CSIR NET Mathematics Syllabus 2022: Download Syllabus PDF

By Renuka Miglani|Updated : April 26th, 2022

Knowledge of the CSIR NET Mathematics Syllabus 2022 is vital for preparing for the mathematical science exam. Candidates who are targeting to clear the exam in the first attempt must go through the important topics provided below. This will help them in formulating a good study plan around the CSIR NET mathematical science syllabus.

Candidates should begin systematically preparing for the exam with the help of the CSIR NET Mathematics Syllаbus 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 may find the most up-to-date topics that cover both Part A and Part B and C.

Also, check CSIR NET Application Form for June Cycle.

Table of Content

CSIR NET Mathematics Syllabus 2022

The first thing that comes to mind is what is the CSIR NET Mathematics Syllabus 2022. What topics should be covered in the preparation and what should be left untouched? This article is written primarily for candidates interested in pursuing a career in the CSIR NET maths JRF & Assistant Professor posts. Here you get comprehensive information on the Mathematics Syllabus of CSIR NET and key topics. A, B, and C are the three sections of the CSIR NET maths exam paper. General aptitude questions are found in Section A, whereas subject-specific questions are found in Sections B and C.

The CSIR NET Syllabus of Mathematical Science covers the following topics:

  • Analysis
  • Linear Algebra
  • Complex Analysis
  • Algebra
  • Ordinary Differential Equations (ODEs)
  • Partial Differential Equations (PDEs)
  • Numerical Analysis
  • Calculus of Variations
  • Linear Integral Equations
  • Classical Mechanics
  • Descriptive Statistics, Exploratory Data Analysis

Download CSIR NET Mathematics Syllabus 2022 PDF

CSIR NET Mathematics PDF file is available for download at the URL below. The CSIR has released the important topics for the maths in a portable document format file. Keep the downloaded CSIR NET Mathematical Science PDF to access it anytime while studying. The whole syllabus is included in the PDF.

Download CSIR NET Mathematics Syllabus PDF

CSIR NET Mathematics Syllabus in detail

CSIR NET Mathematics Syllabus consists of 3 sections, A, B, and C. Section A is about general aptitude, and sections B & C has subject-based questions. Some of the important topics are partial differential equations, numerical analysis, calculus of variations, linear integral equations, classical mechanics, descriptive statistics, exploratory data analysis, etc.

As discussed above, a good understanding of the CSIR NET Mathematics Syllabus is essential in cracking any exam.

CSIR NET Mathematics Syllabus for Part A

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 Mathematics Syllabus for Part B & Part C

CSIR NET Mathematical Science Syllabus: 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.

CSIR NET Mathematics Syllabus in Hindi

यह लेख मुख्य रूप से सीएसआईआर नेट कार्यक्रम में करियर बनाने के इच्छुक उम्मीदवारों के लिए लिखा गया है। इस लेख में परीक्षा पैटर्न, सीएसआईआर नेट योग्यता की समीक्षा और प्रमुख विषयों सहित सीएसआईआर नेट गणित विज्ञान पाठ्यक्रम पर व्यापक जानकारी शामिल है। ए, बी, और सी सीएसआईआर नेट मैथमैटिकल साइंसेज परीक्षा के पेपर के तीन खंड हैं। सामान्य योग्यता प्रश्न अनुभाग ए में पाए जाते हैं, जबकि विषय-विशिष्ट प्रश्न अनुभाग बी और सी में पाए जाते हैं।

सीएसआईआर नेट गणितीय विज्ञान पाठ्यक्रम में निम्नलिखित विषयों को शामिल किया गया है:

  • विश्लेषण,
  • लीनियर अलजेब्रा,
  • जटिल विश्लेषण,
  • बीजगणित,
  • साधारण अंतर समीकरण (ओडीई),
  • आंशिक विभेदक समीकरण (पीडीई),
  • संख्यात्मक विश्लेषण,
  • विभिन्नताओं की गणना,
  • रैखिक अभिन्न समीकरण,
  • शास्त्रीय यांत्रिकी,
  • वर्णनात्मक सांख्यिकी,
  • खोजपूर्ण डेटा विश्लेषण

How to prepare CSIR NET Mathematics Syllabus

It is important to prepare a strategy to cover the whole syllabus of CSIR NET without any fallbacks. If you fail to cover any parts it may cost you a fortune in the exam. The CSIR NET Mathematics Preparation Tips are given below. 

  • Candidates must have a strong desire to keep up with their daily study hours, as this will provide them with the motivation to do so and the consistency to complete the syllabus without a 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 broken into sections based on the amount of time you have before the exam. If the applicants have six months to prepare, they should devote seven to eight hours per day to their studies. If the applicants only have two months to study, they should devote more time to it, perhaps 9 to 11 hours each day, with good strategy and study planning.
  • Candidate should a CSIR NET Mathematics previous year's paper to track their progress. 
  • Candidates should begin their preparation with the subject in which they are best. Candidates will be able to improve their skills in a subject in which they already perform best.
  • While studying and practicing for the CSIR NET Mathematical Science Syllabus, you must also take great care of yourself both emotionally and physically.

Best Books for CSIR NET Mathematical Science Syllabus

Aspirants are advised to check the important points that need to be finished by them during their preparation. These books are recommended by most experts. The Best Books for CSIR NET Mathematics Books are given in the table below.

Best Books for CSIR NET Mathematical Science Syllabus

Mathematical Analysis

S C Malik

Schaum's Outline of Linear Algebra, Sixth Edition

Seymour Lipschutz and Marc Lipson

Algebra: Abstract and Modern

Swamy and Murthy

Who must Check CSIR NET Mathematics Syllabus

After getting into the details of the CSIR NET Syllabus, let us have a look at the CSIR NET Eligibility Criteria for Mathematical Science exam mentioned below:

  • The candidate must have a post-graduate degree in science, such as an M.Sc./BS-MS/BS-4 Years/B-Tech degree/or any other similar qualification in the mathematics field.
  • All General applicants must be at least 28 years old, with three-year age relaxation for OBC candidates and five-year age relaxation for SC/ ST/ PwD/ Female candidates.
  • A Lecturership has no upper age limit.
  • To be eligible for the benefits, the person must be an Indian national.

CSIR NET Mathematical Sciences Syllabus- Weightage

Knowledge of the CSIR NET Exam Pattern is always important when it comes to passing any competitive exam. As a result, we've included the most recent CSIR NET Mathematical Sciences exam pattern below.

Please refer to the table below to know the total number of questions in each section.

Paper Sections

Questions Provided

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

Total Marks

200

Check Out:

CSIR NET Physics SyllabusCSIR NET Life Science Syllabus
CSIR NET Chemistry SyllabusCSIR NET Earth Science Syllabus

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FAQs

  • Latest CSIR NET Mathematics Syllabus 2022 has been released on the CSIR and NTA websites. This time the council has included 11 units in the syllabus of CSIR NET. The main topics are Analysis, Linear Algebra, Complex Analysis, Algebra, Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), etc.

  • The CSIR NET Mathematical Science PDF file can be downloaded using the direct link given here. The official website also has the CSIR NET Mathematical Science PDF. Download the syllabus pdf on your device to access it anytime you need it.

  • Candidates need to follow the study plan to cover the CSIR NET Mathematics Syllabus thoroughly. Experts have suggested good CSIR NET Mathematics Preparation Tips. Follow this strategy to get the desired result in the exam. The first step is to go through the syllabus and exam pattern after that you need to solve the CSIR NET Mathematics Question papers to know the level of questions.

  • It is vital to include the best CSIR NET Mathematics Books in the preparation otherwise you will end up wasting your time. Some of the good books are, Foundations of Functional Analysis by S. Ponnusamy, Contemporary Abstract Algebra by N L Carothers, Complex Variables and Applications by Ruel Churchill, James Brown, etc.

  • 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 are topics covered in the Calculus of variation section of the CSIR NET Syllabus for Mathematics.

  • यह लेख मुख्य रूप से सीएसआईआर नेट कार्यक्रम में करियर बनाने के इच्छुक उम्मीदवारों के लिए लिखा गया है। इस लेख में परीक्षा पैटर्न, सीएसआईआर नेट योग्यता की समीक्षा और प्रमुख विषयों सहित सीएसआईआर नेट गणित विज्ञान पाठ्यक्रम पर व्यापक जानकारी शामिल है। ए, बी, और सी सीएसआईआर नेट मैथमैटिकल साइंसेज परीक्षा के पेपर के तीन खंड हैं। सामान्य योग्यता प्रश्न अनुभाग ए में पाए जाते हैं, जबकि विषय-विशिष्ट प्रश्न अनुभाग बी और सी में पाए जाते हैं।

    सीएसआईआर नेट गणितीय विज्ञान पाठ्यक्रम में निम्नलिखित विषयों को शामिल किया गया है:

    • विश्लेषण,
    • लीनियर अलजेब्रा,
    • जटिल विश्लेषण,
    • बीजगणित,
    • साधारण अंतर समीकरण (ओडीई),
    • आंशिक विभेदक समीकरण (पीडीई),
    • संख्यात्मक विश्लेषण,
    • विभिन्नताओं की गणना,
    • रैखिक अभिन्न समीकरण,
    • शास्त्रीय यांत्रिकी,
    • वर्णनात्मक सांख्यिकी,
    • खोजपूर्ण डेटा विश्लेषण
  • 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, etc are topics covered in the Classic Mechanics Section of the CSIR NET Mathematical Science Syllabus.

  • Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel, etc are topics covered in the Linear Integrated Equations Section of CSIR NET Mathematical Science Syllabus. Check the detailed CSIR NET Exam Pattern for more clarity on the exam.

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