECHNOLOGY?
There is no age criteria for NET exam but for the JRF post you age should be below 28 years..
Good luck... hope it helps!!
Is final year Btech Mechanical student is eligible for NTA CSIR UGC NET exam?
As per the eligibility criteria of CSIR UGC NET exam you should secure at least 50% marks in your B.Tech degree.
But if you are in the final semester you can also submit the application form but then you are have to apply under the result awaited category. in this situation you have to put your aggregate marks after completion of B.Tech degree to avail the fellowship.
For more detailed information about eligibility criteria for CSIR UGC-NET you should visit -
I hope this information helps you.
For further queries feel free to ask in comment section.
in which month Csir net june 2020 is most likely to occour ?
The CSIR NET application form deadline has further been extended till June 15, 2020. In this case, it is difficult to say whether the exam will be held in which month. However, any update related to the exam will be updates in CSIR NET exam dates .
difference between applied and pure mathematics for csir ugc net exam
Pure mathematicians try to generalize and make more abstract the pre-existing concepts , they delve deeper into seemingly simplistic mathematics.
There are two things that can be done with a concept or an idea, you can go uphill or you can go downhill ( look deeper into the concepts).Pure mathematics goes downhill.
Lets say that we have the Cartesian co-ordinate system. A pure mathematician defines a field of numbers, develops the concept of vectors , define vector spaces,find some of the properties of vector spaces ,generalise to functional spaces, define hilbert spaces and so on.
On the other hand an applied mathematician would find how to use this concept of Cartesian co-ordinate system to solve some problems, in other words how can this mathematical concept be applied.
In the light of the above example, they may realise that quantum mechanics is having some sort of link with linear algebra, incorporate the concept of hilbert spaces , get more result out of the equations (as those concepts have already been developed in pure mathematics )
Applied mathematics like pure mathematics plays a crucial role in science. In physics many concepts of pure mathematics are now applied ( so in a sense physics is applied mathematics) .
Hope this helps!