CUET PG Mathematics Syllabus 2025

The syllabus for CUET PG Mathematics (SCQP19) covers a wide range of topics from algebra, analysis, calculus, complex analysis, and applied mathematics. Below is a detailed breakdown of the key areas:
Algebra
Groups, subgroups, Abelian and non-Abelian groups, cyclic groups, permutation groups
Normal subgroups, Lagrange’s Theorem, group homomorphisms, and quotient groups
Rings, subrings, ideals, prime ideals, maximal ideals, fields, and quotient fields
Understanding these topics is crucial for dealing with abstract structures in mathematics. The study of groups and rings forms the foundation for advanced topics such as topology and field theory. Mastering algebra requires problem-solving abilities and a deep understanding of mathematical proofs. Candidates should practice problems from well-known textbooks and previous years’ question papers to strengthen their grasp of the subject.
Linear Algebra
Vector spaces, linear dependence and independence, basis, dimension
Linear transformations, matrix representation, range space, null space, rank-nullity theorem
Determinants, eigenvalues, eigenvectors, Cayley-Hamilton theorem
Types of matrices: symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, unitary
Linear algebra plays a crucial role in various applications, from physics to computer science. The study of eigenvalues and eigenvectors is fundamental in solving differential equations and performing matrix decompositions. Candidates must ensure they develop a strong conceptual understanding of vector spaces and linear transformations. Practicing matrix operations and solving system-of-equation problems will significantly enhance problem-solving skills.
Real Analysis
Sequences and series, convergence and divergence, monotonic sequences
Convergence criteria, Cauchy sequences, absolute and conditional convergence
Tests for series convergence: comparison test, ratio test, root test, Leibnitz test
Functions of one and two variables, limits, continuity, differentiation
Rolle’s theorem, Cauchy’s theorem, Taylor’s theorem, power series, and their properties
Real analysis is essential in understanding the fundamental principles of calculus and mathematical reasoning. This area deals with the behavior of functions, their continuity, and differentiability. Candidates must focus on understanding the concept of limits and continuity before moving on to differentiation and integration. A strong command over series and sequence convergence tests is essential for solving analytical problems efficiently.
Complex Analysis
Functions of a complex variable, differentiability, analyticity, Cauchy-Riemann equations
Power series, line integrals, Goursat’s theorem, Cauchy’s integral theorem and formula
Morera’s theorem, Liouville’s theorem, Fundamental Theorem of Algebra
Harmonic functions and their applications
Complex analysis extends calculus into the complex plane, allowing for deeper exploration of function theory. The subject is fundamental in areas such as fluid dynamics, quantum mechanics, and engineering. Understanding Cauchy’s integral formula and the concept of analytic functions will help candidates tackle various problem types in this area. Practicing contour integration and theorem applications will strengthen their ability to work with complex functions.
Integral and Differential Calculus
Definite integrals, fundamental theorem of integral calculus
Double and triple integrals, change of order of integration, surface areas, and volume calculations
First-order differential equations: Bernoulli’s equation, exact differential equations, integrating factors
Higher-order linear differential equations with constant coefficients, method of variation of parameters
Cauchy-Euler equation, orthogonal trajectories
Integral and differential calculus are widely used in engineering, physics, and economics. Mastery of these concepts enables candidates to solve practical problems related to rates of change and accumulation. Candidates should focus on understanding integration techniques, the applications of differentiation, and solving differential equations efficiently. Practice is key to mastering this section.