CUET PG – Mathematics Syllabus 2026 Released

The CUET PG Mathematics syllabus (Paper Code: SCQP19) is comprehensive and strictly based on undergraduate-level Mathematics. As per the official NTA document, the syllabus includes the following major areas:
Algebra

Groups (subgroups, Abelian/non-Abelian, cyclic, permutation), normal subgroups, Lagrange’s Theorem (finite groups), group homomorphism, quotient groups. Rings (subrings, ideals, prime/maximal ideals), fields, quotient fields. Vector spaces (linear dependence/independence, basis, dimension), linear transformations (matrix representation, range/null space, rank-nullity theorem). Matrix algebra: Rank, inverse, determinants, solutions of linear equations (consistency), eigenvalues, eigenvectors, Cayley-Hamilton theorem. Special matrices: Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, unitary.

Real Analysis

Sequences and series of real numbers: Convergence/divergence, bounded/monotone sequences, Cauchy sequences, absolute/conditional convergence. Convergence tests: Comparison, ratio, root, Leibnitz (alternating series). Functions of one variable: Limits, continuity, differentiation, Rolle’s Theorem, Cauchy’s Mean Value Theorem, Taylor’s theorem. Topology of R: Interior points, limit points, open/closed/bounded/connected/compact sets, completeness of R. Power series (real variable): Taylor’s and Maclaurin’s series, domain of convergence, term-wise differentiation and integration.

Multivariable Calculus

Functions of two real variables: Limits, continuity, partial derivatives, differentiability, maxima and minima, method of Lagrange multipliers. Homogeneous functions and Euler’s theorem.

Complex Analysis

Functions of a complex variable, differentiability, analyticity, Cauchy-Riemann Equations. Power series as an analytic function, properties of line integrals, Goursat Theorem, Cauchy theorem (consequences of simply connectivity), index of a closed curve. Cauchy’s integral formula, Morera’s theorem, Liouville’s theorem, Fundamental theorem of Algebra. Harmonic functions.

Integral Calculus

Integration as inverse differentiation, definite integrals and properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration, applications to surface area and volume.

Differential Equations

First-order ODEs : Bernoulli’s equation, exact equations, integrating factor, orthogonal trajectories, homogeneous equations (separable solutions). Linear ODEs of second and higher order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.

Vector Calculus

Scalar and vector fields, gradient, divergence, curl, and Laplacian. Scalar/vector line and surface integrals. Green’s, Stokes’, and Gauss divergence theorems and their applications.

Linear Programming

Convex sets, extreme points, convex hull, hyperplanes, polyhedral sets, convex/concave functions. Concept of basis, basic feasible solutions. Formulation of LPP, Graphical Method, Simplex Method