By Renuka Miglani|Updated : June 6th, 2023

Knowledge of the CSIR NET Syllabus Mathematics 2023 is vital for preparing for the CSIR NET Mathematical Science exam. Candidates who are aiming to clear the exam on their first attempt must go through the important topics provided below. This will help them formulate a good study plan around the CSIR NET Mathematical Science Syllabus.

Candidates should begin preparing systematically for the exam with the help of the CSIR NET Syllаbus Mathematics PDF. Candidates can check the syllabus in Hindi also. The exam is conducted twice a year, and the CSIR NET Maths Syllabus is divided into three Parts - A, B, and C. In this article, aspirants can find the comprehensive syllabus and refer to it to create a proper preparation strategy.

CSIR NET Exam Analysis 2023:

## CSIR NET Mathematics Syllabus 2023

The CSIR NET Syllabus Mathematics consists of essential topics like Analysis, Linear Algebra, Partial Differential Equations, Numerical Analysis, Calculus of Variations, Linear Integral Equations, etc. The Human Resource Development Group of the Council of Scientific and Industrial Research (CSIR) has prescribed the CSIR NET Mathematics Syllabus. A, B, and C are the three sections of the examination process. The syllabus for Part A is common, while Parts B and C are subject-specific. To prepare for the CSIR NET exam, candidates should go over the syllabus and reference material well ahead of time.

In the CSIR NET Mathematics paper, each incorrect answer will receive a negative marking of 25% in Part A, and Part B and there is no negative marking for Part C. Candidates will get a total of 3 hours to attempt the paper. The syllabus will assist all candidates in developing an effective preparation approach. Candidates can check the detailed CSIR NET Maths Syllabus and can download the PDF from the direct link provided below.

CSIR NET Memory Based Question Papers 2023:

## Important Topics in CSIR NET Mathematics Syllabus

A detailed CSIR NET Syllabus of Mathematical Science will help the students to score better in the CSIR NET and also present better clarity of the topics to be covered. The CSIR NET Mathematics section includes:

• 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

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

Furthermore, the CSIR NET Maths syllabus PDF ensures that candidates do not miss any important topics or sub-topics while studying. Hence, it is always a good idea to have the PDF open while preparing as you can easily cross-check the topics and decide what to pick.

## 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. Candidates can check the detailed CSIR NET Mathematics Syllabus for Parts A, B, and C in the table below.

### CSIR NET Mathematics Syllabus for Part A

Candidates can check the CSIR NET Mathematics Syllabus of Part A, which is General Aptitude in the table below.

 Units Topics Graphical Analysis & Data Interpretation Pie-Chart Line and 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 and Part C

Candidates can check the CSIR NET Mathematical Science Syllabus for Part B and Part C in the table below.

 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 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, Maximummodulus 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, 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. 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, 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, 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 CSIR NET 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 CSIR NET Mathematics Syllabus 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 CSIR NET Mathematical Science 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.
• Candidates should have a CSIR NET Mathematics previous year papers 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, candidates must also take great care of themselves both emotionally and physically.
 CSIR NET Subject wise Previous Year Question Papers CSIR NET Life Science Question Papers CSIR NET Chemical Science Question Papers CSIR NET Earth Science Question Papers CSIR NET Physics Question Papers

## Best Books for CSIR NET Syllabus Mathematics

Aspirants are advised to check the important books that need to be referred by them during their preparation. These books cover the entire CSIR NET Mathematics Syllabus and 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

## CSIR NET Mathematical Sciences Syllabus Weightage

Knowledge of the CSIR NET Exam Pattern is always important when it comes to passing any competitive exam. Candidates can check the CSIR NET Mathematics Exam Pattern in the table below

 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

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## FAQs on CSIR NET Syllabus Mathematics

• The latest CSIR NET Syllabus Mathematics 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 syllabus PDF for the CSIR NET Mathematical Science can be downloaded using the direct link provided below. The official website also provides a PDF for the reference of aspiring candidates. Download the CSIR NET Maths 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 Books in your preparation otherwise you will end up wasting your time. Some of the good books recommended by experts are Foundations of Functional Analysis by S. Ponnusamy, Contemporary Abstract Algebra by N L Carothers, Complex Variables and Applications by Ruel Churchill, and 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.

• 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 Syllabus Mathematics.

• 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 the CSIR NET Mathematical Science Syllabus.

• The CSIR NET syllabus Mathematics covers a wide range of topics in mathematics, including calculus, algebra, real analysis, complex analysis, linear algebra, topology, differential equations, discrete mathematics, and numerical analysis. Ultimately, the level of difficulty can vary from person to person based on their individual strengths and weaknesses in mathematics.

• Covering the entire CSIR NET Maths syllabus in just three months can be a challenging task, but it is not impossible. Break down the syllabus into manageable sections and create a study plan that allocates specific time slots for each topic. Solve previous years' question papers to familiarize yourself with the exam pattern and attempt CSIR NET Mock tests to assess your progress on every step.

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