**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

**The Delhi University** has uploaded the **Comprehensive Syllabus** for the **MA & M.SC Entrance 2016** i**n 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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