DU MA/M.Sc Mathematics Entrance Exam Syllabus 2016

DU MA/M.Sc Mathematics Entrance Exam Syllabus 2016:

The University of Delhi (DU) has released the detailed syllabus for the Master Of Arts (MA) & Master in Science (M.Sc) Entrance 2016 For Mathematics Subject.

DU MA|M.Sc in Mathematics Entrance Syllabus 2016

DU MA/M.Sc Mathematics Entrance Exam Syllabus 2015

The Delhi University has uploaded the Comprehensive Syllabus for the MA & M.SC Entrance 2016 in Mathematics which are as follows:

Entrance Exam syllabus of MA/M.Sc (Mathematics) 2016

  • Elementary set theory
  • Finite
  • Countable and uncountable sets
  • Real number system as a complete ordered field
  • Archimedean property
  • Supremum
  • Infimum
  • Sequence and series
  • Covergence limsup
  • Liminf
  • Bolzano Weierstrass’s 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
  • 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 rings
  • Unique factorization, Domain
  • Euclidean domain, Polynomial rings and irreducibility criteria
  • Vector spaces
  • Subspaces
  • Linear dependence
  • Dimension
  • Algebra of linear
  • Transformations
  • Matrix representation of linear transformations
  • Change of basis
  • Inner product spaces
  • Orthonormal basis
  • 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 non- homogeneous 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 equation
  • Numerical solutions of algebraic equation
  • Method of iteration and Newton-Raphson method
  • Rate of convergence
  • Solution of systems of linear algebraic equations using Guass elimination and Guass-Seidel method
  • Finite differences, Lagrange, Hermite and Spline interpolation
  • Numerical integration
  • Numerical solutions of ODEs using Picard
  • Euler modified Euler and second order Runge- Kutta methods

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