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The syllabus for the entrance exam of M.Sc in Mathematics at Mahatma Gandhi Kashi Vidyapith (MGKVP) can vary from year to year. It is advisable to refer to the official website or information brochure of MGKVP for the most accurate and updated syllabus. However, I can provide you with a general overview of the topics that are commonly covered in the entrance exam for M.Sc in Mathematics. Here are the main subject areas typically included:

1. Calculus: Limits, continuity, differentiation, integration, differential equations, sequences and series.

2. Algebra: Sets, relations, functions, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, quadratic forms.

3. Real Analysis: Real numbers, sequences and series, limits, continuity, differentiability, Riemann integration, convergence criteria.

4. Complex Analysis: Complex numbers, complex functions, analytic functions, contour integration, power series, residues, conformal mappings.

5. Linear Algebra: Vector spaces, linear independence, bases, dimension, inner product spaces, eigenvalues and eigenvectors, diagonalization.

6. Differential Equations: Ordinary differential equations, partial differential equations, methods of solving differential equations, boundary value problems.

7. Probability and Statistics: Probability spaces, random variables, probability distributions, expectation, conditional probability, statistical inference.

8. Number Theory: Prime numbers, divisibility, congruences, modular arithmetic, number-theoretic functions, continued fractions.

9. Numerical Analysis: Numerical methods for solving equations, interpolation, numerical differentiation and integration, numerical solutions of differential equations.

10. Mathematical Logic: Propositional logic, first-order logic, logical reasoning, proof techniques.

Please note that the above-mentioned topics provide a general overview and the actual syllabus may contain additional or slightly different topics. It is recommended to refer to the official website or information brochure of MGKVP for the detailed and updated syllabus.

Additionally, it would be beneficial to thoroughly study your undergraduate mathematics curriculum and textbooks, practice solving previous year's question papers, and take mock tests to familiarize yourself with the exam pattern and improve your problem-solving skills.

Good luck with your entrance exam preparation for M.Sc in Mathematics at MGKVP!