Content Writer | Updated On - Jul 22, 2024
CUET PG Mathematics Syllabus is released by NTA on its official website. The syllabus includes topics such as Algebra, Real Analysis, Linear Programming, Vector Calculus, Complex Analysis, Integral Calculus, and Differential Equations. Candidates preparing for the upcoming session can download the syllabus PDF from the below-given link and begin their preparation.
The syllabus is divided into seven parts, each focusing on a specific area of mathematics. Each unit covers subtopics, providing students a comprehensive understanding of the subject.
Coming to the important chapters, Real Analysis (12-14 questions), Complex Analysis (9 questions), Vector Calculus (11 questions), and Integral Calculus (approx 9 questions) carry high weightage as per the previous years’ analysis.
As per the exam pattern revised in 2024, the exam consists of 75 questions from the domain subject. Each question earns four marks, and there is a negative grading system, with one mark deducted for incorrect responses.
CUET PG Mathematics Syllabus 2025
| Unit | Topics |
|---|---|
| Algebra | Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphism and quotient groups, Rings, Subrings, Ideal, Prime ideal; Maximal ideals; Fields, quotient field. |
| - | Vector spaces, Linear dependence and Independence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, Skew symmetric, Hermitian, Skew-Hermitian, Orthogonal and Unitary matrices. |
| Real Analysis | 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, Leibnitz test for convergence of alternating series. |
| Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Cauchy’s Taylor's theorem. Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domain of convergence, term-wise differentiation and integration of power series. | |
| Functions of two real variable: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem. | |
| Complex Analysis | Functions of a complex Variable, Differentiability and analyticity, Cauchy Riemann Equations, Power series as an analytic function, properties of line integrals, Goursat Theorem, Cauchy theorem, consequence of simply connectivity, index of a closed curves. Cauchy’s integral formula, Morera’s theorem, Liouville’s theorem, Fundamental theorem of Algebra, Harmonic functions. |
| Integral Calculus | Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications. |
| Differential Equations | Ordinary differential equations of the first order of the form y'=f(x,y). Bernoulli's equation, exact differential equations, integrating factor, Orthogonal trajectories, Homogeneous differential equations-separable solutions, Linear differential equations 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 line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications. |
| Linear Programing | Convex sets, extreme points, convex hull, hyper plane & polyhedral Sets, convex function and concave functions, Concept of basis, basic feasible solutions, Formulation of Linear Programming Problem (LPP), Graphical Method of LPP, Simplex Method. |
CUET PG Mathematics 2025 Books
Please find below the books that will help you prepare for the next 2025 session.
1. “Introduction to Linear Algebra" by Gilbert Strang
This book offers a thorough introduction to linear algebra, a crucial mathematical subject, encompassing vector spaces, matrices, determinants, and eigenvalues, with numerous examples and exercises for practice and understanding.
2. “Real Analysis" by Royden and Fitzpatrick
This book offers a comprehensive introduction to real analysis, a crucial mathematical field, covering topics like sequences, limits, continuity, differentiation, and integration, with numerous examples and exercises for practice and understanding.
3. “Higher Engineering Mathematics” by B.S. Grewal
This popular postgraduate mathematics book covers calculus, differential equations, linear algebra, and complex analysis, making it a popular choice for students.
4. “Mathematical Analysis” by Tom M. Apostol
This book covers various mathematical topics like calculus, differential equations, and linear algebra, offering rigorous treatment and numerous practice problems and solutions.
5. "Advanced Engineering Mathematics" by Erwin Kreyszig
This book covers various mathematical topics like linear algebra, differential equations, complex analysis, and numerical methods, providing numerous examples and exercises for practice and understanding.
CUET PG Mathematics Previous Years Question Papers
CUET PG Mathematics question paper of the past years are provided here:
CUET PG Mathematics Question Paper 2023
CUET PG Mathematics was conducted in English and Hindi medium in 2 shifts. Check out the question paper of all the shifts provided below:
| Subject | Medium | Download Link |
|---|---|---|
| Mathematics | English | Check Here |
| Mathematics | Hindi | Check Here |
| Mathematics | English | Check Here |
| Mathematics | Hindi | Check Here |
CUET PG Mathematics Question Paper 2022
| CUET PG Mathematics Question Paper | Download Link |
|---|---|
| CUET PG Mathematics Question Paper 2022 | Check here |
Frequently Asked Questions
Ques. Can a Candidates apply in one more course other than Mathematics?
Ans. Yes, an applicant can apply for two (2) Test Papers by paying the application fee, and can apply for additional papers by paying the applicable fees.
Ques. How can I improve my CUET PG Mathematics 2025 preparation?
Ans. To master mathematics, it is essential to practice more than just studying the subject. Aspirants should list and remember numerous formulae, preparing a formulae chart and dedicate hours to studying them daily. Understanding the derivations and logic behind them is crucial for solving mathematical problems. While learning formulas may not be time-consuming, understanding and applying the logic behind them is essential for success in the examination.
Ques. What will be the Scheme of the CUET (PG) Mathematics 2025 examination?
Ans. The CUET (PG) Mathematics 2025 MCQ type exam will have 75 questions, with candidates having the option to choose up to four paper codes. The exam will last 105 minutes and will be conducted in English or Hindi. Correct answers will earn four marks, while wrong answers will result in one mark.
*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.
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