1. Advanced Calculus
Sequence of real numbers, Infinite series, Function of two variables, Maxima and minima, Jacobian of transformation, Double & triple integrals, Stokes and Gauss theorem
2. Mathematical Analysis
Riemann Integrals, Improper Integrals, Beta & Gamma function, Analytic function, Conformal mapping, Bilinear or Mobius Transformation and Metric space.
3. Linear Algebra
Vector Space, Linear Transformation, Dual Space, Inner Product Space, Modules
4. Modern Algebra
Group and its properties, Cyclic group, Normal Group, Homomorphism of groups, Fundamental theorems of isomorphism, Rings, Ideal, Integral Domain, Field.