• MT 401 - Galois Theory (3 Credit)
  
  
• MT 402 - Measure Theory (3 Credit)
  
  
• MT 403 - Topology II (3 Credits)
  
  
• MT 404 - Complex Analysis II (3 Credits)
  
  
• MT 405 - Functional Analysis (3 Credits)
  
  
• MT 406 - Fluid Mechanics (3 Credits)
  
  
• MT 407 - Optimization Theory (3 Credits)
  
  
• MT 408 - Independent Study/Project Work (3 Credits)
  

Prerequisites: MT 301, MT 305

Field extensions, Ruler and Compass Constructions, Three classical Problems, Galois groups of field extensions, Automorphisms of a field, Theorem of the Primitive Element, Splitting Fields, Automorphisms of a field extension over a fixed field, Galois Groups, Separable and Inseparable Extensions, Normal Extensions and Galois Extensions, Subgroups of the Galois group and intermediate fields of the extension, Fundamental Theorem of Galois Theory, Solubility of polynomials, Galois group of a polynomial, Radical Extensions, Solubility by radicals, Proof that a polynomial is irreducible if and only if its Galois group acts transitively on its roots, Proof of the Fundamental Theorem of Algebra.

Prerequisite: MT 302

Lebesgue Measure on the real line, -algebras, Measurable functions, Measure spaces, Lebesgue integral, Fatou's Lemma, Monotone Convergence Theorem, Dominated Convergence Theorems, spaces, Modes of Convergence, Product measures, Fubini's Theorem.

Prerequisite: MT 306

Box Topology and Tychonoff Topology, Inadequacy of sequences, Nets and Filters; Tychonoff spaces and Normal spaces, Uryshon’s Lemma and Tietze’s Extension theorem; Paracompactness and BNS- Metrization Theorem ; - Sets and Baire Spaces; Totally disconnected spaces, The Cantor set , Homotopy relations, Fundamental group; Triangulating spaces, Infinite Complexes , Euler Characteristics and Surgery, Knots and covering spaces

Prerequisites: MT 306, MT 307

Homotopy of paths and Cauchy's theorem, Winding numbers and Cauchy's integral formulae, Power series and uniform convergence, Miscellaneous contour integrals, Maximum modulus principle, Schwarz’s lemma, Liouville’s theorem, Fundamental theorem of algebra, Morera’s theorem, Argument principle, Rouche’s theorem, Open mapping theorem, Reflection principle, Normal families, Riemann mapping theorem.

Prerequisites: MT 301, MT 306, MT 402

Normed Linear Spaces , Banach Spaces, Riesz-Fischer Theorem, Linear maps and functionals or normal linear spaces, Dual Spaces; Geometry of Banach Spaces , Hanch Banach Theorems (Separation Form, Extension Form); Uniform Boundedness Principle, Open Mapping Theorem, Banach’s Isomophism Theorem, Closed Graph Theorem; Second Dual Space, Projections and direct sums in Banach Spaces , Schauder Basis, Hilbert Spaces; Banach Algebras, Topoligical Vector Spaces.

Prerequisite: MT 310

Perfect Fluid Theory
Two-dimensional flow : Complex potential, Blasius Theorem, Conformal Transformation; Joukowski and Schwartz Christoffel. Discontinuous Motion, Vortex Motion.
Three-dimensional flow : Stokes’ stream function in axi-symmetric flows, Image systems in 3-D.

Viscous Flow
Navier-Stokes equation of motion; its exact solutions, Steady slow motion past a fixed sphere, Reynold’s Number, Prandtl’s Boundary Layer.

Prerequisite: MT 311

Advanced Linear Programming: Dantzig-Wolf decomposition algorithm, Goal programming.
Integer Programming: Cutting plane algorithms, Branch and bound algorithms.
Non-Linear Programming: Kuhn-Tucker conditions, Quadratic programming, Separable programming.

Supervised independent study on a project approved by an academic staff member of the department. Candidates are required to present their work at a seminar and submit the work in a report/dissertation form.