جامعة بوليتكنك فلسطين

عمادة القبول والتسجيل

خطة التخصص

Master of Mathematics

  • 2006

(18)

Course No رقم المساق Course Name اسم المساق Credit hours الساعات المعتمدة Course Description وصف المساق
6002 Real Analysis 1 0
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
6697 Seminar 2 3
6698 Comprehensive Exam 0
6699 Thesis 6

(3)

Course No رقم المساق Course Name اسم المساق Credit hours الساعات المعتمدة Course Description وصف المساق
4351 English for Graduate Students 3