Looking for **CUET (PG) mathematics syllabus** ? then here on examflame you will get CUET (PG) post graduate exam mathematics syllabus is details as provided by NTA . Alot of applicants looks for CUET (PG) syllabus to start their preparation of exam by understanding the areas where they need to study for solving the questions in exam . Download CUET (PG) official maths syllabus pdf below for free .

CUET (PG) stands for common university entrance test for postgraduate courses , It is a national level examination for candidates looking for admission in postgraduate (PG) courses of various central universities . The Common University Entrance Test (CUET) will provide a common platform and equal opportunities to candidates across the country .

In CUET (PG) Mathematics domain subject exam there will be 75 questions given in the questions paper . For every correct answer you will get 4 marks , for every incorrect answer 1 marks will be deducted as negative marking .For Un-answered/un-attempted response will be given no marks. The exam can be given in english or hindi language based on your choice .

**CUET (PG) Mathematics syllabus :**

The syllabus is divided into units as follows :

**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.

### Which are the participating Universities in the CUET (PG) 2023?

PARTICIPATING CENTRAL UNIVERSITIES:

1 Babasaheb Bhimrao Ambedkar University- Central University

2 Banaras Hindu University -Central University

3 Central Tribal University of Andhra Pradesh -Central University

4 Central University of Andhra Pradesh- Central University

5 Central University of South Bihar- Central University

6 Central University of Gujarat- Central University

7 Central University of Haryana- Central University

8 Central University of Himachal Pradesh -Central University

9 Central University of Jammu -Central University

10 Central University of Jharkhand- Central University

11 Central University of Karnataka -Central University

12 Central University of Kashmir -Central University

13 Central University of Kerala -Central University

14 Central University of Odisha -Central University

15 Central University of Punjab -Central University

16 Central University of Rajasthan- Central University

17 Central University of Tamil Nadu- Central University

18 (a) Indira Gandhi National Tribal University Amarkantak

(b)IGNTU-Regional Centre Manipur -Central University

19 Dr. Harisingh Gour Vishwavidyalaya- Central University

20 Guru Ghasidas Vishwavidyalaya -Central University

21 Hemvati Nandan Bahuguna Garhwal University- Central University

22 Jawaharlal Nehru University- Central University

23 Mahatma Gandhi Antarrashtriya Hindi Vishwavidyalaya -Central University

24 Manipur University -Central University

25 North Eastern Hill University -Central University

26 Pondicherry University -Central University

27 Sikkim University- Central University

28 Tezpur University -Central University

29 The English and Foreign Languages University -Central University

30 Tripura University -Central University

31 University of Hyderabad -Central University

32 Mahatma Gandhi Central University -Central University

33 Central Sanskrit University -Central University

34 National Sanskrit University -Central University

35 B.R. Ambedkar School of Economics University –State University

36 Madan Mohan Malviya University of Technology -State University

37 National Rail and Transport Institute- Deemed University

38 Dr. A.P.J Abdul Kalam Technical University- State University

39 Devi Ahilya Vishvavidyalaya -State University

40 Sardar Patel University of Police, Security and Criminal Justice- State University

41 Rajiv Gandhi National Institute of Youth Development- Central University

42 Apex University- State University

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