Master of Mathematics

 

 

 

The mathematics master program was launched in the year 2006. This program aims at providing a specialized cadre in mathematics and it has an important role in stimulating Scientific Research. Moreover, it opens the way for some qualified candidates to continue their higher education.

This Mathematics Master Program is a general math program of 36 credit hours. It consists of two tracks: the Thesis track and the Comprehensive Exam track . The program plan is divided into 3 sections.

  1. Compulsory requirements (18 credit hours)

  2. Electives (12 credit hours): the student chooses four courses of the electives

  3. Either a Thesis or two Seminars and a comprehensive exam.

 

In this program, we are keen to work as a team, and we will work to ensure quality standards in teaching and research activities in order to produce distinctive cadres with a high level of knowledge to meet the developing needs of the labor market and to give them the possibility of completing their study in the world's most prestigious universities.

برنامج الرياضيات

المتطلبات الإجبارية: (18 ساعة معتمدة)

متطلبات التخصص الاجبارية/ عدد الساعات المطلوبة: 18 ساعة

Program's Core Courses/ (18 C.H.)

Course Code

Course Name

C.H.

مسمى المساق

رقم المساق

Math601

Applied Mathematics1

3

رياضات تطبيقية 1

6601

 

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. equation and their applications

 

Math602

Real Analysis

3

تحليل حقيقي

6602

 

Set functions, The outer measure, Measurable sets and measurable space, 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.

 

Math603

Probability Theory

3

نظرية الاحتمالات

6603

 

Kolmogorovs axioms, Random variables, Probability distributions, Mathematical expectation, Independence, Boral-Cantelli theorem, Characteristic functions, Types of convergence, Laws of large numbers, Central limit theorem.

 

Math604

Abstract Algebra1

3

جبر مجرد1

6604

 

Groups: Algebraic structure, Centralizer, commutator, Normal subgroups, Homomorphism and isomorphism, Group action, Sylow's theorems, Direct products, Finitely Generated Abelian groups.

 

Math605

Numerical Analysis

3

تحليل عددي

6605

 

Solving linear systems of equations, Iterative techniques for solving linear systems, Approximating eigenvalues, Numerical solutions of nonlinear systems of equations, Finite differences.

 

Math606

Complex Analysis1

3

تحليل عقدي1

6606

 

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.

 

                                  متطلبات التخصص الاختيارية/ عدد الساعات المطلوبة: 12 ساعة

Program's Core Courses/ (12 C.H.)

Math610

Linear Algebra

3

جبر خطي

6610

 

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.

 

Math611

Applied Mathematics2

3

رياضيات تطبيقية2

6611

 

Approximation method, expansion approximation, Watson's method, Laplace method, Fourier integral. WKB method, perturbation method

 

Math613

Integral Equations

3

معادلات تكاملية

6613

 

Voltera Equations, Fredholm Equations, Solving Integral Equations by Substitution and Approximation, Applications on Integral Equations, Millin Transforms and Applications, Hankel Transforms and Applications.

 

Math614

Abstract Algebra2

3

جبر مجرد2

6614

 

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

 

Math615

Topology

3

تبولوجيا

6615

 

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.

 

Math616

Complex Analsis2

3

تحليل عقدي2

6616

 

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.

 

Math617

Functional Analysis

3

تحليل دالي

6617

 

Metric spaces, Norma 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.

 

Math618

Mathematical Statistics

3

احصاء رياضي

6618

 

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

 

Math619

Operations Research

3

بحوث العمليات

6619

 

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.

 

Math650

Special Studies in  Mathematics Analysis

3

دراسات خاصة في التحليل الرياضي

6650

 

advanced topics chosen from analysis that suit students’ and teachers’ interests.

 

Math651

Special Studies in Abstract Algebra

3

دراسات خاصة في الجبر

6651

 

Advanced topics chosen from abstract algebra that suit students’ and teachers’ interests.

 

Math652

Special Studies in Applied Mathematics

 

3

دراسات خاصة في الرياضيات التطبيقية

6652

 

Advanced topics chosen from applied mathematics that suit students’ and teachers’ interests.

 

SC 651

English for Graduate Students

3

لغة انجليزية للدراسات العليا (استدراكي

4351

 

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.

                                    متطلبات المسار/ عدد الساعات المطلوبة: 6 ساعة

Math699

Thesis

6

رسالة جامعية

6699

 

The student should prepare a thesis, defend it in front of a special committee, and pass the discussion

 

Math696

Seminar 1

3

حلقة دراسية1

6696

 

A study by the student that ends with a presentation and a written report.

 

Math6697

Seminar 2

3

حلقة دراسية 2

6697

 

The student will select, under the supervion of faculty member, a topic in which the student writes a report including literature review

 

Math698

Comprehensive Exam

0

الامتحان الشامل

6698

 

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

 

 

 

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