M.SC Statistics Coaching Entrance Delhi University Syllabus

1. M.SC Statistics Coaching Entrance Delhi University Syllabus Mathematics: Algebra: Linear Algebra. Vector space, subspace and its properties, linear independence and dependence of vector, matrices, rank of matrix, discount to ordinary forms, linear homogeneous and non- homogeneous equations, Cayley-Hamilton theorem, function roots and vectors. M.SC Statistics Coaching.

2. Theory of equation. De Moivere’s theorem, relation among roots and coefficient of nth diploma equation, technique to cubic and biquadratic equation, transformation of equation. Calculus: Diff. Calculus. Limit and continuity, differentiability of functions, successive differentiation, leibnitz’s theorem, partial differentiation, Euler’s theorem on homogeneous functions, tangents and normals, asymoptotes, singular points, curve tracing. M.SC Statistics Coaching. Integral calculus. Reduction formulae, integration and residences of exact integrals, quadrature, rectification of curves, volumes and surfaces of solids of revolution. Differential Equation: Linear, homogeneous equation, first order better diploma equations, algebraic residences of solutions, linear homogeneous equation with consistent coefficients, solution of 2nd order differential equation, linear non-homogeneous differential equations. Real Analysis: Neighbourhood, open and sets, limit point and Bolzano weirstrass theorem, continuous functions, sequences and their properties, restrict superior and limit inferior of a sequence, endless collection and their convergence, Rolle’s theorem, mean fee theorem, Taylor’s theorem, Taylor’s series, Maclaurin’s series, maxima and minima, indeterminate forms. Statistics: Measures of principal tendency and dispersion and their homes, skewness and kurtosis, introduction to probability, theorem of total and compound probability, Bayes theorem, random variables, probability DU M.A./M.Sc Mathematics Entrance Syllabus Elementary set theory, Finite, countable and uncountable sets, Real number gadget as a complete ordered field, Archimedean property, supremum, infimum.

3. Sequence and series, Covergencelimsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, Uniform continuity, Intermediate cost theorem, Differentiability, Mean value theorem, Maclaurin’s theorem and series, Taylor’s collection. Sequences and collection of functions, Uniform convergence. Riemann sums and Riemann integral, Improper integrals. Monotonic functions, Types of discontinuity. Functions of numerous variables,Directional derivative, Partial derivative. Metric spaces, Completeness, Total boundedness, Separability, Compactness, Connectedness. Eigenvalues and eigenvectors of matrices, Cayley-Hamilton theorem. Divisibility in Z, congruences, Chinese remainder theorem, Euler’s φ- function. Groups, Subgroups, Normal subgroups, Quotient groups, Homomorphisms, Cyclic groups, Cayley’s theorem, Class equations, Sylow theorems. Rings,fields, Ideals, Prime and Maximal ideals, Quotient jewelry, Unique factorization domain, Principal perfect domain, Euclidean domain, Polynomial earrings and irreducibility criteria.

4. Vector spaces, Subspaces, Linear dependence, Basis, Dimension, Algebra of linear transformations, Matrix representation of linear transformations, Change of basis, Inner product spaces, Orthonormal basis. M.A Entrance Mathematics Coaching.