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**CSIR NET Syllabus Mathematical Science PDF 2022 (Latest) download**

Table of Contents

**CSIR NET Mathematical Science Latest Syllabus 2022 PDF :** The Council of Scientific & Industrial Research (CSIR) has announced the CSIR NET Syllabus 2022 on its main web portal, i.e., csirnet.nta.nic.in. The CSIR 2022 NET Syllabus can be accessed from their website and also it is available in PDF format So, Candidate can download in a PDF format so that candidates can make use of it without the Internet connection as well.

Every year NTA counduct this CSIR NET 2022 **Mathematical** Science exam in the Month of February . And As per the official notice, the NTA shall be conducting the Joint CSIR-UGC NET **Mathematical** Science 2022 on the scheduled date, i.e., February 5 and 6, 2022. That means only a few days have left. Therefore, we suggest all registered candidates prepare for the NET as early as possible using the detailed syllabus provided on this page below.

To increase the odds of being selected for the fellowship, lectureship, etc., all aspirants must get their hands on the subject-wise syllabus laid down in this all-inclusive article. In addition to offering the comprehensive CBT syllabus, we have also CSIR NET **Mathematical** science Exam Pattern 2022 so aspirants could score good marks on the test. The registered exam-takers must utilise the syllabus on this page and develop the best well-thought-out, exam-taking strategies to get the upper hand over the competition. Continue reading to find out which section of the syllabus the aspirants need to focus on first.

**CSIR NET Mathematical Science Eligibility Criteria 2022:**

On their official website, the NTA has released the CSIR NET eligibility criteria. The new CSIR NET Exam dates have been set for February 15th and 18th, 2022. Interested candidates should check this website regularly for changes in CSIR NET eligibility for the year 2022. Candidates can find all necessary information on the CSIR NET eligibility criteria in this article.

### CSIR NET Mathematical Science Eligibility full Details 2022

To apply for the CSIR NET **Mathematical** Science exam, candidates are required to meet all CSIR NET eligibility criteria required for the exam. CSIR NET **Mathematical** Science is conducted to select the candidates for the position of Lectureship and Junior Research Fellowship. Eligible candidates can apply for the CSIR NET Exam as per the application form date.

The detailed CSIR NET eligibility criteria include age limit, relaxation, and educational qualification. Candidates must also check the subject-wise educational eligibility before applying online. It is important to abide by the CSIR NET Eligibility 2022 for **Mathematical** Science before the exam as it will prevent last-stage disqualification.

### CSIR NET 2022 Educational Qualification

1. M.Sc or equivalent degree/Integrated BS-MS/BS-4 years/BE/BTech/BPharma/MBBS with at least:

**55% marks**for**General and OBC**candidates.**50% marks for SC/ST/PwD**candidates.

2. Students enrolled for M.Sc or completed 10+2+3 years as on the closing date of online submission of the application form, under the **Result Awaited (RA)** category. Candidates will need to submit the attestation form which is duly certified by the Head of the Department.

3. B.Sc (Hons) or students enrolled in **Integrated MS-PhD program** with at least:

**55% marks**for General/OBC candidates.**50% marks for SC/ST/**PwD candidates.

4. Candidates having a bachelor’s degree will be eligible for **CSIR fellowship** only after getting enrolled for a Ph.D. within the validity period of two years. Students who have Bachelor’s degree are eligible to apply only for Junior Research Fellowship (JRF) and not for Lectureship (LS).

5. Ph.D. degree holders who have passed Master’s degree before 19th September 1991 having at least **50% marks** are eligible to apply for CSIR NET Exam for Lectureship only.

## CSIR NET 2022 Age Limit and Relaxation

1. For **JRF (NET):**

- Maximum 28 years as on 01-01-2021
- Maximum 33 years as of 01-01-2021 for SC/ST/Persons with Disability(PwD)/female applicants
- Maximum 31 years as of 01-01-2021 for OBC (Non-Creamy Layer) applicants.

2. For **Lectureship (NET)**: No upper age limit

## CSIR NET 2022 Exam Overview

Before getting into the details of the CSIR NET Syllabus, let us have a look at the overview of the CSIR NET exam mentioned below:

Name of the Exam | CSIR NET Mathematical Science |

Conducting Body | National Testing Agency (NTA) |

Purpose of Exam | Junior Research Fellowship (JRF) and Lectureship (LR) |

Mode of Examination | Computer Based Test (CBT) |

Number of Subjects | Five |

Exam Sections | Three Parts – Part A, Part B and Part C |

Duration of Exam | 3 Hours |

Medium of Exam | English and Hindi |

Maximum Marks | 200 |

Negative marking | Marks deducted for every wrong answer |

Official Website | csirnet.nta.nic.in |

**CSIR NET Syllabus For Part A**

The CSIR NET Part-A Syllabus is common for all papers. It has two sections, reasoning, and quantitative aptitude. The important topics for both sections are mentioned below.

**Reasoning:**

- Blood Relationships
- Arrangements
- Analytical Reasoning
- Syllogisms
- Analogies
- Directions
- Coding-Decoding
- Statements
- Data Sufficiency
- Non-verbal Reasoning
- Visual Ability
- Graphical Analysis
- Classification
- Alphabet Series
- Symbols and Notations
- Similarities and Differences
- Number Series
- Data Analysis

**Quantitative Reasoning & Analysis**

- Simplifications
- Number System
- Average
- Algebra
- Percentage, Time & Work
- Simple & Compound Interest
- Time & Speed
- HCF, LCM Problems
- Area
- Profit & Loss
- Bar Graph, Pictorial Graph, Pie Chart
- Ratio & Proportion
- Permutation & Combination

**CSIR NET 2022 Exam Pattern – Mathematical Sciences**

In **Mathematical** Sciences paper, there will be a total of 120 multiple choice questions, out of which candidates have to attempt only 60 questions.

**Part A, B, and C will have 20, 40 and 60 questions wherein candidates have to attempt a maximum of 15, 25 and 20 questions respectively.**- Each question will have four alternatives or responses, only one of them will be the correct answer.
- Questions in Part A, B and C will carry 2, 3 and 4.75 marks respectively.
**There is a negative marking**in Part A, B and C**of 0.5, 0.75 and 0 marks for each incorrect answers.**

The table below explains the section-wise exam marking scheme for **Mathematical** Sciences:

Section | Part A | Part B | Part C | Total |

Total Questions | 20 | 40 | 60 | 120 |

Maximum Number of Questions to Attempt | 15 | 25 | 20 | 60 |

Marks for each correct answer | 2 | 3 | 4.75 | 200 |

Negative Marking | 0.5 | 0.75 | 0 | – |

Maximum Marks | 30 | 75 | 95 | 200 |

**CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer-ship**

**COMMON SYLLABUS FOR PART ‘B’ AND ‘C’**

**MATHEMATICAL SCIENCES**

**CSIR NET Mathematical Science Latest Syllabus PDF 2022**

**UNIT – I**

**Analysis: **Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum.

Sequences 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.

Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral.

Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems.

Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.

**Linear Algebra:** Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations.

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 – II**

**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, Sylow theorems.

Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain.

Polynomial rings and irreducibility criteria.

Fields, finite fields, field extensions, Galois Theory.

**Topology:** basis, dense sets, subspace and product topology, separation axioms, connectedness and compactness.

**UNIT – III**

**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, system of first order ODEs.

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 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 – IV**

Descriptive statistics, exploratory data analysis

Sample space, discrete probability, independent events, Bayes theorem. Random variables and distribution functions (univariate and multivariate); expectation and moments. Independent random variables, marginal and conditional distributions. Characteristic functions. Probability inequalities (Tchebyshef, Markov, Jensen). Modes of convergence, weak and strong laws of large numbers, Central Limit theorems (i.i.d. case). Markov chains with finite and countable state space, classification of states, limiting behaviour 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.

Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses. Analysis of variance and covariance. Fixed, random and mixed effects models. Simple and multiple linear regression. Elementary regression diagnostics. Logistic regression.

Multivariate normal distribution, Wishart distribution and their properties. Distribution of quadratic forms. Inference for parameters, partial and multiple correlation coefficients and related tests. Data reduction techniques: Principle component analysis, Discriminant analysis, Cluster analysis, Canonical correlation.

Simple random sampling, stratified sampling and systematic sampling. Probability proportional to size sampling. Ratio and regression methods.

Completely randomized designs, randomized block designs and Latin-square designs. Connectedness and orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction. Hazard function and failure rates, censoring and life testing, series and parallel systems.

Linear programming problem, simplex methods, duality. Elementary queuing and inventory models. Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.

All students are expected to answer questions from Unit I. Students in mathematics are expected to answer additional question from Unit II and III. Students with in statistics are expected to answer additional question from Unit IV.

Candidates can download the **CSIR NET Mathematical Science Latest Syllabus PDF 2022** from the below:

**CSIR NET Mathematical Science 2022 Important Instructions**

The important instructions related to CSIR UGC NET 2022 are as follows:

- List of candidates registered for this test will be made available on the official website. Aspirants must refer to the website for checking their registration and for time to time updates.
**The Question paper will be set in Hindi and English Version. Candidate opting for Hindi medium in the Application Form will be displayed questions in both English and Hindi whereas candidates opting for English medium will be asked questions in English Version only.**- The actual number of questions in each Part and Section to be asked and attempted may vary from subject to subject.
**No candidate shall be permitted to leave the Exam Hall before completion of 3 hours from the start of the exam.**- Candidates must carry
**CSIR NET Admit Card**and an original photo Id proof and two passport size photos.

### Can I give CSIR NET after BSC?

CSIR UGC NET Eligibility

M.Sc. or equivalent degree/ Integrated BS-MS/BS-4 years/BE/B. … Candidates with Bachelor’s degree will be eligible for CSIR fellowship only after getting registered/enrolled for **Ph.** **D/Integrated Ph**. D program within the validity period of two years.

### Is CSIR NET syllabus changed?

No, **exam authorities do not change the CSIR NET** Exam Syllabus every year.

### What is a good score in CSIR NET?

CSIR NET Cutoff is the minimum marks on which selection of candidates for JRF and Lectureship will be based. The minimum benchmark to qualify CSIR NET exam is **33% for General, EWS and OBC category** and 25% for SC, ST and PwD candidates.

**Is there any negative marking in CSIR NET Exam?**

Yes, there is negative marking schemes for each part. Please check out the article above for a subject-wise making scheme

### How many paper are there in CSIR NET?

There are 3 parts in all the five sections of Chemical Science, Earth Science, Life Science, Mathematical Science, and Physical Science.

### Who prescribes the CSIR NET syllabus?

The Council of Scientific and Industrial Research (CSIR) Human Resource Development Group (HRDG) prescribes the CSIR NET syllabus for all papers and subjects.

### Is section A of the CSIR NET examination common for all the candidates?

Yes, the section A is common for all the candidates

### How many marks are allotted to CSIR NET written examination?

A total of 200 marks are allotted to the CSIR NET written examination

### What are the important topics for Mathematics in CSIR NET Syllabus 2021?

Some of the important topics are mentioned below Complex Analysis Linear Algebra Algebra Linear Integral Equations

Now that you know everything about **CSIR NET Mathematical** Science **Syllabus 2022** and CSIR NET Exam Pattern, you must start preparing for the CBT by covering each topic laid out above. We hope this detailed article on CSIR NET Syllabus helps you. It’s high time and, therefore, you must stay focused while preparing for the CSIR NET 2022.

The CSIR NET exam for all subjects has a section for aptitude based questions.

*If you have any doubts regarding the CSIR NET Syllabus or the exam in general, drop down your queries in the comment section provided below. We will get back to you as early as possible.*

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