CSIR NET Mathematical Sciences Syllabus 2023

The Council of Scientific and Industrial Research (CSIR) exam is held by National Testing Agency (NTA). NTA conducts the CSIR UGC NET Examination in CBT mode.

The CSIR examination determines the eligibility for Junior Research Fellowship (JRF) along with Assistant professor, Lectureship (LS) of Indian nationals in Indian colleges and Universities. It decides whether a student fulfills the eligibility criteria of the desired subject laid down by UGC.

The online application for NET/JRF is released twice a year on all India basis via Joint CSIR-UGC NET for JRF and LS/AP via press notification. However, due to the pandemic situation, it was held once in 2020.

The Council of Scientific and Industrial Research- National Eligibility Test is for the candidates who choose Junior Research Fellowship (JRF) and Lectureship (LS) as their career.

After passing the exam, the candidates are eligible for research fellowship and lectureship. They can also work as a scientific laboratory technician or as a support executive in the science background and work in the investigation, support analysis, research, and development.

The career scope becomes brighter for candidates qualifying in the CSIR NET. In this article, we will talk more about the CSIR NET and the CSIR NET Mathematical Sciences Syllabus.

Given below are the organizations where you can find opportunities after clearing the CSIR examination.

• Indian Space Research Organization (ISRO)
• Indira Gandhi Centre for Atomic Research (IGCAR)
• Indian Veterinary Research Institute (IVRI)
• Indian Institute of Science (IISc) Bangalore
• Indian Agricultural Research Institute (IARI)
• Tata Institute of Social Sciences (TISS)
• Bhabha Atomic Research Center (BARC)
• Tata Institute of Fundamental Research (TIFR)
• Department of Atomic Energy (DAE)
• Centre for Studies in Social Sciences

Overview

Name of the Exam	CSIR NET 2022
Exam Conducting Body	National Testing Agency (NTA)
Purpose of Exam	Selection for Junior Research Fellowship (JRF) and Lectureship (LR)
Mode of Application	Online
Mode of Fee Payment	Online
Application Fees	For UR – INR 1000/- For OBC/ EWS – INR 500/- For SC/ ST/ PwD – INR 250/-
Mode of Examination	Computer Based Test
Question Paper	Part-A – 20 Questions Part-B – 25 Questions Part-C – 30 Questions
Subjects	Chemical Science, Earth Science, Life Science, Mathematical Science, Physical Science
Helpdesk No.	0120-6895200
Official Website	nta.ac.in or csirnet.nta.nic.in

Eligibility Criteria for CSIR NET

For being eligible for the CSIR examination, the candidate must be of Indian Nationality. The age limit is different for Lectureship and Junior Research Fellowship.

• Junior Research Fellowship (JRF): As per 01/07/2021, the maximum age limit to apply for JRF is 28 years. If the candidate belongs to a reserved category, he or she gets age relaxation as per Government rules. For OBC (NCL) the age relaxation is up to 3 years and for SC, ST, PWD, the age relaxation is up to 5 years.
• Lectureship: There is no age limit for lectureship.

Educational Qualification

The following educational qualifications are a must for appearing in this examination.

• The candidate should have an Integrated BS-MS/ MSc or equivalent degree/ BS-4 years/ B. Pharma/ B.Tech/ BE/ MBBS degree or B.Sc (Hons) or equivalent degree. Students can also be enrolled in Integrated MS-PhD program with an aggregate of marks 50% for SC/ ST/ PwD candidates and 55% for General and OBC categories candidates.
• Candidates will be eligible for Fellowship after enrolling for a Ph.D./Integrated Ph.D. program if they have a Bachelor’s Degree. The validity period is for 2 years.
• Candidates enrolled in M.Sc. or have completed 10+2+3 years can also apply under the category of ‘Result Awaited’ (RA).

Note: A candidate with only a Bachelor’s Degree is eligible for applying only for the Junior Research Fellowship (JRF) and not for the Lectureship (LS).

CSIR NET Mathematical Sciences Syllabus- Important Topics

CSIR NET Mathematical Sciences Syllabus is vast. Therefore it is important to have an estimated idea of the important topics and the marks weightage.

Serial No.	Topic	Marks Weightage
1.	Differential Equations	35 to 40 Marks
2.	Integral Calculus	35 to 40 Marks
3.	Calculus of Variation	19 to 25 Marks

CSIR NET Mathematical Sciences Important Topics

• Integral calculus
• Differential equations
• Complex analysis
• Number Theory
• Classical mechanics
• Calculus of variables
• Probability and statistics
• Linear algebra
• Topology

CSIR NET 2022 Exam Pattern

Duration of the exam	3 hours
Type of questions	MCQ
Examination mode	Online mode
Division of question paper	3 sections
Total number of questions	120
Maximum marks	200
Medium of exam	English and Hindi
Marks in each section	Section A: 30 Section B: 75 Section C: 95

CSIR NET Mathematical Sciences Section Wise question paper description

Sections	Number of questions	Number of questions to be attempted	Total marks	Negative marking in each question
Section A	20	15	30	0.5
Section B	40	25	75	0.75
Section C	60	20	90	0

CSIR NET Mathematical Sciences Syllabus

Unit 1

Analysis:

Elementary set theory, Archimedean property, Sequences and series, finite, countable, and uncountable sets, supremum, infimum. Convergence, Real number system as a complete ordered field, Heine Borel theorem Bolzano Weierstrass theorem. Continuity, Differentiability, Sequences and series, Mean value theorem. Metric spaces, Functions of several variables, connectedness, compactness, and Normed Linear Spaces.

Linear Algebra:

Vector spaces, algebra of linear transformations. Algebra of matrices, determinant of matrices, linear equations. Cayley-Hamilton theorem, Eigenvalues, and eigenvectors. reduction, Quadratic forms, and classification of the quadratic forms Matrix representation of linear transformations. Change of basis, diagonal forms, canonical forms, triangular forms, Jordan forms.

Unit 2

Analysis:

Algebra of complex numbers, polynomials, power series, the complex plane, transcendental functions such as trigonometric, exponential, and hyperbolic functions. Cauchy-Riemann equations, Analytic functions. Contour integral, Cauchy’s integral formula, Liouville’s theorem, Cauchy’s theorem, Maximum modulus principle, Open mapping theorem, Schwarz lemma. Laurent series, Taylor series, calculus of residues. Mobius transformations, conformal mappings.

Algebra

Permutations, congruences divisibility in Z, Fundamental theorem of arithmetic, combinations, Chinese Remainder Theorem, primitive roots, Euler’s Ø- function, Sylow theorems, Cayley’s theorem. Rings, ideals, quotient rings, prime and maximal ideals, Polynomial rings, unique factorization domain, and irreducibility criteria. Fields, field extensions, finite fields, Galois Theory.

Topology:

Basis, subspace and product topology, connectedness, separation axioms, dense sets, and compactness.

Unit 3

Ordinary Differential Equations (ODEs):

uniqueness and Existence of solutions of initial value problems for first-order ordinary differential equations, the system of first-order ODEs, singular solutions of first-order ODEs.

Partial Differential Equations (PDEs):

Charpit and Lagrange methods in solving first-order PDEs, Cauchy problem for first-order PDEs. The general solution of higher-order PDEs with constant coefficients, Classification of second-order PDEs, Heat and Wave equations, and Method of separation of variables for Laplace.

Numerical Analysis:

Method of iteration and Newton-Raphson method, Numerical solutions of algebraic equations, Rate of convergence.

Calculus of Variations:

Necessary and sufficient conditions for extrema, Variation of a functional, Euler-Lagrange equation. Variational methods for boundary value problems in partial and ordinary differential equations.

Linear Integral Equations:

Characteristic numbers and resolvent kernel, eigenfunctions. the first and second kinds of Volterra and Fredholm type of Linear integral equation, Solutions with separable kernels.

Classical Mechanics:

Hamilton’s principle, the principle of least action, Generalized coordinates, Hamilton’s canonical equations, Lagrange’s equations, Euler’s dynamical equations for the motion of a rigid body about an axis, Two-dimensional motion of rigid bodies, and the theory of small oscillations.

Unit 4

Descriptive statistics:

Exploratory data analysis, independent events, discrete probability, Sample space, Bayes theorem. Standard discrete and continuous univariate distributions. Independent random variables, marginal and conditional distributions. Expectation and moments, Random variables and distribution functions (univariate and multivariate). Distribution of order statistics, Sampling distributions, standard errors and asymptotic distributions, and range.

Probability:

Methods of estimation, best linear unbiased estimators, properties of estimators, confidence intervals. Tests of hypotheses, Gauss-Markov models, confidence intervals, estimability of parameters, and tests for linear hypotheses. Multivariate normal distribution, Distribution of quadratic forms Simple and multiple linear regression. Analysis of variance and covariance. Probability is proportional to size sampling.

Data Reduction Techniques:

Discriminant analysis, Cluster analysis, Principle component analysis, Canonical correlation. Stratified sampling, Simple random sampling, and systematic sampling.

Tips to prepare for the CSIR examination

1. Know your syllabus

Before starting, you need to have proper knowledge of the syllabus completely to get a proper idea of the exam. You prioritize the topics that have more marks weightage, focus on them and study accordingly. It would be helpful for you if you have adequate clarity of all the topics of the CSIR NET Mathematical Sciences Syllabus.

2. Make a timetable

It is important to manage time during the preparation of the examination. You have to prepare a proper timetable for the same. As soon as you start working on time management, you can focus better. Start working on each topic separately. As you finish the syllabus, start solving the numerical together.

3. Preparatory material

You can refer to the reference books or find the preparation materials online for the exam. Referring to previous years’ questions papers is a good method to prepare yourself for the exam. But referring to books is equally important as it will help to grasp the knowledge more. There are also several online sites that provide materials and mock tests for preparation.

4. Exam pattern and marking scheme

Next, follow their question paper pattern as given in this article. And also how they mark the negative marking. Refer to previous years’ question papers. This will help to understand the nature and pattern of the sums.

5. Attempt mock tests

Practice is the key to getting perfect in Mathematics. A mock test is the most essential factor no matter what exam you are sitting for. After you complete your syllabus for CSIR Mathematical Science, start taking up a mock test daily. It can be through online or offline mode. A mock test will help you discover your strengths and weaknesses in each of the topics. You can learn more from your errors and practice them.

CSIR NET Mathematical Sciences Reference Books

• Modern Algebra: A.R.Vasistha, I.N.Herstein, Khanna & S.K. Bhambri, R.Kumar, Gallian, Artin
• Matrices: A. R. Vasistha, Schaum
• Operation Research: S. D. Sharma, Kanti Swaroop, H. A. Taha, G. J. Lieberman
• Numerical Analysis: S.S.Shastry, Jain, Iyenger & Jain, Erwin Kreyszig
• Integral Transform: Krishna series, Erwin Kreyszig
• Differential Equation: M. D. Raisinghania, D. A. Murray, N. M. Kapoor, Snedden, T. Amaranath
• Statistics: Gupta & Kapoor, Schaum Series, Gun, Gupta & Dasgupta, Part I &II
• Discrete Mathematics: Kolman, Busby & Ross, Trembly –Manohar, V. K. Balakrishan Number Theory Zuckerman, Burton
• Complex Analysis: Schaum Series, Kasana J. N. Sharma & A. R. Vasistha, Churchil, J. B. Conway
• Higher Engineering Mathematics: B.S.Grewal /Erwin Kreyszig
• Differential Geometry: Krishna series
• Topology: Krishna series, Simmons, J. N. Sharma, MUNKRES
• Functional Analysis: Krishna series, Vasishtha & Sharma
• Mechanics: Krishna series, Gupta &Gupta
• Real Analysis: A. R. Vasistha, Arora & Malik, N. P. Bali, Apostol, W. Rudin, R. R. Goldbarg, Asha Rani Singhal
• Calculus of variation: M. D. Raisinghania, Silverman, Rober
• Integral Equation: Krishna series, M.D.Raisinghania
• Mathematical Analysis: Arora & Malik, N. P. Bali, Rudin, Vasishtha
• Linear Algebra: Schaum Series, G.Hadley & A.R.Vasistha, Hoffman & Kunze , S.Bartle
• PDE: Ian –Snedon, T. Amarnath
• ODE: Erwin Kreyszig, Simmons

Wrapping Up

It is not easy to crack the CSIR NET Mathematical Science examination. You need to have a strong focus and keep practicing all the CSIR NET Mathematical Sciences Syllabus topics. With a long time of preparation, attempting mock tests, and multiple revision of the syllabus, candidates can crack CSIR NET.