The National Testing Agency conducts a national exam to select applicants for Junior Research Fellowships (JRF) and to assess their ability for lecturing positions in Indian colleges and universities. Only those who pass the CSIR NET exam can teach in colleges and universities as science and technology faculties. In this article, let’s understand the CSIR NET Mathematical Science Exam Pattern & Syllabus.
CSIR NET Exam Pattern
The CSIR-UGC (NET) Exam for Junior Research Fellowship and Lecturership Eligibility is a Single Paper Test with Multiple Choice Questions (MCQs). The exam can be divided into three parts.
- Part A – This section will have 20 questions covering General Science, Quantitative Reasoning & Analysis, and Research Aptitude. Candidates must answer any 15 questions. Each question will be worth two marks. This segment is of 30 marks total out of 200.
- Part B – This part will have 40 Multiple Choice Questions (MCQs) generally covering the topics given in the syllabus. Candidates must answer any 25 questions. Each question shall be of three marks. The total marks allocated to this section shall be 75 out of 200.
- Part C – Part ‘C’ shall contain higher-order questions that may test the candidate’s knowledge of scientific concepts and/or application of the scientific concepts. The questions shall be of analytical nature where a candidate is expected to apply scientific knowledge to arrive at the solution to the given scientific problem. A candidate shall be required to answer any 20 questions. Each question shall be 4.75 marks. The total marks allocated to this section shall be 95 out of 200.
| CSIR NET Mathematics Paper 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 Mathematical Science Syllabus
The Mathematical Science syllabus for the CSIR NET exam comprises the following topics:
- Analysis
- Linear Algebra
- Complex Analysis
- Algebra
- Numerical Analysis
- Topology
- Ordinary Differential Equations (ODEs)
- Calculus of Variations
- Linear Integral Equations
- Classical Mechanics
The unit-wise syllabus for the CSIR NET exam is as follows:
| Unit 1Â | Analysis
Elementary set theory, finite, countable and uncountable sets, Bolzano Weierstrass theorem, Heine Borel theorem, Sequences and series of functions, uniform convergence, Riemann sums and Riemann integral, etc. Linear Algebra Vector spaces, subspaces, linear dependence, basis, dimension, Matrix representation of linear transformations, Inner product spaces, orthonormal basis, etc. |
| Unit 2Â | Complex Analysis
Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric and hyperbolic functions,etc. 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 root, etc. Topology Basis, dense sets, subspace and product topology, separation axioms, etc. |
| Unit 3Â | 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,etc. 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, etc 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, etc. Linear Integral Equations Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels, etc Classical Mechanics Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and principle of least action, Two-dimensional motion of rigid bodies, etc. |
| Unit 4 | Descriptive statistics, exploratory data analysis
Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses. Analysis of variance and covariance, Completely randomised designs, randomised block designs and Latin-square designs. Connectedness and orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction, etc. |
The above table has a list of important topics in the CSIR NET Mathematical Science syllabus. Candidates can download the entire syllabus PDF below.
CSIR NET Mathematical Science Syllabus
Given below are a few other related links for CSIR NET exam preparation:
| CSIR NET Syllabus | CSIR NET Admit Card |
| CSIR NET Books | CSIR NET Age Limit |
| CSIR NET Exam Date | CSIR NET Exam Centres |
| CSIR NET Result | CSIR NET Exam Pattern |
| CSIR NET Cut Off | CSIR NET Vacancy |
