برنامج قسم الرياضيات أ نشئق م ئر اضيات ئئ ته ئ شئئ ي ئئن ئمبر ي 1974 ر ورنئذ ذضئئح اض ئال واضس ئئر ئ ي ئئ إر تنتمئل ضمئ يات ر ملئر اضرسئي ايه ئ اضيات

النسخ

1 برنامج قسم الرياضيات أ نشئق م ئر اضيات ئئ ته ئ شئئ ي ئئن ئمبر ي 1974 ر ورنئذ ذضئئح اض ئال واضس ئئر ئ ي ئئ إر تنتمئل ضمئ يات ر ملئر اضرسئي ايه ئ اضيات ئ ته ض لبئ اضتل ئ واضتل ئته اد ئي رئن اضس ئر ي ئ اإل ئئئئتلم اضرم ))ئئئئ راضب ئئئئتضوياوتا ئئئئ اضيات ئئئئ ته و)ئئئئس ت م ))ئئئئت أ ت ئئئئ ت واض ت ئئئئو أو ئئئئ اإل )تء أو اضسالاتء و)س ت م ))ت ر رال و رن ي اإل تلم اضعتض ئ راضرت ئمايا ئ اضيات ئ ته ومئ رئن اضس ئئر أوة شئ ت م ي ئ ئئ اإل ئتلم اض م سئئ راضئ مو اي ا ئ ئئت ئ يع ئئ ر 1995 را ومرئه رنتمش اضي تض متياخ 1999/2/28 ف نئئئتء الئئئ اضسئئئ ايي يمئئئئر ر 892 ا ض ئئئن 1981 ر اض)ئئئت ي رئئئل و اليم اضمعلئئئئ ر بشئئئنل منالئئئ ر ئئئئ اض اي ئته اضعل ئت ئئ اض ترعئته اضلا ئ ومئئ ايي اضرئ مري اضمعل رئئ ئئ اضعئتر اض ئئترع ر 85/84 را ب ئئيويم اض ء اض اي ته اضعل ت بنم تر اضتل ئ اضر ملسئ شئيل اضس ئر ئ منسائذ ينئترس اض اي ئته اضعل ئت ئ يائر ر 86/85 ا م ئئئئئئه إشئئئئئئ ايف أ ئئئئئئتمذم أتسئئئئئئتء وعئئئئئئ أ ب ئئئئئئتض ال سئئئئئئ ورنئئئئئئذ ذضئئئئئئح اضومئئئئئئه و مئئئئئئ يائئئئئئر ر 2005/2004 را م يج ل ر 7 ا تضبت رئل ائن ر ر 1 ا تضبئت ئت ور 7 ا لبئ ائي و تضئ أ ن ئ رت او اآلل بتضس ر ر 4 ا تضبت رن ر ر روا ري ل متب اد يو م رن ي اإل ئتلم اضعتض ئ راضرت ئمايا ئ اضيات ئ ته و سئت ضلشئيو اضمئ مئنع الا ئت ال ئ اض ا ل ضل اي ته اضعل ت بتضتل وبع إن تل اض تض ر 0 ا و م اي رس ر ال اضن و اضمتض : ر 1 ا 15 إ بتيائئ و م اي ر 2 ا 9 و اه اي ا م تيائ ر ا 6 و اه ت) بتد يو أوال : المقر ارت اإلجبارية :

2 وهئئئ ر ئئئ رسئئئي ايه وضتئئئ رسئئئيي و ئئئ اه اي ئئئ وم ئئئ ف اضرسئئئي ايه اإل بتيائئئ إضئئئ نئئئتء اد ئئتت اض ئئيويط ضل تضئئ إلترئئتة ينئئترس اض اي ئئ وم ئئذ هئئذ اضرسئئي ايه الئئ رئئ )ئئلال اي ئئاال واضرسي ايه اإل بتيا ه : م يمر اضرسيي اسم المقرر اضو اه المقر ارت التمهيدية 1401 اض لسته واضلري اض لس ناليا اضرعت ه اضمست ل اضعت اض م لا م وضو يق يات 5 أ ت ئئت ضر ئئتا م اض تضئئ وم ئئ اضرسئئي ايه ا م تيائئ رسئئي ايه اي ئئ ثانيا : المقر ارت االختيارية : وا مئئتي اض تضئئ رن ئئت واضرسئئي ايه اي ئئمل ومع ئئ ائئت م ئئ اضس)ئئ اض اي ئئ اض تضئئ ئئ ئئ ر ئئتة اضم )ئئع اضئئذط ايائئ ا م تيا ه : رقم المقرر م اسم المقرر الوحدات المقر ارت التمهيدية ت اضرمغا ايه اضرعت ه اضمست ل اض ل 2 روا اضر تن ت اضم لا اضع ط اضرن ق اضيات 5 اض ن روا اضم وضو ت اض يا روا ناليا ادا ا روا اضرن ق وناليا اضر رواته ناليا اضلري 10 يتبع المقر ارت االختيارية :

3 رقم المقرر م اسم المقرر الوحدات المقر ارت التمهيدية ناليا اضلري روا ناليا اضس تت ناليا اضر تة اضم لا روا اضم وضو روا اضرعت ه اضمست ل روا ته اض او اضيات روا اضم لا اضع ط روا اض ي روا اضشب ته واض ي اضشتر ته اضسالات اضيات روا ثالثا : األطروحة : )6 وحدات د ارسية(. يمر اضرسيي م اسم المقرر اضو اه المقر ارت التمهيدية 6 اد يو رسي ايل ض ت )ل بتضرو ول وم ف اد يو إض معراق رعي اض تضئ ئ ر ئتة ر ئ رئل اضيات ئ ته ومنر ئ م يمئل ور تيمئل بتإل ئئت إضئئ إت ئئتبل اضتسئئتءم اللرئئ إلن ئئتل اضب ئئ واضمنسائئ اضعلرئئ وم لئئ ر)ئئت ي ورمتبعئئ اضنشئئت اضعلرئئ اضعئئتضر اضرمعلئق برو ئول اد يو ئئ و ئم اض تضئ اض ئ ء ئئ اضب ئ بعئ إترئتة اضرسئئي ايه اإل بتيا واضرسئي ايه ا م تيائ بر ئتا م اد ئمتذ اضرشئيف واضئذط ئول رئل رلئ اإل ئتلم اض م سئ وع ي ئ أ متذ ر تا ال ادم وضغ متب اد يو ه اضعيع أو اضلغ اإلن لالا ر رل ع ضأل يو بتضلغ اضعيع M.SC. PROGRAMS IN MATHEMATICS

4 In accordance with the resolution no. (892) 1981 passed by the general Peoples Congress prescribing the by-laws for the higher education in Libyan Universities, the Department provides a two-year programme of studies leads to the degree of Master of Science (M.SC.) in Mathematics. The minimum requirements needed is 0 credit hours distributed as follows: 1-15 credit hours for compulsory courses. 2-9 credit hours for elective courses. - 6 credit hours for a dissertation. Courses offered during the this programe include: 1-5 compulsory -credit courses. Compulsory courses aim to build up the necessary background required for students to complete this programme. They are distributed over the first two semesters. 2- Three elective -credit courses. Elective courses are specified and offered mainly to meet the need of students specialising in certain fields. They are given in the third semester. Dissertation aims usually to deepen the knowledge of a student in one area and to develop student s skill and independence to carry out mathematical research. Dissertation however, have to be submitted before the end of the second year of thew programme unless permission is obtained for a reasonable delay. The Department can provide during this programme supervision in the following areas: Algebra, Analysis, Topology, Differential Equations, Numerical Analysis and Calculus of Variations. Literature survey and dissertation can be started only when a student has completed at least all compulsory courses. A dissertation can only be made in a field where a student has been completing or has already completed at least 2 related courses.

5 All details concerning examinations, evaluations, fulfillment of course prerequisites, title and specifications of dissertation and appointment of supervisors should be arranged by the department according to the above mentioned by laws. Medium of instruction and communication should be in English. Though courses and areas of supervision should remain unchanged during a declared two-year programme, it is understandable the they may vary in subsequent programmes according to availability of staff members and their research interests and according to priorities considered by the department. (1) Compulsory Courses No. Code Course Title Credits Prerequisites Ring and Modules Theory of Diff. Equations 102, Functional Analysis 106, Topology Mathematical Methods 1407 (2) Optional Courses

6 No. Code Course Title Credits Prerequisites Calculus of Variations 120, 102, Partial Diff. Equations 102,10, Topics in Mechanics Numerical Analysis 102, Mathematical Logic Topics in Geometry Algebraic Topology Topics in Number Theory Topics in Logic and Set Theory Finite Group Theory Topics in Group Theory Measure Theory Field Theory Topics in Analysis Topics in Topology Topics in Diff. Equations Topics in biomathematics Topics in Numerical Analysis Topics in Algebra Lattice and Universal Algebra Topics in Mathematical Physics () Thesis No. Code Course Title Credits Prerequisites Thesis 6 At least two related courses

7 Descriptions of Courses 1500 Calculus of Variations Classical Variational Problems, Spaces of Functions, Derivatives in Normed Spaces (Weak, Frechet, Strong), Linear and Nonlinear Functionals, First and Second Variations of Functionals, Necessary Conditions for Relative Maximum (Minimum), Weak and Strong Relative Extreme Values, Euler- Lagrange Equation, Discussion of Solutions, Boundary Conditions, Applications, Some Generalizations Rings and Modules Definition and Basic Properties of Rings, Ideals, Quotient Rings Homomorphisms of Rings Prime Ideal Domains, Unique Factorization Domains, Rings of Polynomials, Simple Rings, Definition and Basic Properties of Modules (Left and Right, R-Modules), submodules, Bases Homomorphisms of Modules Exact Sequences of Modules, Diagram Chasing, Direct Product of Modules, External Direct Sum of Modules, Free Modules, Projective and Injective Modules, Finitely Generated Modules, Noetherian and Artinian Modules, Tensor Product of Modules Theory of Diff. Equations Existence Theorems: Picard Lindelof, Peano, Caratheodory and Contraction Mapping Theorems, Uniqueness Theorems, Extension Solution, Maximum and Minimum Solutions, Stability and Asymptotic Behaviour of Solution-Laplace, Liapunov and Poincare Stabilities, Liapunov Stability by Direct Methods, Cheyshev Instabilitiy Theorem, Stability Based on First Approximation, Perron Theorem.

8 150 Partial Differential Equations Classification of Second Partial Differential equations, Hyperbolic, Parabolic and Elliptic, Canonical Form of 2 nd Order P.D.E., Eave Equation, Heat Equation, Cauchy Problems, Cauchy-Kowalewski Theorem for 2 nd Order P.D.E Numerical Analysis Numerical Solution of Ordinary Differential Equations: Taylor Series Method, Runge-Kutta Method, Multistep Method, Convergence Criteria, Errors, Systems of Equations and Higher Order Equations, Boundary-Value Problems, Numerical Solution of Elliptic Partial Differential Equations: Representation as Difference Equation, Laplaces Equation on Rectangular Region, Poisson Equation, Derivative Boundary Conditions, Parabolic Partial Differential Equations: Explicit Method, Crank-Nicolson Method, Stability and Convergence Criteria, Hyperbolic Partial Differential Equations: Wave Equation, Stability of Numerical Method, Method of Characteristic Functional Analysis Complete Metric Spaces, Normed Linear Spaces, Banach Spaces, Equivalent Norms in Banach Spaces, Convergence of Series, Bounded Linear Operators and Functionals, Dual Spaces, Open Mapping, Closed Graph and Hanhn-Banach Extension Theorems, Strong and weak Convergence, Hilbert Spaces, Spectral Theory of Self-Adjoint Bounded Linear Operators in Hilbert Spaces Mathematical Logic Classical Logic: Statement Calculus and Predicate Calculus, Non- Classical Logic: Many valued-logic, Fuzzy Logic, Modal Logic, and Intuiotionistic Logic, Consistency, Completeness, and Decidability, Gödel s Theorems.

9 1508 Topology Connectednes, path-connectednes, Local Connectedness and Components, Compactness, Local Compactness and Compactifications, Function Spaces, Topological Groups and Orbit Spaces. Homotopy and Fundamental Groups Algebraic Topology Homotopy, Fundamental Groups, Higher Homotopy Groups, Singular Homology, Singular Cohomology, and Eilenberg Steenrod Axioms, CW- Complexes, Products Advanced Mathematical Methods Laplace and Fourier transforms; theory and applications. Self-adjoint differential equations. Sturm-Louiville form. Eigenfunctions and eigenvalues Green functions. Orthogonal functions. Gram-schmidt orthogonalization. Orthogonal polynomials generated by Gramschmidt. General Integral transform. Sturm-Louiville transforms. Finite Hankel transforms Finite Group Theory Sylows Theorems, P-groups, Free Groups, Group Presentations, Orbit Space, Burnside Theorem, Groups of orders Measure Theory Rings and Fields of sets, Measurable Spaces, Measure Spaces, Properties of Measure, Existence of Measure, Product Measure, Simple Functions, Measurable Functions and their Properties, Convergence a.e and in Measure, Lebesgue Integral, Properties, Limit Theorems, Fubini Theorem, Spaces of Integrable Functions.

10 1517 Field Theory Rings, Ideals, and Quotient Rings, Maximal and Prime Ideals Polynomial Rings, Field Extensions, Splitting Fields, Finite Fields, Galois Theory, Insolvability of Quintic Lattice and Universal Algebra Poset, Lattice, Distributive Lattice, Algebraic Lattice, Closure Operators, Boolean Algebras, Universal Algebras, Subalgebras, Isomorphisms, Quotient Algebras, Homomorphisms, Direct Products, and Free Algebras. Remark Topic courses ( ) are to be decided by instructors Thesis

11 قائمة بأعء هيئة التدريس الذين يقومون بتدريس الدراسات العليا بقسم الرياضيات م االسم الجنسية الدرجة العلمية التخصص أ م هللا )تض اضر مايط لست ر ال اضذياتن ر ر ا اضعتض اضعوار م تل رلم اضلعا ط امشوا نته ميابتم أور ش شن ي شيرت شعبتل ال يانل إ يات ا س ال اضر يوح ا هللا ل س عا )الح اض ال ر ر اض ال ط مري أاالر تل ولط ا اضوا ا ياح ا ايم هن ط هن ط هن ط أ متذ أ متذ ر تا أ متذ ر تا أ متذ ر تا أ متذ ر تا ر ت ي يات ته م س رعت ه مست ل ي موعوضو يات ته م س م لا اض ي رعت ه مست ل يات ته او م لا اض رعت ه مست ل م لا اض رعت ه مست ل