CSIR NET Mathematical Sciences

CSIR NET Mathematical Sciences Syllabus 2020 | Books, Study Materials & Papers

CSIR NET Mathematical Sciences

CSIR NET Mathematical Science Exam to be conducted on 21st June 2020, the Preparation for the Exam Starts with Thourough understanding of CSIR NET Mathematical Syllabus and Exam pattern. Mathematical Sciences Deals with formulating theories and result-driven techniques for mathematical calculations. If you Are you preparing for the CSIR NET Mathematical Science Exam 2020, then here we have latest syllabus and Exam Pattern in Detail.

CSIR NET Mathematical Sciences

If you are dreaming of building your career in the Mathematics Field, then you must appear in the CSIR NET Mathematical Science Exam. It is conducted twice a year. After qualifying CSIR NET Mathematical Science, you will get tremendous chances for job and research opportunities across India.The next CSIR NET Exam for Mathematical Sciences has been scheduled on 21st June 2020.

CSIR NET Mathematics Eligibility Criteria

Before applying for the exam, you should be very well aware of the CSIR NET Mathematics eligibility criteria. Without fulfilling the eligibility criteria, you cannot appear in the exam.

  • You must have an MSc or equivalent degree/Integrated BS-MS/BS-4 years/BE/BTech/BPharma/MBBS degree or B.Sc (Hons) or equivalent degree or students enrolled in Integrated MS-PhD program with an aggregate marks of 55% for General and OBC categories and 50% for SC/ST/PwD candidates.
  • You should have a Bachelor’s Degree. Then you will be eligible for the Fellowship only if you have enrolled for a Ph.D./Integrated Ph.D. program within the validity period of two years.

Age Limit: The upper age limit to appear for the exam is 28 years. The age relaxation is applicable as per government rule.

CSIR NET Maths Syllabus and Exam Pattern

You should know the CSIR NET Syllabus for Mathematics to start solid exam preparation. You should have adequate knowledge about the topics to cover from the CSIR NET Syllabus Mathematics PDF.

CSIR NET Mathematical Science Exam Pattern

For Creating a better strategic plan for the CSIR NET Mathematics exam, you should be aware of the latest exam pattern and marks distribution for various unites to understand the paper format in a very well. An exam pattern will let you know the time duration and number of questions asked in the exam. 

Please check the CSIR NET Mathematics Exam pattern given below.

S.No.

Sections

No. of Ques. Given

No. of Ques. to be Attempted

Marks

Neg. Marking

Duration of Exam

1

PART-A

20

15

30

0.5

3 Hours

2

PART-B

40

20

75

0.75

3

PART-C

60

20

95

0

TOTAL MARKS

200

Detailed CSIR NET Syllabus for Mathematical Sciences

You can see that in CSIR NET Mathematical Sciences Syllabus has four units. Aspiring candidates have to start their preparation now it self since It is tough to cover the vast syllabus for CSIR NET Mathematical Sciences in a short span of time. You should start preparing for the exam as soon as possible. 

Here you can find some important topics for the preparation.

  • Linear Algebra
  • Real Analysis
  • Ordinary and Partial differential equation
  • Modern Algebra
  • Complex Analysis

Check Detailed Unit-wise syllabus of CSIR NET Mathematical Sciences is tabulated below:

Units

CSIR NET Mathematical Sciences Syllabus

Unit 1

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, Differentiability, Mean value theorem, Sequences, and series. Functions of several variables, Metric spaces, compactness, connectedness. Normed Linear Spaces.

Linear Algebra: Vector spaces, algebra of linear transformations. Algebra of matrices, 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.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, Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots, Cayley’s theorem, Sylow theorems. Rings, ideals, prime and maximal ideals, quotient rings, unique factorization 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 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, the system of first-order ODEs.

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, 

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, the theory of small oscillations. 

Unit 4

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.

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, Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses. Analysis of variance and covariance. Simple and multiple linear regression, Multivariate normal distribution, Distribution of quadratic forms. 

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.

 

Download CSIR NET Mathematical Sciences Syllabus PDF

CSIR NET Mathematical Science Books and Study Material

You will find the huge number of books for CSIR NET Mathematical Sciences. But you have to choose wisely the best study materials for CSIR NET Mathematical Science to clear your concept. By picking any random book, you will be losing the chance to crack the exam.

Some best books are as given below.

CSIR NET Mathematical Sciences Reference Books

Topics

Authors

Real Analysis

H.L. Royden

Linear Algebra

Hoffman and Kunze

Complex Analysis

R.V.Churchill

Algebra

Joseph A. Gallian

Topology

G .F. Simmons

Ordinary & Partial Differential Equations

M.D. Rai Singhania

Numerical Analysis

Jain and lyenger

Calculus of Variations

A. S. Gupta

Linear Integral Equations

Shanti Swarup

Classical Mechanics

H. Goldstein

Statics

S. C. Gupta

Kopykitab’s Special Study Package To Boost Your Preparation

To boost your CSIR NET preparation, we are also providing the best . With the package, you will get, 

  • Latest Syllabus
  • Topic-wise Online Tests
  • Study Material eBooks
  • Previous Year Papers 2012-2019

CSIR Study Packages

CSIR NET Previous Years Question Papers For Mathematics

Along with the study of every section, you should start solving previous year question papers. It will give you the brief idea of the exam and time management.

It will also boost up your speed and accuracy while solving the CSIR NET Mathematics Questions. You will have an exact idea about the format of the questions and marking scheme as well.

Career Scope After Qualifying CSIR NET Mathematical Sciences

You will get tremendous career opportunities after passing the CSIR NET Mathematical Sciences 2020 and opportunities after passing the exam.

  • For JRF exam: You will be eligible to perform research in any of the CSIR Laboratories.
  • For Assistant Professor exam: You will be recruited as a lecturer to teach University level students.

Apart from the above, you will also get a chance to work in various private and government organizations.

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