Mathematics
Student must complete 36 credit hours
Speciality Requirements Student must complete 24 credit hours
| Course Code | Course Name | Credit Hours | Prerequests |
|---|---|---|---|
| 421511 | Real Analysis I | 3 |
|
| This course looks at set functions, measurable sets, measurable space, measurable functions, abstract integration, convergence theorems, Lebesgue measure, Borel measure, spaces, Riez representation theorem, differentiation and absolute continuity, decomposition of measures, Radon –Nikodym theorem and inner and outer measures . | |||
| 421513 | Complex Analysis | 3 |
|
| Vector Spaces, Linear Transformations, linear Functionals, Dual Space, Characteristic Polynomials and Minimal Polynomials of Linear Transformations, Diagonalizations, Jordan and Rational Forms of Maticies, Cayley Hamilton Theorem, Inner Product Spaces. | |||
| 421521 | Numerical Analysis | 3 |
|
| Direct methods for solving linear systems, Iterative techniques for solving linear systems, Numerical methods for solving nonlinear systems, Interpolation and polynomial approximation, Approximation theory, Numerical integration and Numerical methods for solving boundary value problems (BVP’s). | |||
| 421523 | Operational Research | 3 |
|
| Brief introduction to Operational Research, Network analysis: Theory and applications, Heuristic methods, Introduction to stochastic analysis, Markov chains and Markov processes, Introduction to queuing theory, Optimization methods: non-linear, linear and integer programming, Game theory, PERT and CPM Techniques | |||
| 421531 | Applied Statistics | 3 |
|
| Statistical inference with one and two population, Categorical Data, Analysis of variance, Simple linear regression and correlation analysis, Some non-parametric tests. | |||
| 421532 | Mathematical Statistics | 3 |
|
| This course includes topics in univariate and multivariate distributions, sufficient statistics, efficient point and interval estimation, tests of hypotheses and Neyman –Pearson lemma Non –Parametric tests. | |||
| 421542 | Algebra I | 3 |
|
| This course consists of a review of groups, group action, Sylow theorems, commutators, direct product of groups, review of rings, commutative rings, principle ideal domains, unique factorization domains, polynomial rings F[x], unique factorisation over F[x], field of fractions, field theory, field extensions, algebraic extensions, algebraic closed fields, algebraic closure, splitting fields and normal extensions. | |||
| 421561 | Topology I | 3 |
|
| Topics covered in this course include topological spaces, continuous functions, product spaces, quotient spaces, convergence, nets and filters, separation axioms, countability axioms, connected spaces and compact spaces. | |||
| 421598 | Comprehensive Exam | 0 |
|
| A graduate student must pass a qualifying examination (See Academic Rules and Regulations for Graduate Students). | |||
Speciality Optional Requirements Student must complete 12 credit hours
| Course Code | Course Name | Credit Hours | Prerequests |
|---|---|---|---|
| 421514 | Functional Analysis | 3 |
|
| Topics in this course include topological vector spaces, normed spaces, inner product spaces, Banach spaces, Hilbert spaces, Hahn –Banach theorem, spaces of continuous functions, dual spaces, uniform boundedness principle, open mapping theorem, closed graph theorem, convex sets and fixed-point theorems. | |||
| 421522 | Dynamic Programming | 3 |
|
| This course includes a dynamic programming introduction and some simple examples, functional equations, basic theorem, one-dimensional DPP, Analytic and computational solutions, multi-dimensional problems, reduction of state dimensionality and approximations and the application of DP. | |||
| 421541 | Advanced Linear Algebra | 3 |
|
| Vector Spaces, Linear Transformations, linear Functionals, Dual Space, Characteristic Polynomials and Minimal Polynomials of Linear Transformations, Diagonalizations, Jordan and Rational Forms of Maticies, Cayley Hamilton Theorem, Inner Product Spaces. | |||
| 421543 | Algebra II | 3 |
|
| This course looks at modules, direct sum and direct product of modules, projective and injective modules, module homomorphisms, cross product and tensor product of modules, exact sequences, algebras and graded algebras, finite fields and Galois Theory . | |||
| 421562 | Topology II | 3 |
|
| Metric spaces and metric topologies, metrization of topological spaces, uniform spaces, topological groups, function spaces and covering spaces. | |||
| 421571 | Applied Mathematics I | 3 |
|
| Series solutions of differential equations about ordinary and singular points (Frobenius method), Fourier series and Fast Fourier transform, Special functions includes; Legendre functions, Chebyshev polynomials, Bessel functions, Hermite functions and Laguere polynomials, Nonlinear differential equations and stability includes; Autonomous systems, Predator-Prey equation, Liapunov’s second method, periodic solutions and limit cycles. | |||
| 421581 | Special Topics in Mathematics "1" | 3 |
|
| This course consists of studying special mathematical topics approved by the department. | |||
| 421582 | Special Topics in Statistics | 3 |
|
| This course consists of a study of special mathematical topics, as approved by the department. | |||
| 421583 | Special Topics in Mathematics "2" | 3 |
|
| This course consists of studying special mathematical topics approved by the department. | |||
| 429525 | Advanced Linear Programming | 3 |
|
| This course consists of an introduction and vector analysis of simplex method, duality and sensitivity, special simplex forms, transportation and assignment problems and networks and linear programming. | |||
| 429573 | Graph Theory | 3 |
|
| This course consists of a survey of several of the main ideas of general graph theory with applications to network theory, oriented and non-oriented linear graphs, spanning trees, branches and connectivity, accessibility, planar graphs, networks and flows, matching and applications. | |||
| 429575 | Fuzzy Sets | 3 |
|
| Topics covered in this course include fuzzy sets, fuzzy numbers, ranking of fuzzy numbers, fuzzy difference equations, fuzzy matrices, fuzzy vector spaces, decision – making with fuzzy preference relation, fuzzy relation equation and fuzzy logic. | |||