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:
- Linear Algebra
- Complex Analysis
- 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.
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
Line & Bar Chart
Mode, Median, Mean
Measures of Dispersion
Clock and Calendar
Direction and Distance
Coding and Decoding
Ranking and Arrangement
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
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.
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
Algebra of complex numbers, the complex plane, polynomials, power series,
Analytic functions, Cauchy-Riemann equations.
Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum
Taylor series, Laurent series, calculus of residues.
Conformal mappings, Mobius transformations.
Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle,
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.
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
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
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.
Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s
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:
- लीनियर अलजेब्रा,
- जटिल विश्लेषण,
- 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
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.
Marks for Each Section
Marks Per Question
|CSIR NET Physics Syllabus||CSIR NET Life Science Syllabus|
|CSIR NET Chemistry Syllabus||CSIR NET Earth Science Syllabus|
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