CSIR NET MATHEMATICAL SCIENCE SYLLABUS AND EXAM PATTERN 2025

CSIR NET Mathematical Science Syllabus and Exam Pattern 2025

CSIR NET Mathematical Science Syllabus and Exam Pattern 2025

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The National Testing Agency conducts the CSIR NET exam to select candidates for Junior Research Fellowships (JRF) and assess their eligibility for lecturing positions in Indian colleges and universities. Passing the CSIR NET exam is mandatory for teaching science and technology subjects in higher education institutions. This article provides a detailed overview of the CSIR NET Mathematical Science Exam Pattern and Syllabus.

CSIR NET Mathematics Syllabus for Part A

Part A is all about general Paper which is common for all post. Some of the important topics of  CSIR NET Mathematical Science are partial differential equations, numerical analysis, calculus of variations, linear integral equations, classical mechanics, descriptive statistics, exploratory data analysis, etc.

Graphical Analysis & Data Interpretation:


  • Pie-Chart

  • Line & Bar Chart

  • Graph

  • Mode, Median, Mean

  • Measures of Dispersion

  • Table


Reasoning:

  • Puzzle

  • Series Formation

  • Clock and Calendar

  • Direction and Distance

  • Coding and Decoding

  • Ranking and Arrangement.


Numerical Ability:

  • Geometry

  • Proportion and Variation

  • Time and Work

  • HCF and LCM

  • Permutation and Combination

  • Compound and Simple Interest.


CSIR NET Mathematics Syllabus for Part B & Part C
The CSIR NET Maths course spans pure and applied mathematics, testing concepts, reasoning, and problem-solving skills. Divided into 4 major units, it includes topics like algebra, topology, analysis, and more. Thorough preparation ensures success.

CSIR NET Exam Mathematical Science syllabus covers the following topics.

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, 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.


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'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.


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'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.

  • 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.


Unit - 4.

Descriptive Statistics, Exploratory Data Analysis:

  • 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.

  • Simple random sampling, stratified sampling, and systematic sampling. Probability is proportional to size sampling. Ratio and regression methods.

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


CSIR NET Mathematics Exam Pattern

There is a negative marking of 25% in Parts A and B of CSIR NET Mathematical Science Subject, and there is no negative marking for Part C. Important topics include Combinations, Fundamental Theorem of Arithmetic, Divisibility in Z, Congruences, etc.

Subject : Mathematical Sciences

Part - A         

  • Total Questions. = 20

  • Max No of Questions to attempt. = 15

  • Marks for each correct answer. = 2

  • Negative marking. = 0.5


Part - B          

  • Total Questions. = 40

  • Max No of Questions to attempt. = 25

  • Marks for each correct answer. = 3

  • Negative marking. = 0.75


Part - C         

  • Total Questions. = 60

  • Max No of Questions to attempt. = 20

  • Marks for each correct answer. = 4.75

  • Negative marking. = No Negative Marking.


Total

  • Total Questions. = 120

  • Max No of Questions to attempt. = 60

  • Marks for each correct answer. = 200


CSIR NET Mathematics Syllabus & Topic-Wise Weightage

The total number of questions in each section and their marking schemes.

Mathematical Science

Total marks: 200

Negative Marking:

  • Part A: -0.5

  • Part B: -0.75

  • Part C: No Negative Marking Part


Marking Scheme:

  • Part A: +2

  • Part B: +3

  • Part C: +4.75


Follow the CSIR NET Maths syllabus with topic-wise previous years' question papers.

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