Master of Mathematics
- 2006
(18)
| Course No رقم المساق | Course Name اسم المساق | Credit hours الساعات المعتمدة | Course Description وصف المساق |
|---|---|---|---|
| 6601 | Applied Mathematics1 | 3 | Partial differential equations in two variables, Method of separation of variables, Fourier series, Greens function, Monges equations, Fourier and Laplace transforms for solving P.D. equations and their applications |
| 6602 | Real Analysis | 3 | Set functions, Outer measure, Measurable sets and measurable function, Lebesgue measure, Borel measure, Measurable functions, Integration, Convergence theorems, Banach space, Minkowski's inequality and Holder 's inequality, Spaces, Differentiation and absolute continuity, Functions of bounded variation, Convex functions. |
| 6603 | Probability Theory | 3 | Kolmogorovs axioms, Random variables, Probability distributions, Mathematical expectation, Independence, Boral-Cantelli theorem, Characteristic functions, Types of convergence, Laws of large numbers, Central limit theorem. |
| 6604 | Abstract Algebra 1 | 3 | Groups: Algebraic structure, Centralizer, commutator, Normal subgroups, Homomorphism and isomorphism, Group action, Sylow's theorems, Direct products, Finitely Generated Abelian groups. |
| 6605 | Numerical Analysis | 3 | Solving linear systems of equations, Iterative techniques for solving linear systems, Approximating eigenvalues, Numerical solutions of nonlinear systems of equations, Finite differences. |
| 6606 | Complex Analysis 1 | 3 | Complex numbers and their representation, Complex functions and their derivatives, Analytic functions and Cauchy-Riemann equations, Conformal Mappings, Linear fractional transformations , Complex Integration and Cauchys' theorems, Singularities. |
(12)
| Course No رقم المساق | Course Name اسم المساق | Credit hours الساعات المعتمدة | Course Description وصف المساق |
|---|---|---|---|
| 6610 | Linear Algebra | 3 | Matrix algebra, Determinants, Inverse of a matrix, Euclidean and unitary spaces, Linear transformation, Jordan forms, Calay-Hamilton theorem, Simple matrices, Positive definite matrices, Hermitian matrices, Unitary and normal matrices, Schurs decomposition, Jordans decomposition. |
| 6611 | Applied Mathematics 2 | 3 | Approximation method, Expansion approximation, Watson's method, Laplace method, Fourier integral. WKB method, perturbation method |
| 6613 | Integral Equations | 3 | Voltera Equations, Fredholm Equations, Solving Integral Equations by Substitution and Approximation, Applications on Integral Equations, Millin Transforms and Applications, Hankel Transforms and Applications. |
| 6614 | Abstract Algebra 2 | 3 | Review of basic rings and ideals, R-modules, Products and sums of R-modules, Exact sequences and split exact sequences, Simple and semi simple R-modules, Essential and small sub modules, The ring of endomorphism of an R-modules, Projective and injective modules, Regular rings, The radical of an R-module, Noetherian and Artinian R-modules |
| 6615 | Topology | 3 | Topological spaces, Neighborhoods, Bases and subbases, Continuous functions, Product spaces, Weak topologies, Nets and filters, Separation axioms, Regular and completely regular spaces, Lindel of spaces, Compact spaces, and countably compact spaces, Sequentially and countably spaces, One point Compactification, Para compact spaces, Connected spaces. |
| 6616 | Complex Analysis 2 | 3 | Maximum modulus principle, Schwarzs lemma, Phragmen-Lindelof theorem. Spaces of analytic functions, Riemann mapping Theorem, Runges theorem and Mittag-Leffers theorem, Analytic continuation and Mondromy theorem, Harmonic functions and Drichlet problem. |
| 6617 | Functional Analysis | 3 | Metric spaces, Norm spaces, Banach spaces, linear operators and linear functionals, Inner product spaces, Hilbert spaces, Representation of functions on Hilbert spaces, Hahn-Banach theorem, Uniform bounded principle, Open mapping and closed graph theorems, Fixed point theorem. |
| 6618 | Mathematical Statistics | 3 | One variable and multivariate distributions, Methods of estimation, Properties of estimators, Hypothesis testing, Properties of tests, Relationship between confidence regions and tests, Large sample properties of tests and estimators |
| 6619 | Operations Research | 3 | Advanced programming: Bases of linear programming, Revised simplex method, Bounded variables, Parametric linear programming. Decision theory: Decision under risk, Decision tree. Game theory, Inventory models, Queueing theory, Optimization techniques. |
| 6650 | Special Topics in Mathematics | 3 | advanced topics chosen from analysis that suit students’ and teachers’ interests. |
(6)
| Course No رقم المساق | Course Name اسم المساق | Credit hours الساعات المعتمدة | Course Description وصف المساق |
|---|---|---|---|
| 6696 | Seminar 1 | 3 | A study by the student that ends with a presentation and a written report. |
| 6697 | Seminar 2 | 3 | The student will select under the supervion of faculty member, a topic in which the student writes a report including literature review |
| 6698 | Comprehensive Exam | 0 | An exam in specified fields of mathematics that measures students knowledge, understanding of basic and advanced concepts in those fields, and the ability to use this knowledge and understanding in applications in the field of specialty |
| 6699 | Thesis | 6 | The student should prepare a thesis, defend it in front of a special committee and pass the discussion |
(3)
| Course No رقم المساق | Course Name اسم المساق | Credit hours الساعات المعتمدة | Course Description وصف المساق |
|---|---|---|---|
| 4351 | English for Graduate Students | 3 | This course is intended to help the Ma /MSc program students improve their English language proficiency in general. However, it emphasizes two crucial skills necessary for graduate students, namely speaking and writing. A very important component comprises issues necessary for those students during their study at the university as well as in their professional lives. |