**Announcement (12-June-2014)**

The examination topics for the Entrance Examination to the Master's Programme are as follows:

Calculus (40)

Foundations of Mathematics (15)

Linear Algebra (15)

Mathematical Analysis (15)

Ordinary Differential Equations (15)

Note: The number in brackets next to each subject indicates the relative weight that subject in the Examination.

More detailed information on the subtopics of each topic is given below:

**Calculus**- Differentiation
- Curve Sketching
- Integration
- Double and Triple Integrals
- Polar and Cylindrical Coordinate Systems
- Infinite Series
- Series Tests for Convergence or Divergence
- Taylor Series
- Partial Derivatives
- Three-Dimensional Coordinate Systems
- Vector Algebra

**Foundations of Mathematics**- Mathematical Logic: General Statements, Open Names, Inference, Quantifiers
- Mathematical Proofs: Mathematical Induction, Direct Proof, Proof by Contradiction
- Set theory: Operations on sets, DeMorgan’s Laws and Power Sets
- Relations: Composition of Relations, Types of Relations and Invertible Relations, Partitions and Equivalence Relations
- Functions: Composition of Functions, One-to-One and Onto Functions and Invertible Functions, Injective, Surjective and Bijective Functions
- Denumberable and Nondenumberable Sets
- Cardinal Numbers

**Linear Algebra**- Systems of Linear Equations
- Row Reduction and Echelon Forms
- Solutions to Linear Systems of Equations
- Linear Independence and Bases
- Change of Basis
- Matrix Operations
- Invertible Matrices
- LU Factorisation
- Dimension and Rank
- Linear Transformations
- Eigenvalues and Eigenvectors
- The Characteristic Equation
- Orthogonality
- The Gram-Schmidt Process

**Mathematical Analysis**- The Real Number System
- Sequence of Real Numbers
- Metric Spaces and Convergent Sequences in Metric Spaces
- Continuous Functions in Metric Spaces
- Compactness and Connectedness in Metric Spaces
- The Riemann Integral

**Ordinary Differential Equations**- Solving First and Second ODEs and their Applications
- Solving ODEs using the Series Method
- Systems of ODE's
- Solving Differential Equations using Laplace Transforms