MTH 502 Linear Algebra:

Vectors in Euclidean space – Vector spaces and subspaces – Basis and dimensions – Linear equations and matrices – Linear mapping , matrices and change of basis – Bilinear and quadratic forms.

MTH 503 Functional Analysis (1):
Metric spaces – Completeness – Accumulation – Contraction rule – Normed vector spaces – Hilbert space – Orthogonal Projection – Linear functionals – Dual spaces – Hahn Bannch theorem – Linear functional equations – Finite differences – Dense operators – Inverse Operators – Integral equations with operators in Hilbert space

MTH 504 Real Analysis and Topology:
 Sets – Functions – Topological spaces – Metric spaces – Continuous mapping – Separation axioms – Measurability – Accumulation – Product topology – Hoptology .

MTH 505 Numerical Analysis :
Linear and nonlinear equations – Iterative methods – Finite differences and interpolation – Numerical solution of ordinary differential equations - Numerical Solution of Partial differential equations – Matrix Eigenvalue problem

MTH 506 Mathematical Theory of Quantum Mechanics:
Old quantum theory – Physical basis of quantum mechanics – Properties of the operators – Application on Schrodinger wave equation – Quantum mechanical treatment of the Hydrogen atom – Time independent perturbation theory .

MTH 507 Functions of Complex Variable (1) :
Analytic function – Line integral – Cauchy theorem – Taylor and Laurent series – Singular points – Evaluation of real integrals – Theorems for infinite contours – Integration through a branch cut – Conformal mapping and bilinear transformation – Two dimensional fluid flow – Potential theory.

MTH 508 Differential Equations :
First order equations – General theory of linear differential equations – Systems of linear equations – Basic concepts of partial differential equations – Classification of second order partial differential equations – Cauchy Solution of the wave equation – Fourier series – Separation of variables for mathematical physics equations .
MTH 509 Fuzzy Algebra :
Fuzzy subsets – Operations on fuzzy sets - Relations on fuzzy sets – Zadeh principle – Fuzzy partitioning and fuzzy equivalence relations- Fuzzy groups – Fuzzy quotient groups – Ideal Fuzzy rings .

MTH 510 Probability and Statistics (1) :
Probability axioms – Sample space and events – Conditional probability – Statistical independence – Random variables – Distribution functions – Expectation – Continuous and conditional distributions – Sample distribution – Point and interval estimation – Hypothesis tests for the mean and variance – Nonparametric Methods.

MTH 511 Differential Geometry (1) :
Space curves – Tangent and normal line – Osculating plane – Curvature – Torsion – Christoffel symbols.

MTH 512 Projective Geometry (1) :
Euclidean and projective Geometry – Principle of duality – Projective and perspective pencils and sets – Theorems of projectivities – Cross ratio – Invariance of cross ratio – Disargue’s theorem – Plane and space configuration – Harmonic sets - Projectivities and Pappus theorem – Parabolic and hyperbolic projections – Conic sections – Pole and polar line – Pascal axis and Brianchon center’s theorems – Steelier circle – Plane affine and Euclidean geometry.

MTH 513 Computer Science :
Computer architecture – Information Systems – Operating systems – File organization and database design – Data communication and networks – Graph theory.