Jobs of education programme
Statistician Applications developer
High school math teacher
High school physics teacher
The field
Science Type of certificate
Bachelor degree Name of certificate
Certificate in Math The specialization
Math Place and address of the program
Damascus- BaramkehTelephone: 0093-011-2121978
0093-011-3392-4966
Fax: 00963-011-2119896
Aims of the department
The department of Math aims to be the pioneer in graduating excellent students in Math and its applications and contributing in enriching the society of knowledge to develop the students’ intellectual, cultural, and educational level. Conditions of acceptance
- Having a scientific baccalaureate by 1920 degree at least and getting 390 mark in Math.
- Applying to the system of the university’s acceptance.
Preferable skills
- The ability to think logically and analytically.
- To havescientific creativity skill.
- The ability to use technical information and some computer programs in all branches of Math.
- The ability to express ideas orally and through practical reports written in scientific and professional way.
Number of enrolled students per year
750 students. Length of study
Four years Language of study
Arabic Sectors of careers that are worked in
- Working as a teacher.
- Working as a researcher: A graduate will be able to conduct researches and studies in the fields of planning by using available information and statistics, analyzing them, andusing studied mathematical samples.
- Working as a statistical researcher: He/she will be able to collect information, prepare data and statistical numbers, analyze them, and popularize these results.
- Working as an economical researcher: He/she will be able to prepare studies and researches in the economic field by using mathematical samples.
- Working as a programmer: He/she will be able to prepare and write programs in one of computer languages.
- Working as an analytical to computer systems: He/she will be able to examine results and choose the suitable system.
- A graduate will be able to do the tasks which concern with insurance, accounting, banking, and auditing.
Pursuing academic study
Master and doctorate Course description
| Subject | Description |
| Linear Algebra(1) [1st year] |
The course covers: Basic concepts in the theory of sets - Matrices - The rank of amatrix -The operations on matrices -The direct sum of square matrices -The system of linear equations -The invert of a square matrix - Gauss method forsolving alinear equations - Kramer method for solving alinear equations -Vectorspaces -Linear independence -Linear dependence -Basis and spanning sets - Linear mappings -Linear mappings spaces -Rank and nullof a linear mapping - Linear mapping matrix -Similar matrices -Thetransformation matrix |
| Analysis (1) [1st year] | Preliminary concepts and methods of proof: Numbers sets and their properties, The absolute value of its properties, The supremum and the infimum of a set, Methods of proof: direct proof, proof by contradiction, proof by mathematical induction.The proof of the Archimedean property, and that is densein . Infinite numerical sequences: An extensive study about the sequences and their convergence, The famous limits of some sequences, and the proof of some theorems in this context. Studying the partial sequences, the monotonic sequences, and Cauchy sequences. Examples and applications. Infinite numerical series: the definition of series and convergence, series properties. Famous series: geometric series,numerical harmonic series. Standards of convergence and divergence. Alternating series and mixed series, and its convergence standards. Limits and continuity of functions: the definition of the limit, The properties of the limits, Famous limits. Definition of continuity, The types of discontinuity points. Studyingthe inverse functions, and hyperbolic functions. Differentiable functions: The definition of the derivative, The geometric meaning of the derivative, The derivation of composite functions, implicit functions, and intermediate functions. The higher order derivation, Taylor and Maclaurin expansions. Definition of differentiation, differentiation properties, differentiation of the composed function. Basic theorems in the differential calculation. L’hôspital rule in removing indeterminacy. Studying the maxima and the minimavalues, and drawing functions. |
| Analytic Geometry [1st year] | This course deals with thevertices, the coordinates, and the directions in thespace. The plane in thespace. The line in the space. The surfaces and curves in thespace. The second-degreesurfaces.The Ball. The surfaces generated by mediator curve. Drawing curves in the plane. |
| Linear Algebra(2) [1st year] | This course deals with: The characteristic polynomial and the minimal polynomial for a linear mapping (a square matrix). Eigenvalues, eigenvectors and eigenvector spaces. Similarity, diagonalization, and triangulation of a linear mapping (a square matrix), Calculation power of a matrix. The dual space. Bilinear forms and the operations on them and their properties, Inner-product spaces, Euclidean spaces, and Hermitian spaces. Linear mappings on unitary spaces. |
| Analysis (2) [1st year] | The course covers: Indefinite Integrals:The definition of Indefinite Integral, the properties of Indefinite Integrals. Famous integrals Table. Changing variable method for calculating an integration. Integration by partsmethod for calculating an integration.Using fraction decomposition in calculating an integration.Concluding of some reductionformulae. Trigonometric integrals. Hyperbolic Integrals.Root Integrals. Definite Integrals:The definition of definite integration using the Riemann sum. The properties of definite integrals. Improper integrals, without the study of the convergence criteria.The definition of parametric integration and calculating its valuewhen the upper and the lower limits are constants. The numerical integration using the method of rectangles and trapezia. Applications of definite Integrals: (The area ofplane figuresand surfaces, volume, length) Multiple integrals:The definition ofdouble integration and its properties, calculating the double integral, changing the variable in the double integral, and applications of the double integration. The definition of the triple integration and its properties, calculating the triple integral, changing the variable in the triple integral, and applications of the triple integration |
| Programming Languages[1st year] | The course covers: algorithms, algorithm description, flowchart, translator / interpreter, types of variables, the definition of variables, initialization of variables, constants, comments, input and output, simple standard types, floating point, arithmetic operations, logical operations ,the assignment operator, comparison operators, priority of operations, conditional statements, control statements, if statement, if/else statement, the structure of nested if/else statement, case statement, for loop, while loop, repeat loop, matrices/vectors, strings,strings functions, pointers, functions, procedures, modules / Librariesfunctions, declaring of functions, reference variables, recursive algorithms, records, with phrase. |
| Computer operation Principles [1st year] |
The course covers: 1. Counting systems: Decimal counting system - Binary counting system - Octal counting system - Hexadecimal counting system. 2. Basic Concepts in Computer Science: The definition of the computer - Types of computers - Generations of computers - Computer components: Hardware & Software - Data (information) - the human components. 3. operating systems 4. computer networks:networks definition - Types of networks - The benefits of networking 5. Internet and the World Wide Web: The definition of Internet - The services provided by the Internet. 6. Viruses:The definition of the virus - Types of viruses -How viruses work - Ways of avoiding viruses. 7. Some application software: office software - databases - math-processing system – statistical analysissystem. |
| Vector Analysis and Differential Geometry Principles [1st year] |
Considering a student: Vector Analysis: • concepts and basic definitions: Scalar and vector fields - Vector concept (analytically and geometrically) and position vector - Vector concept (the symbol and the direction) - projection and representation - vector elements, and the physical meaning of the point of application of the vector - vector, has no invert. • Operations on Vectors: Vector adding and decomposing - Multiplying vectors and vector division - Vectors and complex numbers - The analytical formula and the tensorform of a vector - powers: (powers and balance - the study of the vertical movement). • moment of a vector: mathematical concept and its physical meaning - The moment of a vectorabout a point, and two points - The moment of a vector around an axis, around an axis and a point –Moment of a couple - Moment of sum of vectors. • The differential operator▼ and the operations on it: the differential operator▼, symbolic vector - gradient, divergence, rotation - Vector differentiation and integration (linear, surface, volumetric) - Gausstheorem, Stokes theorem, Green theorem. Differential Geometry: • Basic concepts and definitions. • Vector function with one variable and multivariable. • Derivation and differentiation of one variable function in Cartesian, polar, and momentum coordinates - Curvature radius of a curve, wrapping curve and Frenet formulas. |
| Algebraic structures(1) [2nd year] |
The course covers: Groups, subgroups, normal subgroups, and the quotient group - Cyclic group - Permutations groups- Groups homomorphism and isomorphism- Direct sum and directproduct of groups- Finite abelian groupsand finitely generated groups - p-groupsand Sylow's theorems- Groups classification. |
| Algebraic structures(2) [2nd year] |
This course deals with: 1. Rings: Subrings - Integral domain- The ideal field in the ring- Ring homomorphism - The kernel of ring homomorphism - isomorphism theorems- Quotient field. 2-Theory of ideals: The left and right ideals - Maximal and Minimal ideals - The basis of a ring (The root of a ring) - The root of an ideal - Jacobson basis - Ideals in abelian rings - Prime ideal -Maximal ideal, prime ideal and Integral domain - The maximal ideal and the field - Principle ideal domain - Euclidean Ring - Unique factorization domain. 3- Polynomials ring: division algorithm - ideals in polynomials ring - Irreducible polynomials - irreducible polynomials criteria. 4-Localrings:Artinian Ring- Noetherian Ring. |
| Analysis (3) [2nd year] | This course deals with: Numerical sequences and series - Functional sequences and series - Improper integrals - ParametricIntegrals - Fourier series |
| Analysis (4) [2nd year] | The course covers:1-Multivariable real functions.2-Limits and continuity of multivariable real functions. 3-Partial derivatives - vertical derivatives. 4-Applications of differential calculation of multivariable real functions (Local maxima and minima - Mean value theorem - Taylor's theorem). 5-Differential calculation of multivariable vertical functions6-Multiple integrals theorem. |
| Topology(1) [2nd year] |
The course covers: Metric spaces: Definitions - Sequences - The convergence of sequences - The continuity of functions - closed and opensets - Exact spaces - Downsizing - Banach fixed-point theorem and its applications in solving algebraic and differential equations - Picard's theorem - compact spaces - an idea about connected spaces Topological spaces:Definitions and principles- meterizablespaces – generating topology - topological subspaces. |
| Numerical Analysis (1) [2nd year] |
The course covers: 1- Errors: - sources of error - error in calculations. 2- Solving nonlinear equations: repeated bisection method - Newton's method. - Iteration method - numerical solutions for a system of linear equations. 3-Solution of linear equations: Cramer's method - Matrix inverse method - Jacobi method - Gauss method - Gauss-Seidel method - Eigenvalues and eigenvectors. 4-Interpolation:General method in interpolation- Lagrange's method - Newton forward method - Divided difference method. 5- Numerical Differentiation:Forward differences formula - Central differences formula - numerical formulas for derivatives based on interpolation. 6-Numerical integration: Trapezia method –Simpson's method. 7-Solving differential equations:Euler’s method - Taylor's method - Runge-Kutta method. |
| Differential Equations(1) [2nd year] | The course covers: Basic definitions:1- Differential equation. 2- Differential equation solution. 3- General solution. 4- Particular solution. 5 - Singular solution. 6- Sources of ordinary differential equations. 7- Formation of differential equations. 8-Initial conditions problems and boundary conditions problems. 9-Solving some forms of ordinary differential equations using direct integration. First order differential equations solved regard the derivative: The separable equation - equation that could transform to a separable - homogeneous equation - equation that could transform to ahomogeneous equation-exact equation - inexact equationand integrating factors - linear equation regard y – linear equation regard x - Bernoulli's equation - Riccati equation. Linear differential equations with constant and variablecoefficients:Solving the second order linear equation of with constant coefficients- solving the order n linear equation with constant coefficients- solving some special forms of the second order linear equation with variable coefficients-Euler’s equation - Reducing the order method. The system ofdifferential equations: The definition of the systemof differential equations- The definition of the system of differential equations with constant and variable coefficients - solving the systemof order n linear differential equations solved regard the derivatives with constant coefficients. |
| Differential Equations(2) [2nd year] | This course deals with: 1- Quick Review of differential equations (1). 2- Solving second order linear differential equations using series. 3-Systems of differential equations in general. 4-Detailed study of linear differential equations - physical and geometric applications on the system ofdifferential equations. 5-Differential equations with total differentials (Pfaff differential equation). 6- First order partial differential equations. 7- Classification of second order partial differential. 8- Laplace transforms and their use in solving differential equations. |
| Mechanics(1) [2nd year] |
Student recognize the following concepts: 1-Motion of a material point:(A) Motion science - Vector study ofmotion - Position vector - Velocity vector -Acceleration vector. (B) Some special motions of a material point (vector and analytical study) - Straights motion - Circular motion - Harmonic motion - The motion subject to the law of surfaces - Curved motion. 2-Balance of material point:(A) Principles of balance - Links and their types (fixed and variable geometric links - Differential links - The ideal links - links with friction).(B) Powers and theirs balance - work - virtual work. (C) The general conditions of balance - The principle of virtual work - Lagrange's multipliers - the stability of balance. 3- Moving a material point:(A)Basic laws of mechanics - Thedynamic elements of a materialpoint. (B) General theories of movinga material point (The movement quantity theory - Momentum theory - Kinetic energy theory) - D'Alembert's principle and its applications.(C) Somespecial motions of a material point (Circular motion - straight motion in resistance environment - Themotion that subject to surfaces law -missiles motion). |
| Programming and Algorithms [2nd year] |
Students learn through it: Introduction to C++ language - types of variables - definition of variables - initialization of variables - Public/Protected/Private variables - Global/Local variables - variables without signal - constants - Comments - input and output streams - mathematical operators - logical operations - increase / decreaseoperators - assignment operator–sizeof operator - comparison operators -operators priorities - casting between variables types - conditional statements - control statements- if statement - if/else statement - the structure of nested if/else statement -case statement (switch) -for loop |
| Algebraic structures(3) [3rd year] |
Students learn through it: 1- Module on a ring R: Module definition - Submodule - Module generated by a set - operations on Modules -Quotient module. 2-Modules homomorphism: Definition of Modules homomorphism - homomorphism theorems. 3-Commutative diagrams for modules. 4-Noetherian Modules - Artinian Modules. 5- Directsum and product ofmodules. 6-FreeModules. 7-Exact sequences. 8-ProjectiveModules. 9-Horizontal Modules. 10- Modules on Euclidean ring. 11-Tensor product of modules. |
| Numerical Analysis (2) [2ndyear] |
This course deals with 1. Solving linear equations:Solving a system of linear equations using primary matrices - Methods of Iteration in solving a system of linear equations - Eigenvalues problem. 2. Solving differential equations:linear differences equations with constant coefficients - The K-steps cell method,Runge-Kutta methods. 3. Solving partial differential equations: Theexplicit and implicit methods for solving partial differential equations. 4. Optimal solutions:search methods - methods with gradient included - Newton's methods. 5. Functions approximation: Functions approximation by polynomials - Interpolation - Approximation by Legendre polynomials - The least squares method. 6. Solving integral equations: Volterra integral equations - Iterative approximations method - Fredholm integral equations - The solvent kernel method. |
| Functional Analysis (1) [3rdyear] |
Students learn through it: Normalized spaces - Banach spaces - Inner product space and Hilbert space - An overview aboutHahn-Banach theorem and its applications - An overview about Banach-Steinhaus theorem and its applications. |
| Analysis (5) [3rdyear] | Students learn through it: 1-Chapter I: Functions with limited variability. 2- Chapter II: Steljes integration (The concept of Steljes integration - Existence conditions for Steljes integration - Steljes integration properties - applications). 3- Chapter III:Measurable sets (operations on measurable sets - internal and external measure for measurable sets). 4- Chapter IV: Measurable functions (measurable functions definition - measurable functions properties - limits and convergence by measure for measurable functions - applications). 5- Chapter V: Lebesgue Integration (Lebesgue Integration definition - Lebesgue Integration main properties - applications - a comparison between Lebesgue Integration and Riemann integration). |
| Complex Analysis (1) [3rdyear] |
The course covers: Complex plane: Complex number field - Topology Complex-variable functions:limits, continuity, and derivation – studying some famous functions - analytical functions and harmonic functions. Integration of Complex-variable functions: Cauchy theorem in integration-Cauchy rules. Complex power series: Complex sequences and series - uniform convergence - uniform functions in power series - some special methods in expansion functions in power series. |
| Complex Analysis(2) [3rdyear] |
The course covers: Singular isolated points: a glimpse into polynomial functions - classification of singular isolated points - Laurent series and Laurent classification for singular points - using integrations method in finding Laurent expansion within anannulus. Analytical extension:analytical extension concept-analytic functions and the identity theorem - analytical branches. Residues theorem and its applications: The definition of residue and residue in infinity - Calculatingthe definite integrals - the principle of Alergoumenat - The expansion of meromorphic functions in simple fractions - The zeros of analytical function - Rouché's theorem - Using the residues theorem in calculation the sum of power series Infinite products, Euler functions: absolute convergence and uniform convergence - Representing transcendental polynomial function as an infinite product - Gamma and Beta functions. Preserved function:Möbius transformations - the principle of orientation - applying the upper half of the plane on the unary disk - applying the upper half of the plane on the lower half - applying the unary disk on itself - Schwarz Lemma- Riemann theorem in the preserved function -Schwarz-Christoffel rule. |
| Mechanics(2) [3rdyear] |
Students learn through it: Material bodiesmotion: (Simple - Rectilinear - Circular - Spiral - General - Planar) - Balance science - Tensor rectilinear |
| History of Mathematics [3rdyear] | The course covers: 1. Ancient Egyptians mathematics: Numbering - Calculations - The most important achievements. 2. Ancient Babylonians mathematics: Numbering - Calculations - The most important achievements - zero. 3. Ancient Greeks Mathematics: Numbering - Calculations - Perfect numbers - Amicable numbers-Constructible numbers with compass and straightedge - The most important Greek scientists. 4. Indian Mathematics: Numbering - Calculations - The most important achievements and discoveries. 5. Arabs Mathematics: Numbering - Calculations - Their mathematical achievements and discoveries - Some Arab scientists and the most important creations. 6. Modern mathematics: some scientists and achievements. |
| Discrete Mathematics [3rdyear] |
The course covers: Basic principles of the methods of counting - Sets theory - The number of mappings (respectively: injective, surjective, bijective, completely increasing, increasing) between two finite sets - Combinations and permutations - some binomial identities - mathematical induction and recursive functions - advanced counting techniques - Generating functions - The principle of inclusion and exclusion - Binary relations - Set partitions - S (n, k) - Stirling numbers of the second kind. |
| Graph Theory [3rdyear] |
The course covers: Introduction to graph theory - Basic definitions -Connected graph-Disconnected graph -Directed graph - Regular graph - Weighted statement -Hamiltonian graph - Isomorphic graphs - matrices in graph theory - Adjacency matrix - Input matrix - Bipartite graph - Trees - Lattices - The maximum flow problem - The coloring problem - Graph algorithms - The cost of algorithms - applications of graph theory. |
| Integral Equations and Calculation of Variations [4thyear - Mathematical Analysis] |
This course deals with: 1- Integral equations: Fredholm integral equation - Volterra integral equation. 2- Using Laplace transforms in solving integral equations: Using Laplace transforms in solving differential equations - Using Laplace transforms in solving differential- integral equations. 3- Calculation variations principle: The basic theorem in calculating variations- Euler equation - Ostrogradsky equation - Hamilton - Isoperimetric problems - The maxima and the minima values. |
| Mathematical Modeling [4thyear - Mathematical Analysis] |
This course includes: Basic concepts in modeling - linear models -Non-linear models - Integer models - Dynamic models - inventory models. |
| Differential Geometry [4thyear - Mathematical Analysis] |
This course deals with: 1- Curves in space: Vectors - Vector functions - Vector fields - Parametric representation of a curve - The length of a curve - Singular points ofa curve - Tangency of curves and tangency of a curve and a plain - Expansion and expansive of a curve - Normal equations of a curve - Frenet frame and Frenet formulas - Curvature and wrapping of a curve. 2-Surfaces in space: Parametric representation of surfaces - Some famous surfaces (rotational - ruled) - Envelope of a family of surfaces - Developable surfaces. 3-The two fundamental quadratic formsof a surface: The first fundamental quadratic form - Isometric applications - The second fundamental quadratic form - The classification of the points on a surface - Gauss curvatureand Christoffel symbols - Geodesic curvature and geodesic lines - Selgeodesic Coordinates -Normal curvature and fundamental curvatures. 4- Tensors and external forms: Tensors and operations on them - multiple linear forms-Associate Space - Anti-synmetric forms - Exterior product. 5-Differential manifolds: Patch - Local coordinate system or local chart - Differential manifold Atlas -Differentiable functions on manifold - Tangent vectorson manifold - Induced Maps - Lie groups and Fiber bundle - Vector fields and tensors on differentialmanifolds - Riemann manifolds - Riemann Metric - Riemannian connection. |
| Operations Research [4thyear - Mathematical Analysis&4thApplied Mathematics and Information] |
This course deals with: 1-Introduction to Mathematics: methods of solving linear equations systems.2- Introduction to convex analysis. 3- Mixing problems. 4- Linear Programming: General model of a linear program -The geometric solution to a linear program in - Simplex algorithm - The sensitivity of a solution - Dual programs. 5-Integer linear programs.6-Branching programming: Transportation problem - The general model of the transportation problem -Algorithms for solving transportation problems. 7- The appointment problem. 8- Introduction to game theory. 9- Network analysis: - PERT networks. 10- Simulation. 11- Introduction to queues theory. 12- Decision Analysis. |
| General Topology(2) [4thyear - Mathematical Analysis] |
Students learn through it: Topological spaces and subspaces –Product topology - Filters and Networks -Connectivity - Compactness - Separation axioms - Counting axioms - Topological vector spaces - Spaces. |
| Functional Analysis(2) [4thyear - Mathematical Analysis] |
This course deals with: Spectral theory of bounded linear operators - a glimpse of the spectral theory of unbounded linear operator and its application - Banach Algebras - An overview of distributions theory (Laurent Schwartz distributions). |
| Number Theory [4thyear - Mathematical Analysis] |
This course covers: 1- Integers and their properties. 2-Divisibility 3- Prime numbers: Mersenne numbers - Fermat numbers. 4- Diophantine equations: Methods to solve diophantine equations - Pythagorean triples - Finite continued fractions. 5-Congruence and its properties: - Solving linear congruence – solving a system of linear congruencies. 6- Numerical functions: the integer part function - Euler Function - function - function - Perfect numbers - Mobius function - Liouvilles function - Mangoldt function - primary roots. |
| Measure Theory [4thyear - Mathematical Analysis] |
This course covers: 1-Measures: Algebra - -Algebra - Measures -Outer Measures -Lebesgue - monotonic classes.2- Measurable functions and their integrations: Measurable functions -Step functions (Simple functions) - Integration of real measurable functions- Integration of complex measurable functions -Limits theorems: (a) Increasing convergence theorem. (b) Fatou's lemma. (c) Monotone convergence theorem (Lebesgue's theorem). 3-Patterns of convergence and spaces, and their applications in the possibilities. 4-Complex measures,and Radon-Nikodym theorem and its applications. 5- Product Measures and Fubini's Theorem.6- Measures on locally compact space and Ritts theorem - a glimpse of Daniell integration. |
| Differential Equations Theory [4thyear - Mathematical Analysis] |
This course covers: 1-Existence and uniqueness theorem in differential equations. 2- Second-order linear differential equations: The solution in the neighbor of a regular point and in the neighbor of singular regular point - The solution in the neighbor of infinity point - Representation solutions in circumferential integration - Asymptotic expansion. 3-Applications in hypergeometric equation: Bessel equation - Legendre equation - studying some other special functions. 4-Boundary value problems. 5.Partial differential equations theory: Parabolic partial differential equation - Hyperbolic partial differential equations - Elliptic partial differential equation. |
| Algebraic structures(4) [4thyear-Algebra and Geometry] |
This course covers: 1- Categories. 2- Functor. 3- Functor fixing the objects (Fixob). 4- Natural Transformations. 5- Universal Arrows. 6- Yoneda lemma. 7- Products and limits. 8- Adjoints. 9- Equivalence of categories. 10- Applications. |
| Mathematical Logic [4thyear -Algebra and Geometry] |
This course covers: I. Assumptions calculation (classical logic) 1.Syntax: Formula calculation - Proofs by induction on a set of formulas - Formula tree analysis - Unique factorization theorem -Definitions by induction on a set of formulas - Substitution in logical formulas. 2.Semantics: truthtables -Tautology and equivalence of logical formulas -Some Tautologies. II.Quantifiers logic:Free variables -Restricted variables - fundamental laws in Quantifierslogic. III.Boolean Algebras: Boolean algebra structure - dual principle -Boolean fundamental calculation - order relation in boolean algebra - The maxima and the minima termsin boolean algebra - simplification of boolean statements -harmonic terms method - Queen Method - McCloskey network - Boolean functions - Representing boolean functions - Logical operator - Karnaugh map. IV.Predicate calculation: 1. Syntax: First-order logic - The words in the language - The formulas in the language - Pending formulas - Substitution in formulas. 2.Structures: Language models- Sub structures and restricted formulas - Verifying formulas in structures -Prenex formulas - Skolem formulas - The first step in model theory. |
| Mathematical Modeling [4thyear -Algebra and Geometry] |
This course deals with: The importance of mathematical modeling (cost, profit, income) – Decision problems - Models types - Linear models - Simplex algorithm - Integer models - Binary models - Dynamic models - Projects scheduling - Languages - Automata. |
| Differential Geometry [4thyear -Algebra and Geometry & 4th Applied Mathematics and Information] |
This course deals with: 1- Curves in space: Vectors - Vector functions - Vector fields - Parametric representation of a curve - The length of a curve - Singular points of a curve - Tangency of curves and tangency of a curve and a plain - Expansion and expansive of a curve - Normal equations of a curve - Frenet frame and Frenet formulas - Curvature and wrapping of a curve. 2- Surfaces in space: Parametric representation of surfaces - Some famous surfaces (rotational - ruled) - Envelope of a family of surfaces - Developable surfaces. 3- The two fundamental quadratic forms of a surface: The first fundamental quadratic form - Isometric applications - The second fundamental quadratic form - The classification of the points on a surface - Gauss curvature and Christoffel symbols - Geodesic curvature and geodesic lines - Selgeodesic Coordinates - Normal curvature and fundamental curvatures. 4- Tensors and external forms: Tensors and operations on them - multiple linear forms - Associate Space - Anti-synmetric forms - Exterior product. 5- Differential manifolds: Patch - Local coordinate system or local chart - Differential manifold Atlas - Differentiable functions on manifold - Tangent vectors on manifold - Induced Maps - Lie groups and Fiber bundle - Vector fields and tensors on differential manifolds - Riemann manifolds - Riemann Metric - Riemannian connection. |
| Groups and Algebras Representa-tion [4thyear -Algebra and Geometry] |
The course covers: 1- Introduction to the theory of finite groups. 2- Act of a group over a set: Orbits -fixing group. 3- Basic Concepts in groups’representations: linear representation of groups - Matrices representation of groups - Equivalent representations - Regular representation of finite groups. 4-Reducible and irreducible representations: G-space concept – Groups representations over G-subspace. 5- Groupsrepresentations over an inner product space: Unitary representations - Reducible and irreducible representations over an inner product space. 6- Representation characteristics. 7- Dual representations. 8-Tensor product of representations. 9- Algebras representations: Basic Concepts in Algebras representation - Lie algebras representations. |
| Fields Extensions [4thyear -Algebra and Geometry] |
The course covers: 1- Review of some of the issues in groups’ theory and rings theory and mainly related to the subject of fields extensions. 2- Fields Extensions: definitions and primary properties - the degree of extension. 3- Algebraic & Transcendental Extensions. 4- Finite Extension and its relation to algebraic extension. 5- Geometric Constructions. 6- Finite Fields, Primitive Roots of Unity. 7- Automorphism of Fields and Galois Theory. 8- Automorphism of Fields and Fixed Fields. 9- Splitting Fields - Separable Extension. 10- Simple Extension - Cyclic Extension. 11- Galois Group - Solvable Extensions. 12- Extension by Radicals. 13- Normal Extension - Perfect Field. 14- Symmetric Functions and representation of Galois theory. |
| Numbers Theory [4thyear -Algebra and Geometry] |
This course covers: 1- Integers and their properties. 2-Divisibility 3- Prime numbers: Mersenne numbers - Fermat numbers. 4- Diophantine equations: Methods to solve diophantine equations - Pythagorean triples - Finite continued fractions. 5-Congruence and its properties: - Solving linear congruence – solving a system of linear congruencies. 6- Numerical functions: the integer part function - Euler Function - function - function - Perfect numbers - Mobius function - Liou villes function - Mangoldt function - primary roots. |
| Algebras Theory [4thyear -Algebra and Geometry] |
The course includes: 1- Modules Theory and Algebras: rings and fields - Lattices – Modules - Homomorphisms and exact sequences - Quotient modules and isomorphism theorems - Algebras. 2-Lie Algebras:Lie algebras - Derivation applications on Lie algebras -Lie sub algebras and ideals - Quotient Lie algebra and isomorphism theorems. 3- Solvable and Semi simple Lie Algebras:The derived sequence in Lie algebra -Solvable Lie algebra- Centraldecreasing sequence in Lie algebra - Semisimple Lie algebra. 4- Nilpotent lie Algebras and Bilinear Forms on Lie algebras: Nilpotent lie Algebras - The center and the centralizer in Lie algebra - Central increasing sequence in Lie algebra - Representations of Lie algebra - Bilinear Forms on Lie algebra - Killing formula. 5-Lie Algebras Extension and Lie Algebras Direct sum:Exact sequences -Lie algebras extensions- Simple and central extensions - External direct sum of Lie algebras - Internal direct sum of Lie algebras - Semi direct sum of Lie algebras. 6-BCK algebras: BCK algebras - commutative and implicit BCK algebras - ideals and primary ideals in BCK algebras - Homomorphisms and isomorphism theoremsin BCK algebras. 7- Bounded BCKalgebras Bounded BCK algebras - Bounded BCK algebras and boolean lattices - Primary spectrum of bounded BCK algebras. 8- BCH algebras and BH algebras: Analog BCH algebras - Analog BCH algebras and BCI algebras - Ideals and the rectilinear ideals in BH algebras - Quotient BH algebra and isomorphism theorems. 9-BCC algebras:Proper BCC algebras - Bounded BCC algebras - BCC sub algebras - The ideals of BCC with n-arrangement - Maximal ideals in BCC algebras - Atomic elements BCC algebras - methods of building BCC algebras. |
| Lattice Theory [4thyear -Algebra and Geometry] |
This course includes: Universal algebra principles - binary relation and their properties -Equivalence relations and order relations and their properties -Ordered set - Zorn's lemma and the equivalent statements with the proof of equivalence - Lattice and its properties - Complete lattice and its properties - Associative lattice and its properties – Standard lattice and its properties - Complement lattice and its properties - Boolean lattice (Boolean algebra) - Boolean ring, significant patterns of modern algebras patterns, which are algebraic classes of type (2,0), which represents an important and interesting application of the concept of Boolean lattices. |
| Algebraic Geometry [4thyear -Algebra and Geometry] |
This course includes: Polynomials ring: The definition of a polynomial - Ideals - Hilbert basis theorem - One variable case - order relations on polynomials - The division algorithm. Gröbner bases: The definition of Gröbner basis - Finding Gröbner basis for an ideal in polynomial ring -Reduced Gröbner basis –Applications of Gröbner bases in algebraic geometry. Algebraic affine varieties:The definition of affine space - The definition of affine variety - Hilbert's zeros theorem (weak & strong versions) - vector space - Euclidean zeros and zeros in infinity - Bezout theorem. Outputstheorem: One variable case - Sylvester matrix -More than one variable case - Macaulay matrix - Output theorem Applications. |
| Numerical Solutions of Integral Equations [4th Applied Mathematics and Information] |
This course includes: - Introduction: Partial differential equations and integral equations - boundary value problems. - Finite difference methods in one dimension and two dimensions -Finite elements methods in onedimension and twodimensions - The iterative methods. |
| Fuzzy Logic and its Applications [4th Applied Mathematics and Information] |
This course includes: 1. Fundamental concepts in logic theory.2. Types of logic. 3.Reasoning.4. Inference.5.Propositional logic: Elements of proposition logic - Truth tables- Connectives- Logical equivalences - Inference rules in propositional logic- Conjunctive normal form- Reasoning methods in propositional logic. 6. Predicate Logic: Elements of predicate logic - Inference rules in predicate logic - Converting to context normal form. 7.Fuzzy Logic: Fuzzy sets - Operations on fuzzy sets - Fuzzy numbers- Fuzzy relations- Operations on fuzzy relations - Fuzzy propositions - Linguistic variable - Membership function- Logical operations - Fuzzycation- Fuzzy inference - Defuzzification - Example of Fuzzy System. |
| Mathematical Modeling [4th Applied Mathematics and Information] |
This course deals with: The importance of mathematical modeling (cost, profit, income) - Decision problems - Models types - Probabilistic optimization models - Decision tree- Accumulation tests - Markov chains - Transitions matrix - Game theory -Nash equilibrium - Zero sum games - Nonzero sum games - Simulation - Queueing theory. |
| Graph Theory Applications [4th Applied Mathematics and Information] |
This course includes: Graph theory algorithms - Cascada algorithm - Dijkstra's algorithm -Shortest path algorithm - Networks algorithm to solve Transportation problems -The algorithm of maximum flow in a network - Fulkerson algorithm - Sort Priorities algorithm- PERT method and the method of finding the critical path - Basic concepts in simulation - Basic concepts in queuing theory. |
| Category Theory Applications [4th Applied Mathematics and Information] |
This course includes: The category and sub category - direct functions and indirect functions - Functional morphisims - adjacent functions - Categories equivalence - Sum and product in categories - Kernel and cokernel - projective and horizontal limits. |
| Automata and Formal Languages [4th Applied Mathematics and Information] |
This course includes: 1. Fundamentalconcepts in automata theory:Alphabets -Strings - Languages- Operations on strings. 2. Finite automata: Definition of automata - Determinants Finite Automata (DFA) - Non-Determinants Finite Automata (NFA) - Equivalence of DFA and NFA - Non-Determinants Finite Automata with transition ( -NFA) - Equivalence of NFA and -NFA. 3. Regular expressions and languages: Regular expressions - The operators of regular expressions - Converting DFA to regular expression - Converting regular expression to DFA - Converting DFA to regular expression - Properties of regular languages - Pumping lemma - Minimal finite automata. 4. Context-Free grammars: Derivation tree - Simplification of CFG - Chomsky Normal Form - Greibach Normal Form. 5. Push Down Automata:Definition of PDA - Relationship between PDA and context free languages - Properties of context free languages. 6. Turing Machine: Definition of Turing Machine - The Language of Turing Machine. |
| Mathematical Applications [4th Applied Mathematics and Information] |
This course includes: Introduction to databases - Databases management system - Databases languages - Data definition language - Data definition language (Data dictionary) - The language of dealing with data - The language of controlling data - Database diagram - Data integration - Models of Databases management systems - Relations model - Descriptive - Descriptive scope - Records - Relational algebra - Union operation - Intersection operator - Difference operator - Select operator - Projection operator - Complement operator - Cartesian product operator - linking two tables (Merging) - Conditional linking operator - Normal linking operator - Auto linking operator - Outer linking operator - Partial linking operator - Division - Useless duplication of data - Organizing a database - Functional linking (Functional dependency) - Primary key - Foreign key - Complete functional linking - Direct functional linking - First normal form - Second normal from - Third normal from – Boyce-Codd normal form- Multi values linking - Forthnormal from-Linking dependency - Fifthnormal from - Splitting relations - SQL - Query - Subquery - Associative functions - One class subqueries - Multi classes subqueries. |
| Algorithms and Advanced Programming [4th Applied Mathematics and Information] |
This course includes: The concepts of object oriented programming - Objects concept -Systems analysis and design using objects: types and variables in Java language - Classes in Java language: The abstract class concept and the internal class in Java language - Some special classes: Libraries - help -Generate random numbers -Complex types - The concept of interfaces in Java language: Dealing with files - Types of files - The concept of temporary memory - Interactive reading - Object files -Inheritance in Java: Multiple figures concept - The concept of multiple inheritance in Java - Designinguser interfaces - Java and Web services. |