CSIR NET Mathematics Syllabus 2022 PDF Details  

PDF Name  CSIR NET Mathematics Syllabus 2022 PDF 
No. of Pages  4 
PDF Size  0.07 MB 
Language  English 
Category  English 
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CSIR NET Mathematics Syllabus 2022
Here in this post, we are going to present CSIR NET Mathematics Syllabus 2022 PDF. The knowledge of CSIR NET Mathematics Syllabus 2022 is important for the preparation for the Mathematical Science exam. Candidates aiming to crack the exam in the first attempt must go through the essential topics given below. This will help them to prepare a good study plan around the CSIR NET Maths Science syllabus.
Candidates should start preparing for the exam systematically with the help of the CSIR NET Mathematics Syllabus 2022 PDF. Check the Syllabus in Hindi also. The exam is conducted twice a year but the CSIR NET Mathematics syllabus remains the same for both exams. Candidates can find the most uptodate topics covering Part A and Part B and C.
CSIR NET Mathematics Syllabus 2022 PDF – Overview
CSIR NET Mathematics Syllabus 

Unit 1  Analysis 
Linear Algebra  
Unit 2  Complex Analysis 
Algebra  
Ordinary Differential Equations (ODEs)  
Partial Differential Equations (PDEs)  
Unit 3  Numerical Analysis 
Calculus of Variations  
Linear Integral Equations  
Classical Mechanics  
Unit 4  Descriptive Statistics 
Exploratory Data Analysis 
CSIR NET Mathematics Exam Pattern
Sections  No. of Questions Asked  No. of Questions to be Attempted  Marks  Neg. Marking 
PARTA  20  15  30  0.5 
PARTB  40  25  75  0.75 
PARTC  60  20  95  0 
TOTAL MARKS  200 
CSIR NET Mathematics Syllabus in detail
CSIR NET Mathematics Syllabus for Part A
Graphical Analysis & Data Interpretation  PieChart 
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
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, CayleyHamilton 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, CauchyRiemann 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, pigeonhole principle, inclusionexclusion 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 firstorder ordinary differential equations, singular solutions of firstorder ODEs, and the system of firstorder ODEs. 
A general theory of homogenous and nonhomogeneous linear ODEs, variation of parameters, SturmLiouville boundary value problem, Green’s function.  
Partial Differential Equations (PDEs)  Lagrange and Charpit methods for solving firstorder PDEs, Cauchy problem for firstorder PDEs. 
Classification of secondorder PDEs, General solution of higherorder 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 NewtonRaphson method, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and GaussSeidel methods, Finite differences, Lagrange, Hermite, and spline interpolation, Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and RungeKutta methods. 
Calculus of Variations  Variation of a functional, EulerLagrange 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, Twodimensional 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 nstep transition probabilities, stationary distribution, Poisson, and birthanddeath 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 chisquare 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. 
How to prepare CSIR NET Mathematics Syllabus
It is important to prepare a strategy to cover the entire syllabus of CSIR NET without any fallback. If you fail to cover any part then it may favor your luck in the exam. CSIR NET Maths preparation tips are given below.
 The candidates must have a strong desire to maintain their daily study hours, as this will motivate them to do so and give them the continuity to complete the syllabus without any problem. Each day’s record should be included in the candidate plan, and you can also keep a chart for your study schedule.
 The mathematics syllabus should be divided into sections based on the amount of time you have before the exam. If applicants have six months to prepare, they should devote seven to eight hours a day to their studies. If applicants only have two months to study, they should devote more time, perhaps 9 to 11 hours each day, to a good strategy and study plan.
 Candidates must have a previous year’s CSIR NET Maths paper to track their progress.
 Candidates should start their preparation with the subject in which they are best. Candidates will be able to improve their skills in the subject in which they are already performing best.
 While studying and practicing CSIR NET Mathematics Science Syllabus, you must take great care of yourself emotionally and physically as well.
Here you can free download CSIR NET Mathematics Syllabus 2022 PDF by clicking the link given below.