# CSIR NET Mathematics Syllabus 2024 and Exam Pattern

CSIR NET Mathematics Syllabus 2024: The CSIR NET Mathematics Syllabus 2024 has been released by the Human Resource Development Group (HRDG) on its official website. The syllabus for the CSIR NET Mathematics exam is divided into three sections. Candidates preparing for the CSIR Mathematical paper should thoroughly understand the topics outlined in the NET Math syllabus. Below, we provide a detailed discussion of the CSIR NET Mathematics Syllabus 2024.

## CSIR NET Mathematics Syllabus 2024

CSIR NET Mathematics Syllabus 2024 is a crucial resource that candidates must be familiar with for effective exam preparation. It is advisable for candidates, especially those appearing for the mathematical sciences section, to develop a well-organized CSIR NET Study Plan based on the structure outlined in the CSIR NET Maths syllabus. The CSIR Maths exam encompasses a wide range of topics, including Analysis, Linear Algebra, Complex Analysis, Algebra, Topology, Ordinary Differential Equations, Partial Differential Equations, and more. Familiarity with the syllabus aids candidates in targeted and strategic preparation.

## CSIR NET Mathematical Science Syllabus – Topic Wise

Here is the CSIR NET Mathematical Science Syllabus for Part A (General Aptitude) and Part B & Part C:

## 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 Mathematical Science 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.

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.

Unit 2: 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.

Unit 3: 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.

Unit 4: 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.

Unit 5: 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.

Unit 6: 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.

Unit 7: 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 8: 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 system.

Candidates are encouraged to revise these important topics before appearing for the main exam.

## CSIR NET Mathematics Paper Pattern 2024

The CSIR NET examination encompasses various subjects, including Physical Science, Chemical Sciences, Earth Sciences, Life Sciences, and Mathematical Sciences. Each candidate needs to select their preferred subject for the exam. The total marks for the exam are 200, and candidates are allotted 3 hours to complete the test. The examination is conducted in online mode. Below is the detailed CSIR NET Exam Pattern for 2024:

## What is CSIR NET Mathematics Exam 2024?

The CSIR NET Mathematics Exam 2024 is a nationwide test by the Council of Scientific and Industrial Research (CSIR). It checks if candidates are suitable for roles like Assistant Professor or Junior Research Fellowships. The exam focuses on various math topics like analysis, algebra, topology, and differential equations. It has three parts: Part A for general aptitude, and Parts B and C for subject-specific questions. The exam is out of 200 marks, and there’s a penalty for wrong answers. It’s a significant opportunity for those wanting to contribute to mathematical research and teaching.

## CSIR NET Mathematics Syllabus 2024 – FAQs

Q1. What is the purpose of CSIR NET Mathematics Exam?

Ans. CSIR NET Mathematics Exam aims to assess candidates for eligibility as Assistant Professors and Junior Research Fellows in the field of Mathematics.

Q2. How is CSIR NET Mathematics Syllabus 2024 structured?

Ans. The CSIR NET Mathematics Syllabus 2024 comprises three parts: Part A (General Aptitude), Part B, and Part C (Subject-specific questions).

Q3. Is there negative marking in the CSIR NET Mathematics Exam?

Ans. Yes, there is negative marking for incorrect answers in Parts A and B.

Q4. How many marks is the CSIR NET Mathematics Exam out of?

Ans. The CSIR NET Mathematics Exam is out of 200 marks.

Q5. What is the duration of the CSIR NET Mathematics Exam?

Ans. The CSIR NET Mathematics Exam has a duration of 3 hours.

Q6. What topics are covered in CSIR NET Mathematics Syllabus 2024?

Ans. The syllabus includes areas like Analysis, Linear Algebra, Complex Analysis, Algebra, Topology, Ordinary and Partial Differential Equations, and more.

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