Post Name : CSIR NET Mathematical Science Syllabus 2024
Post Date : 12 April, 2024
Post Description : The CSIR NET (Council of Scientific and Industrial Research National Eligibility Test) is a national-level examination conducted by the National Testing Agency (NTA). The examination is commonly referred to as CSIR NET. It is conducted to identify candidates suitable for Junior Research Fellowships (JRF) and to assess their eligibility for teaching positions in universities and colleges across India.
CSIR NET Mathematical Science Syllabus 2024 Overview
The CSIR NET Mathematics Syllabus covers important topics like Analysis, Linear Algebra, Partial Differential Equations, Numerical Analysis, Calculus of Variations, and Linear Integral Equations. It is set by the Human Resource Development Group of the Council of Scientific and Industrial Research (CSIR). Candidates can find a detailed overview of the CSIR NET Mathematics Syllabus 2024 in the article below:
| CSIR NET Mathematical Science Syllabus 2024 Overview | |
|---|---|
| Exam Name | CSIR NET (Council of Scientific and Industrial Research National Eligibility Test) |
| Conducting Body | National Testing Agency (NTA) |
| Exam Level | National |
| Exam Frequency | Twice a year |
| Mode of Exam | Online – CBT (Computer-Based Test) |
| Total Questions | 150 MCQs in each Paper |
| Exam Duration | 180 minutes |
| Language/Medium of Exam | English and Hindi |
| No. of Test Cities | 225 |
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| No. of Papers and Total Marks |
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| Official Website | csirnet.nta.nic.in |
CSIR NET Mathematical Science Syllabus 2024 PDF
It’s crucial for candidates to have easy access to the CSIR NET Mathematical Science PDF during their study sessions. This comprehensive document encompasses the entire syllabus, preventing candidates from overlooking any important topics or sub-topics. Keeping the PDF open while studying enables candidates to cross-reference topics and make well-informed decisions about their study focus. The CSIR NET Mathematics PDF file can be conveniently downloaded by clicking on the link provided in the table below:
| CSIR NET Mathematical Sciences Syllabus 2024 PDF Free Download | |
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| CSIR NET Mathematical Sciences Syllabus 2024 PDF | Download Here |
CSIR NET Mathematical Science Unit Wise Syllabus 2024
The CSIR NET Mathematics Syllabus for 2024 encompasses a wide range of topics crucial for exam preparation. Below are key topics from each unit:
| CSIR NET Mathematical Science Unit Wise Syllabus 2024 | |
|---|---|
| Units | Topics |
| Unit 1: Analysis | Elementary set theory, finite, countable, and uncountable sets, Real number system, Archimedean property, supremum, infimum. Sequence and series, convergence, limsup, liming. 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 1: 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, diagonal, triangular, and Jordan forms. Inner product spaces, orthonormal basis. Quadratic forms, reduction, and ification 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, and 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, 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 3: 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 3: 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 3: 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 3: 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, ification 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, 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 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 Mathematical Science Syllabus 2024 Weightage of Topics
For any competitive examination, understanding the exam pattern is crucial for strategic preparation. Familiarity with the CSIR NET Exam Pattern, including the distribution of questions, marks per section, and other relevant information, is essential for devising a thorough preparation strategy. Candidates are encouraged to review the CSIR NET Mathematics Exam Pattern, as it provides valuable insights into the weightages assigned to different sections. Below is a table outlining the marking weightages for Part A of the CSIR NET Life Sciences examination:
| CSIR NET Mathematical Science Syllabus 2024 Weightage of Topics | |||||
|---|---|---|---|---|---|
| Sections | Total Questions | Marks for Each Section | Marks Per Question | Negative Marking | Total Time |
| Part A | 20 | 30 | 2 | 0.5 | 3 hours |
| Part B | 40 | 75 | 3 | 0.75 | |
| Part C | 60 | 95 | 4.75 | 0 | |
CSIR NET Mathematical Science Syllabus 2024 Preparation Tips
Understand the Syllabus and Weightage Allocation:
- Review the official CSIR NET Mathematical Science Syllabus 2024 to understand the topics covered and their weightage allocation in the exam.
- Identify key areas to focus on based on the syllabus to prioritize your study efforts effectively.
Choose High-Quality Study Materials:
- Select textbooks, reference books, and study guides that are reputable and align with the CSIR NET Mathematical Science syllabus.
- Ensure the study materials provide comprehensive coverage of the exam topics and offer practice questions for self-assessment.
Develop a Structured Study Plan:
- Create a structured study plan that outlines a schedule for covering each topic within a specified timeline.
- Allocate dedicated study time for each subject area based on its importance and your current proficiency level.
- Break down larger topics into smaller, manageable study sessions to prevent overwhelm and ensure thorough understanding.
Focus on Conceptual Understanding:
- Instead of rote memorization, prioritize developing a deep conceptual understanding of the mathematical principles and theories.
- Practice applying these concepts to solve problems and understand their real-world applications.
- Engage in active learning techniques such as problem-solving, concept mapping, and teaching others to reinforce understanding.
Regular Revision and Practice:
- Schedule regular revision sessions to reinforce learned concepts and identify areas that need further clarification.
- Solve previous years’ question papers and sample tests to familiarize yourself with the exam pattern and improve problem-solving skills.
- Analyze your performance in practice tests to identify weaknesses and adjust your study plan accordingly.
