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CSIR NET Mathematics Syllabus 2022 PDF

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CSIR NET Mathematics Syllabus 2022 PDF Details
CSIR NET Mathematics Syllabus 2022
PDF Name CSIR NET Mathematics Syllabus 2022 PDF
No. of Pages 4
PDF Size 0.07 MB
Language English
CategoryEnglish
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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 up-to-date 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
PART-A 20 15 30 0.5
PART-B 40 25 75 0.75
PART-C 60 20 95 0
TOTAL MARKS 200

CSIR NET Mathematics Syllabus in detail

CSIR NET Mathematics Syllabus for Part A

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

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.

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.


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