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GATE-2021 Mathematics(MA) Modified Syllabus (New)

Note: The syllabus of GATE-2021 has been revised. New Syllabus is presented here. (Check Old Syllabus of GATE-2020)

Calculus: Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

Abstract Algebra: Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Group action,Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.

Linear Algebra: Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial, Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.

Complex Analysis: Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.

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Free Test Series for CSIR-NET, SET, GATE, PSC

We have started providing topic-wise FREE test series for CSIR-NET, GATE, SET Aspirants. After the topic-wise test, we will start full tests. Test your knowledge here.


  1. The result will be released on 08:00 PM on respective days of tests. The result will be sent on your email id which you will enter in a test.
  2. Related information will be shared on Telegram Channel: https://t.me/pkalika_mathematics
  3. We welcome those who are interested in questions setting for a test, write to us on maths.whisperer@gmail.com.
  4. Next Test: ODE+PDE+COV+IE Test-1 on 30/05/2020
  5. Next Test: Abstract Algebra on 01/06/2020

CSIR-NET, SET & PhD Entrance Test(07/06/2020): Attend Test

Algebra(Abstract+Linear) Tests:-

Analysis(Real+Complex) Tests

  • Complex Test-1(28/05/20): Attend Test-1
  • Complex Test-2: – – – – – – – – – – –

Applied Part(ODE+PDE+LPP+NA) Tests

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CSIR-NET Exam Tricks for Qualifying

Exam Tips:
Try to solve all previous year questions of CSIR-NET and GATE exam. By doing this, you will get an idea about the important and scoring topics of CSIR-NET. Also during the Study of any study materials, prepare your own short/quick revision notes(of 3 or 4pages) on each topic, So that at the time of examination you may do a quick revision.

Now, stop reading books and start solving problems of previous year CSIR-NET exams. Also, analyze yourself that in which topics you can gain marks easily, and make them stronger.

Not only read theory & solve problems but also make a strategy for the exam a/c to your strong points & preparation.

Keep in mind that, it is not necessary to solve all problems in an exam, your guessing power should also be strong which comes by solving a lot of problems. So that you can easily discard the wrong options and can identify correct options.Tips for NETGate

Numerical Analysis, Dynamical System & Markov Chain:  These are easy and scoring topics for NET. So complete them first. You may practice and solve all problems of NET from these topics within about 1 day.

Note: All the above mentioned topics may be practiced and solved in a maximum of 2 or 3 days.

Important Topics and Marks weightage for Upcoming CSIR NET Exam

NET Marks wt_1

Also, during study/practice make a chart of important key points for quick revision in the last days of preparation. Here is a sample (Sample PDF download).MarksDistribution

CSIR-NET Cut off analysis and setting up the target for You

Important links:  Quick revision Notes for CSIR-NET, GATE & SET exam and Study Materials for NET/GATE/SET/ JAM/PhD

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Practice Set For NET, GATE, SET, JAM

Topic-wise Practice Set/Que for CSIR-NET, GATE, SET

Previous Yr. Que. Papers Collection

  1. MSc Entrances, JAM, BHU, CUCET, …etc
  2. PhD Entrances, CUCET, GATE, NBHM, IIT, …etc
  3. CSIR-NET Mathematics

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If you wish to donate Practice Sets/Que or Need any help or suggestions, write us on help@pkalika.in