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Re: DU MSC Entrance Exam Syllabus
please tell me the entrance exam date for msc from DU on sonibhardwaj54@gmail.com 
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Re: DU MSC Entrance Exam Syllabus
As you are looking for the Entrance Examination Syllabus of M.Sc Mathematics for University of Delhi, so here I am sharing the same with you Entrance Examination Syllabus of M.Sc Mathematics SECTION 1 Elementary set theory, Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequence and series, Convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, Uniform continuity, Intermediate value theorem, Differentiability, Mean value theorem, Maclaurin’s theorem and series, Taylor’s series. Sequences and series of functions, Uniform convergence. Riemann sums and Riemann integral, Improper integrals. Monotonic functions, Types of discontinuity. Functions of several variables, Directional derivative, Partial derivative.  Metric spaces, Completeness, Total boundedness, Separability, Compactness, Connectedness. SECTION 2 Eigenvalues and eigenvectors of matrices, CayleyHamilton theorem. Divisibility in Z, congruences, Chinese remainder theorem, Euler’s  function. Groups, Subgroups, Normal subgroups, Quotient groups, Homomorphisms, Cyclic groups, Permutation groups, Cayley’s theorem, Class equations, Sylow theorems. Rings, Fields, Ideals, Prime and Maximal ideals, Quotient rings, Unique factorization domain, Principal ideal domain, Euclidean domain, Polynomial rings and irreducibility criteria. Vector spaces, Subspaces, Linear dependence, Basis, Dimension, Algebra of linear transformations, Matrix representation of linear transformations, Change of basis, Inner product spaces, Orthonormal basis. SECTION 3 Existence and Uniqueness of solutions of initial value problems for first order ordinary differential equations, Singular solutions of first order ordinary differential equations, System of first order ordinary differential equations, General theory of homogeneous and nonhomogeneous linear ordinary differential equations, Variation of parameters, Sturm Liouville boundary value problem, Green’s function. Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs, Classification of second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations. Numerical solutions of algebraic equations, Method of iteration and Newton Raphson method, Rate of convergence, Solution of systems of linear algebraic equations using Guass elimination and GuassSeidel methods, Finite differences, Lagrange, Hermite and Spline interpolation, Numerical integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and second order RungeKutta methods. Velocity, acceleration, motion with constant and variable acceleration, Newton’s Laws of Motion, Simple Harmonic motion, motion of particle attached to elastic string, motion on inclined plane, motion of a projectile, angular velocity and acceleration, motion along a smooth vertical circle, work, energy and impulse, Collision of elastic bodies, Bodies falling in resisting medium, motion under action of central forces, central orbits, planetary motion, moment of inertia and couple, D’Alembart’s principle. Equilibrium of particle and a system of particles, Mass centre and centres of gravity, Frictions, Equilibrium of rigid body, work and potential energy. Rest of the syllabus is attached in below file which is free of cost for you Address: University of Delhi North Campus Zakir Husain College, J L N Road, New Delhi, Delhi 110002 Map: 
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