การสอบวัดคุณสมบัติ

2301610   Linear and Multilinear Algebra
– Basic concepts; linear maps; linear geometry; multilinear algebra; quadratic forms.

2301613   Abstract Algebra I
– Groups; group actions; Sylow theorems; rings; ideals; polynomial rings; unique factorization domains;
  fields and field extensions.

2301614   Abstract Algebra II
– Jordan-Holder theorem; solvable groups; free groups; classification of extension fields; Galois theory;
   Noetherian ring; modules.

2301620   Mathematical Analysis
– The real number system; metric spaces; sequences and series of real numbers; continuity;
   differentiation; the Riemann integral; uniform convergence; the Arzela-Ascoli theorem; the Stone-
  Weierstrass theorem.

2301621   Real Analysis I
– Measures; integration; normed linear spaces;  – spaces; Hilbert spaces.

2301622   Real Analysis II
– Product measures; signed and complex measures; differentiation; Banach spaces.

2301623   Complex Analysis
– Holomorphic functions; complex power series; complex line integrals; Cauchy theorem, Cauchy integral
  formula and applications; calculus of residues; maximum modulus principle; conformal mappings,
  normal families, Riemann mapping theorem; harmonic functions.

2301631 Topology
– Topological spaces; complete metric spaces; product spaces; quotient spaces; countability axioms;
  separation axioms; connectedmess; compactness; compactifications; net convergence; function
  spaces.

2301632   Algebraic Topology
– Homotopy; fundamental groups; covering spaces; van Kampen’s theorem; simplicial homology; singular
  homology CW-complexes; cellular homology; Eilenberg-Steenrod axioms.

2301635   Differentiable Manifolds
– Differentiable manifolds, tangent spaces; vector fields and flows; immersions and submersions;
  Frobenius’ theorem; integration on manifols, differential forms, Stokes’theorem; introduction to Lie
  groups and Lie algebras.

บังคับสอบรายวิชา  2301653   Numerical Analysis
– Solutions of systems of linear and non-linear equations, numerical methods for ordinary 
  differential equations, finite difference methods for two-point boundary value problems and finite
  difference methods for partial differential equations.

และเลือกสอบอีก 1 รายวิชาจาก 3 รายวิชาต่อไปนี้

2301641  Method of Applied Mathematics I
– Theory of distribution, Green’s functions, operator theory, perturbation method.

2301650  Partial Differential Equations
– First-order equations; linear second-order PDEs; representation of solutions; introduction to Hamilton-
  Jacobi equations; other ways to represent solutions. 

2301676  Stochastic Models
– Stochastic programming models, probabilistic dynamic programming models, Markov chain, waiting line
  models, birth-death process.