Fall Semester

Course Name

No.

Credits

Real Analysis I

8033511

3

Algebra I

8033582

3

Elective Course

3

Total:

9

Spring Semester

Complex Analysis

8033512

3

Algebra II

8033682

3

Elective Course

3

Total

9

Fall Semester

Courses name

No.

Credits

Functional Analysis I

8033513

3

Elective Course

3

Thesis

8033699

3

Total

9

Spring Semester

Topology I

8033562

3

Thesis

8033699

3

Total

6

Fall Semester

Course Name

No.

Credits

Real Analysis I

8033511

3

Algebra I

8033582

3

Elective Course

3

Total:

9

Spring Semester

Real Analysis II

8033611

3

Algebra II

8033682

3

Elective Course

3

Total

9

Fall Semester

Courses name

No.

Credits

Functional Analysis I

8033513

3

Advance Linear Algebra

8033581

3

Elective Course

3

Total

9

Spring Semester

Complex Analysis I

8033512

3

Topology I

8033562

3

Total

6

Fall Semester

Course Name

No.

Credits

Real Analysis I

8033511

3

Theory of Ordinary Differential Equation’s

8033503

3

Elective Course

3

Total:

9

Spring Semester

Complex Analysis I

8033512

3

Numerical Analysis I

8033521

3

Elective Course

3

Total

9

Fall Semester

Courses name

No.

Credits

Operation Research

8033571

3

Partial Differential Equation’s

8033601

3

Thesis

8033699

3

Total

9

Spring Semester

Courses name

No.

Credits

Elective Course

3

Thesis

8033699

3

Total

6

Fall demester

Course Name

No.

Credits

Real Analysis I

8033511

3

Theory of Ordinary Differential Equations

8033503

3

Elective Course

3

Total:

9

Spring Semester

Complex Analysis

8033512

3

Numerical Analysis I

8033521

3

Elective Course

3

Total

9

Fall Semester

Courses name

No.

Credits

Operation Research

8033571

3

Advance Linear Algebra

8033581

3

Partial Differential Equations

8033601

3

Total

9

Spring Semester

Special functions

8033505

3

Elective Course

3

Total

6

Course #

8033503

Title

Theory of Ordinary Differential Equations (1)

Credits

3

Prerequisites

Dept. Approval

Lecturer

Tahseen Mughrabi

Taha Abu Kaff

Existence and uniqueness theorem, continuation of solution with respect to a parameter, Homogeneous and nonhomogeneous linear systems, nth-order linear differential equation, equilibrium point, periodic systems, autonomous systems, Lyapunov function and stability.

Course #

8033505

Title

Special Functions.

Credits

3

Prerequisites

Dept. Approval

Lecturer

Naji Qatanani

Taha Abu Kaff

Appel’s symbols, Hypergeometric series, vandermond’s theorem, Wallis formula, sterling’s formula, Gamma and Beta functions. Dirichlet averages: (of power series, of ex, of xt, of Cauchy integral).

Course #

8033511

Title

Real Analysis (1)

Credits

3

Prerequisites

Dept. Approval

Lecturer

Mohammad Khalil

Yousef Bdier

Set functions, measurable sets, measurable spaces, measurable functions, abstract integration, convergence theorems, differentiation and absolute continuity, decomposition of measures, Randon-Nilodym theorem.

Course #

8033512

Title

Complex Analysis

Credits

3

Prerequisites

Dept. Approval

Lecturer

Ibrahim Grouz

Analytic functions, local Cauchy’s theorem, power representations, open mapping theorem, global Cauchy’s theorem, residue theory, harmonic and sub-harmonic functions, argument and maximum modulus principles, reflection principle, conformal mapping, linear functional transformations, normal families.

Course #

8033513

Title

Functional Analysis (1)

Credits

3

Prerequisites

  8033511

Lecturer

Naji Qatanani

Topological vector spaces, Normed spaces, inner product spaces, Banch spaces, Hilbert spaces, Hahn-Banach theorem, lp, Lp, spaces of continuous functions, dual spaces, uniform boundedness principle, open mapping theorem, closed graph theorem, Hahn-Banach theorem, convex sets, fixed point theorem.

Course #

8033521

Title

Numerical Analysis (1)

Credits

3

Prerequisites

Dept. Approval

Lecturer

Naji Qatanani

Review of linear algebra including vector and matrix norms and canonical forms. Analysis of numerical methods for linear systems (direct and iterative), conditioned systems. Eigen value problems.

Course #

8033531

Title

Probability Theory

Credits

3

Prerequisites

Dept. Approval

Lecturer

Tahseen Mughrabi

Kolmogorov axioms, random variables, probability distributions, expectations, conditional independence. Borel-Cantly theorem, characteristic functions, central convergence theorem, Martingale theory, Laws of large numbers.

Course #

8033532

Title

Mathematical Statistics

Credits

3

Prerequisites

Dept. Approval

Lecturer

Tahseen Mughrabi

Univariate and multivariate distributions, sufficient statistics, point and interval estimation, Test of hypothesis, Neyman-Pearson lemma, Non-Parametric tests.

Course #

8033533

Title

Stochastic Processes

Credits

3

Prerequisites

Dept. Approval

Lecturer

Tahseen Mughrabi

Stochastic processes, Bernoulli processes, Poisson processes, arrival counting process, Compound Poisson processes, non-stationary PP, Markov chains, Markov Processes, Regenerative processes and R. Theory, stationary process.

Course #

8033535

Title

Regression Analysis

Credits

3

Prerequisites Dept. Approval

Lecturer

Taha Abu Kaff

Simple and multiple regression, multiple and partial correlation, testing hypothesis in regression, one and two factors experimental designs, multiple comparison, Kruskel-Wallis test, Fredman’s test.

Course #

8033562

Title

Topology (1)

Credits

3

Prerequisites

Dept. Approval

Lecturer

Yousef  Bdier

Topological spaces, continuous functions, product spaces, Quotient spaces, Convergence, Nets an filters, Separatin Axioms, Countability of topological spaces, Connected, compact, Paracompact, Compactification.

Course #

8033563

Title

Differential Geometry

Credits

3

Prerequisites

Dept. Approval

Lecturer

Naji Qatanani

Curves in R³, formulas, covariant derive, frame fields, connection forms of the structural equations, patch computations, differential forms on surfaces, Integration of forms manifolds, the shape operator, normal and Gaussian Curvature, Riemannian geometry, geodesics, the Gauss-Bonnet theorem.

Course #

8033571

Title

Operations Research

Credits

3

Prerequisites

Dept. Approval

Lecturer

Tahseen Mughrabi 

Advanced linear programming, Foundations in LP Revised simplex method. Bounded variables, Parametric LP, Decision Theory and Gaues, Decision under risk, decision trees, decision uncertainty, game theory, Inventory models, deterministic inventory models, Probabilistic models, Queuing Theory, Basic elements of the Queuing theory, Queues with combinal arrivals and departure, Queues with priorities service, Some optimization techniques, unconstrained external problems, Constrained external problems.

Course #

8033573

Title

Dynamic Programming

Credits

3

Prerequisites

Dept. Approval

Lecturer

Taha Abu Kaff 

Special functions: gamma, beta and error functions, Sterling’s formula, Fourier series, Vector analysis, Laplace transforms, surface integrals, Introduction to chaotic behavior.

Course #

8033578

Title

Topics in Operational Research

Credits

3

Prerequisites

Dept. Approval

Lecturer

Taha Abu Kaff 

Selected topics from operational Research.

Course #

8033581

Title

Advanced Linear Algebra

Credits

3

Prerequisites

Dept. Approval

Lecturer

Amena  Affaneh

Ali Muhsen 

Matrix algebra, Determinants, Inverses of matrices, Euclidean and unitary spaces, Linear transformation, Jordan forms, Calay-Hamilton Theorem, Matrices:(simple, positive definite, Hermitran, unitary, normal).  Decomposition: (Schur’s, Jordan’s, singular value).

Course #

8033582

Title

Algebra

Credits

3

Prerequisites

Dept. Approval

Lecturer

Amina Affaneh

Mohammad Khalil

Groups: group actions Sylow theorem, direct product of groups Ideals, factorization in commutative rings and in polynomial rings, Quotient field, Field extension, algebraic and normal extensions, algebraic closure, splitting fields. 

Course #

8033601

Title

Partial Differential Equations

Credits

3

Prerequisites

8033503

Lecturer

Taha Abu Kaff

Naji Qatanani

Partial Differential Equations in two variables, Separation of variables, Fourier series, Lioville theorem, Fourier transform, Laplace transforms. Green’s functions, Method of characteristics for 1^st order equations.

Course #

8033603

Title

Theory Of Ordinary Differential Equations (2)

Credits

3

Prerequisites

8033503

Lecturer

Taha Abu Kaff

Continuation of subject in M503, periodic solutions for homogeneous and nonhomogeneous linear systems.

Course #

8033608

Title

Topics in ODE

Credits

3

Prerequisites

8033503

Lecturer

Taha Abu Kaff

Naji Qatanani

Selected Topics from ordinary differential equations, stability of linear systems of ordinary differential equations, and periodic solutions of certain systems.

Course #

8033609

Title

Topics in PDE

Credits

3

Prerequisites

8033503

Lecturer

Naji Qatanani

Tahseen Mughrabi

Continuation of M 603. Green’s function max. Principles.

Course #

8033610

Title

Integral Equations

Credits

3

Prerequisites

8033503

Lecturer

Naji Qatanani

Introduction, Integral Equation with separable kernels, Method of successive approximation, Classical Fredholm theory, Application to ODE’s and PDE’s, Symmetric Kernels, singular Integral Equations, perturbation method.

Course #

8033611

Title

Real Analysis (2)

Credits

3

Prerequisites

8033511

Lecturer

Mohammad Khalil

Yousef  Bdier

Banach spaces, linear operators, Hahn-Banach theorem, Hilbert spaces, spectral theory, Vital’s theorem, outer measure, product measures, Fubini’s theorem.

Course #

8033612

Title

Complex Analysis (2)

Credits

3

Prerequisites

8033512

Lecturer

Ibrahim Grouz

Analytic continuation, Monodromy theorem, Pocards theorem, infinite product, entire functions, Jensen’s formula, Hadamard factorization theorem, Dirichlet problem, Green’s function.

Course #

8033613

Title

Functional Analysis (2)

Credits

3

Prerequisites

8033513

Lecturer

Naji Qatanani

Hilbert spaces, orthonormal sets, operators on Hilbert spaces, projections, subspaces, invariant subspaces, reducing subspaces, positive operators, polar decomposition, normal and unitary operators, spectrum, numerical range, Banach algebra’s and spectral theory.

Course #

8033615

Title

Topics in Analysis

Credits

3

Prerequisites

Dept. Approval

Lecturer

Aminah Affaneh

Selected topics from analysis.

Course #

8033621

Title

Numerical Analysis (2)

Credits

3

Prerequisites

8033521

Lecturer

Naji Qatanani

Tahseen Mughrabi

Interpolation and approximation using polynomials, trigonometric functions and orthogonal polynomial’s, numerical integration, multiple integrals, error analysis  of numerical methods for differential equations.

Course #

8033625

Title

Numerical Analysis of Partial Differential Equations

Credits

3

Prerequisites

8033601

Lecturer

Naji Qatanani

Tahseen Mughrabi

Partial differential equations and techniques for their numerical solutions.

Course #

8033662

Title

Topology (2) 

Credits

3

Prerequisites

8033562

Lecturer

Yousef  Bdier

Metric spaces, Metric topologies, matrization of topological spaces, uniform spaces, topological groups, Function spaces, covering spaces.

Course #

8033663

Title

Algebraic Topology

Credits

3

Prerequisites

8033582

Lecturer

Amina. Afaneh

Ali  Muhsen

Categories, Abelian groups and Homotopy, Complexes. Homology of chain complexes, Singular Homology, Applications of the exact Homology Sequences, Homotopy, Invariance, and Excision.

Course #

8033682

Title

Algebra (2) 

Credits

3

Prerequisites

8033582

Lecturer

Aminah. Afaneh

Mohammad. Khalil

Direct sum and direct product of modules, projective and injective modules, Module Homomorphims, Cross and tensor product of modules, exact sequences, algebras and graded algebra’s, Categories, directed and inverse limits. Field Extensions, Galois Theory.

Course #

8033683

Title

Algebraic Functions  

Credits

3

Prerequisites

Dept. Approval

Lecturer

Aminah Afaneh

Ali Muhsen

Valuations places and Valuation rings. The valuations of rational function field extension of places, the valuations of algebraic function fields, divisors and differentials of algebraic function fields. Riemann-Roach Theorem, rational function fields, the fields of genus zero and one. 

Course #

8033685

Title

Topics in Algebra 

Credits

3

Prerequisites

Dept. Approval

Lecturer

Mohammad. Khalil

Ali  Muhsen

Selected topics from Algebra.  Consent of instructor. Department approval