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# How to prepare CSIR Net for mathematics

Exam pattern

There is only one paper in CSIR net mathematics

There are three sections in the paper

Section      number of      no. of question      marks       time

Question         to be attempted

A                      20                           15                       30

B                      40                            25                      75

C                      60                            20                     95

Total                 120                                              200        3 hours

Syllabus for mathematics

Section A (Quantitative aptitude) – as per the all competitive exam

Section B and C(B.Sc. and M.Sc. mathematics ) –

1. Real Analysis – supremum and infimum, sequence and series and their convergence, limits and continuity, differentiability, uniform continuity, uniform convergence, power series, radius of convergence, Riemann integration,

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1. Linear Algebra  – vector spaces, sub-spaces, linear span, dependent and independent vectors, basis , dual basis, linear transformation, nullity and rank, linear operator, eigenvalues and eigenvectors, eigenfunctions, diagonalisation, matrices and system of linear equations, inner product space, characteristic polynomial, minimal polynomial, Jordan canonical form,

1. Abstract algebra – functions, binary operation,groups , subgroup, permutation group, normal group, homeomorphism, isomorphism, internal direct product, external direct product, rings, sub-rings, ideals, irreducibly, PID, fields, integrable domain, ED, Galois theorem,

1. Differential equation  – existence and uniqueness of solutions of first order ordinary differential equations, singular and particular solutions, system of first order ODE, homogeneous and non- homogeneous equations, variation of parameters, sturm – liouville boundary value problems, green’s functions

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1. Partial differential equations – Lagrange and char-pit methods for first order PDEs, Cauchy problems for first order PDEs, classification of second order PDEs, general solutions of higher order PDEs with constant coefficients, methods of separation of variables for laplace, heat and wave equation.

1. Numerical analysis _  numerical solutions of algebraic equations, newton raphson methods, rate of convergence, solution of system of algebraic equations using Gauss elimination and Gauss-seidal method, finite difference, Lagrange, Hermite and interpolation method, numerical differentiation and integration, numerical solutions of ODE using Pi-card, Euler and Runge-kutta methods

1. Calculus of variations – variation of a functional, Euler Lagrange equation, necessary and sufficient condition for extreme.

1. Linear integral equations – Fredholm and Volterra type integral equation of first and second type, kernels, characteristic number and eigenfunctions.

1. Probability and statistics – sample space, random variables, discrete and continuous probability, independent events, probability distribution function and cumulative distribution function, central limit theorems, Markov chains, methods of estimators, properties of estimators, test of hypotheses , chi – square test of goodness of fits, large sample fits etc.

Tips to crack CSIR net

• If you don’t want to read all these topics, read any three of the first 4 topics ( don’t leave linear algebra because it covers an average 60 – 70 marks
• Timing is not an issue in CSIR net, learn perfectly whatever do you learn
• Don,t leave section A completely. Give 15 – 20 minutes to this section and you can the about 10 questions in that time which covers 20 marks