Advanced Linear Algebra
The structure of a linear operator: the characteristic polynomial, the Cayley-Hamilton theorem, Diagonalizable operators, primary decomposition theorem , Cyclic decomposition theorem Jordan Canonical Form, the Rational Canonical form. Spectral theorem for normal operators  Self-adjoint operators, unitary operators. The polar decomposition of an operator. Singular Value decomposition. Bilinear forms and Quadratic forms.

Multivariate Calculus
Limits And Continuity, Partial Derivatives, Directional Derivatives, Total Derivatives, Mean Value Theorem, Sufficient Condition for differentiability, Inverse and Implicit Function Theorems, Extrema of real valued functions of several variable. Integration and Introduction to Differential Equations.

 Time- Table