Unit 1: Analysis & Linear Algebra
This is the most critical unit, carrying approximately 40% of the total weightage.
Real Analysis
- Sequences and Series of Real Numbers
- Functions of One Real Variable
- Topology of R
- Riemann Integration
Linear Algebra
- Vector Spaces, Subspaces
- Linear Transformations
- Matrices & Determinants
- Eigenvalues & Eigenvectors
Unit 2: Complex Analysis, Algebra & Topology
This unit focuses on abstract structures and functions of complex variables.
Complex Analysis
- Analytic Functions
- Complex Integration
- Singularities & Residues
Algebra
- Groups, Subgroups, Homomorphisms
- Rings, Fields, Ideals
- Number Theory Basics
Unit 3: Applied Mathematics
Essential for candidates opting for Applied Statistics or Physics backgrounds.
Ordinary Differential Equations (ODE)
- First Order ODEs
- Higher Order Linear Equations
- Systems of ODEs
Partial Differential Equations (PDE)
- First Order PDEs
- Wave, Heat, Laplace Equations
Numerical Analysis
- Numerical Solutions of Algebraic Equations
- Interpolation
- Numerical Integration
Calculus of Variations
- Euler-Lagrange Equation
- Extremals
Exam Pattern
| Part | Subject | Questions | Marks | Negative Marking |
|---|---|---|---|---|
| Part A | General Aptitude | 20 (Attempt 15) | 30 | 0.5 |
| Part B | Mathematics (MCQ) | 40 (Attempt 25) | 75 | 0.75 |
| Part C | Mathematics (MSQ) | 60 (Attempt 20) | 95 | No Negative Marking |
| Total | - | 120 (Attempt 60) | 200 | - |