CUET PG Maths Syllabus 2025: Download PDF

The common university entrance exam (postgraduate) for Mathematics will be conducted by National Testing Agency (NTA). The syllabus for this exam for the year 2025 will be released soon on the official website prepared by the agency ie pgcuet.samarth.ac.in.

The CUET PG Maths exam offers students a pathway to enroll in postgraduate mathematics programs at various universities across India. However, looking forward, the syllabus for 2025 is expected to align closely with the previous versions.

Candidates are encouraged to review the previous year syllabus to get a thorough idea of the frequently asked topics. The CUET PG Maths syllabus comprises fundamental subjects and topics that test candidates’ knowledge acquired during their undergraduate studies.

This syllabus is carefully structured to test the undergraduate coursework, covering essential areas commonly studied in a bachelor's mathematics program. For a detailed overview, please see the syllabus provided below.

CUET PG Maths Syllabus 2025: Overview

Applicants must check the highlights for the CUET PG 2025 syllabus mentioned in the tabular below. The table shared will help the candidates in learning the CUET syllabus in detail.

CUET PG Maths Syllabus Details 2025

The CUET PG syllabus 2025 for Maths comprises topics like Algebra, Real Analysis, Complex Analysis, Integral Calculus, Differential Equations, Linear Programming, and Vector Calculus.

Here below are the topic-wise details of the CUET PG Maths Exam.

Algebra

Applicants must check the detailed syllabus of the Algebra paper mentioned below.

Group Theory

• Groups, Subgroups, Abelian Groups, Non-Abelian Groups, Cyclic Groups, Permutation Groups
• Normal Subgroups, Lagrange’s Theorem, Group Homomorphism, Quotient Groups

Ring Theory

• Rings, Subrings, Ideals, Prime Ideals, Maximal Ideals
• Fields, Quotient Field

Linear Algebra

• Vector Spaces, Linear Dependence and Independence, Basis, Dimension
• Linear Transformations, Matrix Representation, Range Space, Null Space, Rank-Nullity Theorem
• Rank, Inverse of a Matrix, Determinant, Systems of Linear Equations, Consistency Conditions
• Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem
• Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Orthogonal, Unitary Matrices

Real Analysis

The detailed syllabus for the Real Analysis paper has been mentioned below for reference.

Sequences and Series

• Sequences and series of real numbers
• Convergent and divergent sequences, bounded and monotone sequences
• Convergence criteria for sequences of real numbers, Cauchy sequences
• Absolute and conditional convergence
• Tests of convergence for series of positive terms: comparison test, ratio test, root test
• Leibniz test for convergence of alternating series

Functions of One Variable

• Limit, continuity, differentiation
• Rolle's Theorem, Cauchy’s Theorem, Taylor's Theorem
• Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets
• Completeness of Power series, including Taylor's and Maclaurin's
• Domain of convergence, term-wise differentiation, and integration of power series

Functions of Two Real Variables

• Limit, continuity, partial derivatives, differentiability
• Maxima and minima, Method of Lagrange multipliers
• Homogeneous functions, including Euler's Theorem

Complex Analysis

Applicants must check the detailed Compex Analysis paper syllabus provided below.

• Functions of a complex variable
• Differentiability and analyticity
• Cauchy-Riemann Equations
• Power series as an analytic function
• Properties of line integrals
• Goursat's Theorem, Cauchy’s Theorem, consequences of simple connectivity
• Index of closed curves
• Cauchy’s Integral Formula
• Morera’s Theorem
• Liouville’s Theorem
• Fundamental Theorem of Algebra
• Harmonic functions

Integral Calculus

The detailed syllabus shared for the Integral Calculus paper will help the students prepare effectively for the paper.

Integration as the Inverse Process of Differentiation

• Integration reverses differentiation.

Definite Integrals and Their Properties

• Definite integrals calculate the area under a curve between two limits.
• Properties include linearity and additivity.

Fundamental Theorem of Integral Calculus

• Connects differentiation and integration, stating that the definite integral of a derivative gives the net change of the function.

Double and Triple Integrals

• Double Integrals: Integrate functions of two variables.
• Triple Integrals: Integrate functions of three variables.

Change of Order of Integration

• Allows for changing the order of integration in double integrals.

Calculating Surface Areas and Volumes Using Double Integrals

• Used for finding surface areas and volumes in two-dimensional space.

Calculating Volumes Using Triple Integrals

• Used for calculating volumes in three-dimensional space.

Applications

• Used to find areas, volumes, and average values.

Differential Equations

Students must check the Differential Quations paper syllabus provided below.

Ordinary Differential Equations (ODEs)

• First-order ODEs of the form.

Bernoulli's Equation

• A specific type of first-order differential equation that can be transformed into a linear form.

Exact Differential Equations

• Equations that can be expressed as a total differential, allow for direct integration.

Integrating Factor

• A function used to multiply a non-exact differential equation to make it exact.

Orthogonal Trajectories

• Curves that intersect a family of curves at right angles.

Homogeneous Differential Equations

• Equations that can be expressed in a separable form.

Separable Solutions

• Solutions are derived by separating variables and integrating them.

Linear Differential Equations

• Second-order and higher-order linear differential equations with constant coefficients.

Method of Variation of Parameters

• A technique for finding particular solutions to non-homogeneous linear differential equations.

Cauchy-Euler Equation

• A type of linear differential equation with variable coefficients that can be solved using specific methods.

Must Practice: CUET PG Previous Year Question Papers

Vector Calculus

The detailed syllabus of the Vector Calculus paper has been mentioned below.

Scalar and Vector Fields

• Scalar Fields: Functions that assign a single value (a scalar) to every point in space.
• Vector Fields: Functions that assign a vector to every point in space.

Gradient

• A vector that represents the rate and direction of change of a scalar field.

Divergence

• A scalar that measures the magnitude of a vector field's source or sink at a given point.

Curl

• A vector that measures the rotation of a vector field around a point.

Laplacian

• A scalar operator that combines divergence and gradient, providing information about the rate of change of a field.

Integrals

• Scalar Line Integrals: Integrate scalar fields along a curve.
• Vector Line Integrals: Integrate vector fields along a curve.
• Scalar Surface Integrals: Integrate scalar fields over a surface.
• Vector Surface Integrals: Integrate vector fields over a surface.

Theorems and Applications

• Green's Theorem: Relates line integrals around a simple closed curve to double integrals over the plane region it encloses.
• Stokes' Theorem: Relates surface integrals of vector fields to line integrals around the boundary of the surface.
• Gauss' Theorem (Divergence Theorem): Relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.

Linear Programming

Candidates must check the Linear Programming paper syllabus shared below for reference.

Convex Sets

• A set where any line segment connecting two points in the set lies entirely within the set.

Extreme Points

• Points in a convex set that cannot be expressed as a combination of other points in the set.

Convex Hull

• The smallest convex set contains a given set of points.

Hyperplanes and Polyhedral Sets

• Hyperplane: A flat affine subspace of one dimension less than its ambient space, used to separate different regions of space.
• Polyhedral Sets: Sets are defined by a finite number of linear inequalities, forming a polyhedron.

Convex and Concave Functions

• Convex Functions: Functions where the line segment between any two points on the graph lies above or on the graph.
• Concave Functions: Functions where the line segment between any two points on the graph lies below or on the graph.

Concept of Basis

• A set of linearly independent vectors that can be used to describe other vectors in the space.

Basic Feasible Solutions

• Solutions to a linear programming problem that satisfies all constraints and has many non-zero variables equal to the number of constraints.

Formulation of Linear Programming Problem (LPP)

• The process of defining a linear programming problem, including the objective function, constraints, and variables.

Graphical Method of LPP

• A visual approach to solving linear programming problems with two variables by graphing the constraints and identifying the feasible region.

Simplex Method

• An algorithm for solving linear programming problems, moving along the edges of the feasible region to find the optimal solution.

Adhering closely to the CUET PG maths syllabus will provide a comprehensive understanding of the fundamental concepts of mathematics covered in this course.

Mastery of these topics is crucial for developing strong analytical and problem-solving skills, which are applicable across various disciplines and real-world scenarios.

Covering the whole syllabus will not only lay a solid foundation for the future academic and professional world but will also allow you to score high in the CUET PG Mathematics Examination.

Also Read: CUET PG Exam Day Guidelines 2025

CUET PG Maths Syllabus 2025: Tips and Tricks

There is no specific guide to preparing for an examination. Students always have to figure out their weaknesses and work on their strengths.

However, here are some expert-curated tips and tricks to boost your preparation.

1. Familiarise Yourself with the Syllabus: Gain a clear understanding of the entire syllabus to prioritize your study topics based on their relevance and complexity.
2. Develop a Study Plan: Create a structured timetable that allocates sufficient time for each topic, ensuring you cover everything while also incorporating time for review.
3. Engage in Regular Practice: Work on a variety of mathematical problems to strengthen your grasp of concepts and enhance your ability to solve different types of questions.
4. Analyse Exam Conditions with Mock Tests: Take practice exams under timed conditions to familiarise yourself with the test format and improve your time management skills.
5. Consistent Review and Revision: Regularly revisit key concepts and formulas, and prepare concise summary notes for quick reference, especially as the exam date approaches.

Must Refer: CUET PG Exam Centres 2025

How to Download CUET PG Maths Syllabus 2025?

The CUET PG maths syllabus for the year 2025 will be released soon. Meanwhile, you can download the previous year's syllabus by following the steps given below.

1. Visit the Official Website: Go to pgcuet.samarth.ac.in.
2. Navigate to Syllabus Section: On the homepage, look for the "Syllabus" link. This is typically found in the main menu or under a section labeled “Information.”
3. Select Mathematics Syllabus: Within the syllabus section, search for "Mathematics (SCQP19)." This document specifically contains the syllabus for CUET PG in Mathematics.
4. Download the PDF: Click on the syllabus title to view or download the document in PDF format.

This syllabus document is provided by the National Testing Agency (NTA) and will outline all the topics covered in the CUET PG Mathematics exam.

Also Read: CUET PG Exam Pattern 2025