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CSIR NET Mathematics Syllabus: CSIR NET Mathematics Syllabus 2024 has been issued by the Human Resource Development Group (HRDG) on its official website. The topic asked in CSIR NET Mathematics exam is broken into three sections: A, B, and C. Part A is a general paper i.e., General Aptitude, is the same for all candidates. However, Part B and Part C totally depend on the subject-specific which is chosen by the candidate in CSIR NET Exam.

CSIR NET All Subject Syllabus 2024

## CSIR NET Mathematics Syllabus

CSIR NET Mathematics Syllabus 2024 is an important tool that students must be aware of it. Here, we have provided the complete CSIR NET Mathematics Syllabus for all the subjects as prescribed by the CSIR. Candidates should go through the syllabus well in advance to prepare for the exam.

## CSIR NET Mathematics Syllabus in Hindi

CSIR NET गणित का सिलेबस 2024 मानव संसाधन विकास समूह (HRDG) द्वारा अपनी आधिकारिक वेबसाइट पर जारी किया गया है। इस परीक्षा में पूछे गए विषय को तीन खंडों में बांटा गया है: A, B और C। पार्ट A एक सामान्य पेपर है यानी जनरल एप्टीट्यूड, जो सभी उम्मीदवारों के लिए समान है। हालाँकि, पार्ट B और पार्ट C पूरी तरह से उस विषय-विशेष पर निर्भर करते हैं जिसे उम्मीदवार द्वारा चुना जाता है।

## CSIR NET Mathematics Syllabus -Topic Wise

Here we are mentioning each & every topic of the CSIR NET Mathematics Syllabus in the tabulated form for easy access. As mentioned above, a good understanding of the CSIR NET Mathematics Syllabus is essential in cracking any exam. The direct link to download CSIR NET Mathematics Syllabus is given below.

### 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.

 CSIR NET Mathematical Science Syllabus: Part A (General Aptitude) 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

Here we are sharing the important topic which is asked in the CSIR NET Mathematical Science exam.  Candidates may revise all the important topics before appearing for the main exam.Parts B & C majorly consist of the subject concerned part which is based on the domain of the students.

 CSIR NET Mathematical Science Syllabus: Part B & Part C Unit 1 Analysis Elementary set theory, finite, countable, and uncountable sets, Real number system, Archimedean property, supremum, infimum. Sequence 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. Linear Algebra Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformation 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, and Sylow theorems. Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain. Topology: basis, dense sets, subspace and product topology, separation axioms, connectedness, and compactness. 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, and the system of first-order ODEs. A 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 the 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

 Mathematical Sciences Part A Part B Part C Total Total Questions 20 40 60 120 Max No of Questions to attempt 15 25 20 60 Marks for each correct answer 2 3 4.75 200 Negative marking 0.5 0.75 0 –

## CSIR NET Mathematics Syllabus: Topic-Wise Weightage

Please refer to the below-mentioned table to know the total number of questions in each section & their marking scheme

 Subject Total marks Negative Marking Marking Scheme Mathematical Science 200 Part A: -0.5 Part A: +2 Part B: -0.75 Part B: +3 Part C: No Negative Marking Part C: +4.75

## CSIR NET Mathematics Syllabus PDF

Check out the CSIR NET Mathematics Syllabus 2024 PDF given in the following.  The CSIR NET Syllabus PDF given below contains all the essential topics elaborately. CSIR NET Mathematics Syllabus PDF is easily shared or saved for future reference.

CSIR NET Mathematics Syllabus PDF

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## FAQs

### Is it mandatory to appear for three parts of the CSIR NET exam?

Yes, it is mandatory for candidates to appear for all three parts of the CSIR NET exam to qualify for the award of CSIR NET E-Certificate. Only those candidates are awarded the certificate who clear all three parts.

### For how many subjects is the CSIR NET exam conducted?

The CSIR NET exam is conducted for a total of five subjects. The five subjects are – Mathematical Science, Life Science, Chemical Science, Earth Science, and Physical Science.

### What is CSIR NET Mathematics Syllabus 2024?

CSIR NET Mathematics Syllabus 2022 has been released on the CSIR and NTA websites. The main topics are Analysis, Linear Algebra, Complex Analysis, Algebra, Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), etc.

### What is the marking scheme for the CSIR NET exam?

The CSIR NET exam carries a total of 200 marks. Two marks are awarded for each correct answer and there is a negative marking for wrong answers marked by the candidates.