CSIR NET 2026 Mathematics Candidates Appeared

Below is the detailed breakdown of high-weightage and frequently repeated topics that candidates must master:
Linear Algebra & Real Analysis (Approx. 120 Marks)
Vector Spaces, Subspaces, Basis, and Dimension.
Linear Transformations, Rank-Nullity Theorem.
Eigenvalues, Eigenvectors, and Diagonalization.
Jordan Canonical Form, Quadratic Forms, and Inner Product Spaces.
Sequences and Series, Tests of Convergence.
Riemann Integration, Continuity, and Differentiability.
Uniform Convergence, Fixed Point Theorems, and Mean Value Theorems.
Complex Analysis & Modern Algebra (Approx. 75 Marks)
Analytic Functions and Cauchy-Riemann Equations.
Cauchy Integral Formula, Liouville’s Theorem, and Maximum Modulus Principle.
Laurent Series, Residue Theorem, and Contour Integration.
Group Theory: Cyclic Groups, Homomorphisms, Isomorphisms, and Sylow Theorems.
Ring Theory: Ideals, Principal Ideal Domain (PID), Unique Factorization Domain (UFD).
Field Extensions, Irreducibility Criteria, and Galois Theory.
Differential Equations, PDE & Numerical Analysis (Approx. 70 Marks)
Ordinary Differential Equations: Homogeneous and Non-Homogeneous Solutions.
Sturm-Liouville Boundary Value Problems and Green’s Function.
Partial Differential Equations: Heat, Wave, and Laplace Equations.
Lagrange’s and Charpit’s Methods.
Numerical Techniques: Newton-Raphson, Runge-Kutta, and Finite Difference Methods.
Vector Calculus, Topology & Probability (Approx. 50 Marks)
Divergence, Curl, and Gradient.
Green’s, Gauss’s, and Stokes’ Theorems.
Metric and Topological Spaces: Compactness, Connectedness, and Continuity.
Probability Distributions, Random Variables, Bayes’ Theorem, and Expectation.