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A Bridge Towards Knowledge

103101 Calculus (1)                                                                        (3:3-0)

Prerequisite: None

Functions of one variable. Limits and continuity. Differentiation and its applications. The Mean Value Theorem and its applications. Definite integral and the Fundamental Theorem of Calculus. Exponential functions, their derivatives and integrals. Logarithmic functions and their derivatives.

103102 Calculus (2)                                                                        (3:3-0)

Prerequisite: 103101

L'Hopital’s Rule. Inverse trigonometric functions. Hyperbolic functions. Techniques of integration. Improper integrals. Applications of the definite integral to volumes, areas, arc lengths and surface areas. Infinite sequences and series. Power series. Maclaurin and Taylor Series.

103201 Calculus (3)                                                                        (3:3-0)

Prerequisite: 103102

Conic sections. Parametric equations. Polar coordinates and graphs. Derivatives and integrals of functions in polar coordinates. Vectors and analytic geometry in space. Functions of several variables and partial differentiation. Multiple Integrals.

103212 Introduction to Real Analysis                                            (3:3-0)

Prerequisite: 103251

Topology of real numbers: Ordering, bounded and connected sets. Sequences: Limits, Cauchy sequences, increasing and decreasing sequences. Functions: Limit of a function, continuity at a point and on an interval, uniform continuity. Differentiation: Rolle's Theorem, Mean Value Theorem.

103222 Differential Equations                                                        (3:3-0)

Prerequisite: 103102

Introduction and classification. Solutions of first order differential equations and their applications. Solutions of higher order linear differential equations and their applications. Series solutions of differential equations near ordinary points. Laplace transforms method.

103231 Principles of Statistics                                                        (3:3-0)

Prerequisite: 103101

Introduction to statistics; Descriptive statistics; Measures of centrality and variation; Percentiles; Chebyshev's inequality and empirical rules; Introduction to probability; Probability laws; Counting rules, conditional probability and independence of events; Discrete and continuous random variables; Probability distribution; Expected and standard deviation of random variable; Binomial and normal probability distribution; Sampling distributions; Estimation and test of hypotheses.

103241 Linear Algebra (1)                                                              (3:3-0)

Prerequisite: 103102

Systems of linear equations. Matrices and matrix inverses. Row echelon forms. Determinants and Cramer rule. Vector spaces and subspaces. Basis and orthogonal basis. Linear transformations. Eigenvalues and eigenvectors.

103242 Abstract Algebra (1)                                                          (3:3-0)

Prerequisite: 103251

Groups and subgroups; cyclic groups; permutation groups; isomorphisms; external direct product of groups; cosets and Lagrange 's theorem; normal subgroups and factor groups; group homomorphisms; the first isomorphism theorem; the fundamental theorem of finite abelian groups.

103250 Discrete Mathematics (1)                                                  (3:3-0)

Prerequisite: 103101

Propositional and Predicate Calculus: Propositions, truth tables, connectives tautologies, contradiction (fallacies) and quantifiers, valid and invalid arguments. Proofs, Sets, functions, Cardinality of sets and countable and uncountable sets. Divisibility, congruence. Mathematical induction. Relations, equivalence relation, partial order relations, equivalence classes, upper and lower bounds, supremum and infimum. Graphs and graph terminology, special types of graphs, connected graphs and graphs isomorphism. Introduction to trees.

103251 Fundamental of Mathematics                                             (3:3-0)

Prerequisite: 103102

Logic and proofs; quantifiers; rules of inference mathematical proofs. Sets: set operations; extended set operations and indexed families of sets. Relations: Cartesian products and relations; equivalence relations; partitions; functions; bijective functions. Denumerable and nondenumerable sets: finite and infinite sets; equipotence of sets. Cardinal numbers: the concept and ordering of cardinal numbers.

103253 Discrete Mathematics (2)                                                  (3:3-0)

Prerequisite: 103250

Prime integers, Composite integer, greatest common divisor, least common multiple, recursive definition. Basics of counting, Pigeonhole Principle. Permutations and Combinations. Binomial coefficients. Generating Functions. Linear recurrence relation. Euler path and circuit, Hamilton path and circuit, planar graph, graph coloring. Rooted trees, spanning trees. Boolean algebra, Boolean function and models.

103262 Euclidean Geometry                                                           (3:3-0)

Prerequisite: 103201

A study of the origin of geometry. The method of axiomatic reasoning. Euclid's and the connection postulates. The postulate of parallel lines. Congruence and similarity in the Euclidean plane. Introduction to ordered and affine geometry, including neutral, Euclidean geometries and hyperbolic and elliptic geometries, constructions, transformations, various models for geometries.

103313 Real Analysis (1)                                                                (3:3-0)

Prerequisite: 103212

Riemann-Stieltjes integrability and its properties, Fundamental Theorem of Calculus, The integral as limit, Sequences of functions, Pointwise and uniform convergence, Interchange of limits, The exponential and logarithmic functions, Infinite series, Convergence of infinite series and some tests of convergence. Open and closed sets on R.

103314 Real Analysis (2)                                                                (3:3-0)

Prerequisite: 103313

Limsup, liminf of sequences of real numbers, series of real numbers, convergence absolute, conditional convergence, Dirichlet test, sequences of functions, pointwise convergence, uniform convergence, and continuity, and integrability, Dini’s Theorem, series of functions, pointwise and uniform convergence, Weierstrass M-test, space C [a, b]. Improper integrals, tests of Convergence.

103322 Partial Differential Equations                                            (3:3-0)

Prerequisite: 103222

Boundary value problems and Sturm-Liouville problem, Integral transforms (Laplace Transformation, Fourier sine and cosine transformation), The concept of partial differential equations. The classification of partial differential equations into linear and nonlinear and based on their order. The classification of the second order linear PDEs into Hyperbolic, Elliptic, and Parabolic, The concept of the steady state solutions, The derivation of the heat equation, The heat problem on one dimension (on finite, semi-infinite, and infinite domains), The heat problem with advection, The heat problem on a plat (the heat problem on rectangular domains), The wave equation and its derivation, The wave equation on a finite domain (finite string), The wave equation on the space (D'Alembert solution), The Laplace equation on a rectangular domain, The Laplace equation on a disk (the Dirichlet Problem).

103332 Probability Theory                                                              (3:3-0)

Prerequisite: 103201

Probability and its properties. Distributions of random variables; conditional probability and independence; some special distributions (discrete and continuous distributions); univariate, bivariate; distributions of functions of random variables (distribution function method, moment generating function method, and the Jacobian transformation method).

103333 Biostatistics                                                                        (2:2-0)

Prerequisite 103101

This course helps the student to know the branches of statistics which are descriptive statistics and inferential statistics. The course contains statistical measures, probability rules and their applications, random variables, probability distributions (discrete and continuous), confidence intervals, and hypothesis testing.

103344 Number Theory                                                                   (3:3-0)

Prerequisite: 103251

Division. Diophantine equations. Prime numbers. The Fundamental Theorem of Arithmetic. Congruence, linear congruence equations. Fermat's and Wilson's Theorems. Arithmetic functions, Euler's Theorem.

103365 General Topology                                                               (3:3-0)

Prerequisite: 103251

Topological spaces, closed sets. Bases and products. Continuous functions. Separation axioms and Housdorff spaces. connected spaces. Compact spaces.

103373 Numerical Analysis (1)                                                      (3:3-0)

Prerequisite: 103102

Taylor's Theorem and its applications. Errors. Root findings. Solving systems of linear equations numerically. Interpolation. Numerical differentiation and integration. Discrete Least Squares Approximation.

103376 Graph Theory                                                                      (3:3-0)

Prerequisite: 103241+103251

Definition of graphs and examples, operations on graphs, subgraphs and induced subgraphs, important types of graphs, isomorphism, trees and bipartite graphs, distance in graphs, graph coloring, adjacency and distance matrices, connected graphs, Eulerian graphs, Hamiltonian graphs, planar graphs, directed graphs, networks.

103381 Linear Programming                                                          (3:3-0)

Prerequisite: 103241

Formulation of linear programs and their basic properties. Basic solutions. Graphic solutions. The simplex method. Duality. Sensitivity Analysis. Applications to the transportation model and networks.

103401 History of Mathematics                                                     (3:3-0)

Prerequisite: Fourth Year

Introduction to the history of ancient mathematics: Egyptians, Hindu and Babylonians. Greek math. The school of Pythagoras. A brief biography of Euclid, Archimedes and Ptolemy. Math. In the Arab and Islamic world. Contributions of Arabs in Algebra, geometry and analysis. A brief biography of Al-Khawarismi, Ibn Qurra and Al-Bayrouni. A brief account of the contributions of: Newton, Leibniz, Gauss, Cauchy and Laplace.

103402 Teaching Mathematics                                                       (3:3-0)

Prerequisite: Fourth Year

The special nature of mathematics, learning and teaching it. Basis for various approaches in mathematics teaching, especially in schools of different levels: Elementary, intermediate and secondary. Preparation and analysis of teaching materials, plans and tests for effective math teaching.

103413 Theory of Special Functions                                               (3:3-0)

Prerequisite: 103314

Gamma and Beta functions. Legendre polynomials and functions. Bessel functions. Other special functions (incomplete gamma functions, the error functions, Riemann’s zeta function). Elliptic integrals.

103414 Complex Analysis                                                               (3:3-0)

Prerequisite: 103313

Complex numbers. Analytic functions. Limits and continuity. Differentiability. Cauchy- Riemann conditions. Complex integration. Residues and poles. Evaluation of improper integrals. Basic properties of conformal mapping.

103415 Functional Analysis                                                            (3:3-0)

Prerequisite: 103314

Metric spaces, complete metric spaces. Normed spaces and compactness, equivalent norms. Linear spaces, linear operators and functional. Banach spaces as Â, C, Ân, Cn, lp, Lp ,l¥, L¥ C0, C[a, b]. Inner product spaces. Hilbert spaces: Definition, parallelogram Law, orthogonal of vectors. Bounded continuous linear operators. Hahn-Banach theorem. Adjoint operator. Open mapping theorem. Closed graph theorem.

103422 Advanced Differential Equations                                       (3:3-0)

Prerequisite: 103222

Linear systems: Homogeneous, nonhomogeneous, constant coefficients and autonomous. Stability. Linear and almost linear systems. Lyapunov’s method. Existence and uniqueness theorems.

103431 Mathematical Statistics (1)                                                (3:3-0)

Prerequisite: 103332

Limiting distribution; Sampling distributions; Estimation: Point estimation, Interval estimation, MLE, MME; Sufficient statistics and its properties; Complete statistics; Exponential family; Fisher Information and the Cramér–Rao inequality; Test of hypotheses.

103432 Mathematical Statistics (2)                                               (3:3-0)

Prerequisite: 103431

Estimation, some types of estimators; Sufficient statistics; Minimal sufficient statistics; Completeness; Methods of point estimation and properties of point estimators; Bayesian estimator confidence intervals, testing hypotheses; Neman-Pearson theorem; Randomized tests; Likelihood ratio tests.

103433 Applied Statistics                                                                (3:2-1)

Prerequisite: 103431

This course offers a broad treatment of statistics, concentrating on specific statistical techniques used in science. Topics include: Statistical Inference for Two Samples; Simple Linear Regression and Correlation; The Analysis of Variance.

103442 Abstract Algebra (2)                                                          (3:3-0)

Prerequisite: 103242

Rings and subrings. Integral domains. Factor rings. Ideals. Ring homomorphisms, polynomial rings. Factorization of polynomials. Reducibility and irreducibility tests. Divisibility in integral domains. Principal ideal domains and unique factorization domains. Algebraic extension of fields. Introduction to Galois Theory.

103443 Linear Algebra (2)                                                              (3:3-0)

Prerequisite: 103241

Abstract treatment of finite dimensional vector spaces. Linear transformations and matrices. Direct sums and factor vector space. Minimal polynomials and Jordan canonical forms. Inner product. Nonnegative and irreducible matrices.

103445 Matrix Theory                                                                     (3:3-0)

Prerequisite: 103241

Eigenvalues and corresponding eigenvectors of a matrix, Jordan canonical form,Types of matrices, Schurs Theorem, Gereralized Schurs theorem, Positive definite matrix, Positive semidefinite matrix, Hermitian matrix, Unitary matrix, Normal matrix, Singular values of matrices, Norm of a matrix, Inequalities including singular values and norm of  matrices, Numerical radius of a matrix.

103451 Set Theory                                                                          (3:3-0)

Prerequisite: 103251

Axioms of set theory: Zermelo-Fraenkel axioms. Equipollence, finite sets, and cardinal numbers. Finite ordinals and denumerable sets. Transfinite induction and ordinal arithmetic. The axiom of choice: Zorn’s lemma and other equivalences.

103474 Numerical Analysis (2)                                                      (3:3-0)

Prerequisite: 103373

Introductory numerical integration, Gauss integration. Numerical solutions for ordinary and partial differential equations. Initial value problems, Single step and multistep methods. Boundary value problems and finite difference method.

103470 Math. Software Packages                                                   (3:3-0)

Prerequisite: 9600101

Training on Mathematica: Build algorithms for problem solving, do numerical and analytical computations and plot specific graphs. Applications on calculus, differential equations, linear algebra, statistics, number theory, programming, calculus of variations, optimal control and graph theory. Writing programs to solve specific problems.

103472 Applied Mathematics                                                          (3:3-0)

Prerequisite 103322

The D'Alembert solution of the wave equation, The finite vibrating string, The vibrating beam, Canonical form of the hyperbolic equation, The wave equation in two and three dimensions, The finite Fourier transforms (sine and cosine transforms), Superposition method, First-order equations (method of characteristics), Nonlinear first-order equations, Systems of PDEs, The vibrating drumhead (wave equation in polar coordinates), The Laplace equation on rectangular and circular domains, Non homogeneous Dirichlet problem (Green's functions), Laplace's equation in spherical  coordinate, Finite-difference method for solving some PDEs explicitly and implicitly, The variational, perturbation, and conformal-mapping methods for solving PDEs.

103479 Mathematical Modeling                                                      (3:3-0)

Prerequisite: 103322

Introduction to mathematical classification of Models, constraints and terminology on Models, modeling process, population dynamics models for single species, stability analysis of growth models, Fishing management models, scaling variables, bifurcation analysis of the ODE y’ = f(y, c); Saddle-node, transcritical and Pitchfork bifurcations, models from science and finance, Newton’s law of cooling or heating, Chemical Kinetic reactions, modeling by systems of equations, modeling interacting species; Model building, different types of interactions models.

103481 Nonlinear Programming                                                     (3:3-0)

Prerequisite: 103381

Introduction to nonlinear programming. Necessary and sufficient conditions for unconstrained problems. Minimization of convex functions. A numerical method for solving unconstrained problems. Equality and inequality constrained problems. The Lagrange multipliers theorem. The Kuhn-Tucker condition. A numerical method for solving constrained problems.

103482 Calculus of Variation                                                          (3:3-0)

Prerequisite: 103201

The simplest problem of calculus of variation and examples. Necessary conditions for an extremum to include: Euler-Lagrange, Weierstrass, Jacobi and corner conditions. Sufficient conditions for an extremum.

103483 Optimal Control Theory                                                      (3:3-0)

Prerequisite: 103222

Statement of the optimal control problem and examples. The Pontryagin maximum principle. Transversality conditions. Dynamic programming in continuous-time and the Hamilton-Jacobi theory. The linear regulator problem.

103492 Special Topics in Mathematics                                           (3:3-0)

Prerequisite: Fourth Year

Variable contents. Open for Fourth Year Students interested in studying an advanced topic in mathematics with a departmental faculty member. A student can take this course for credit only once.

103498 Seminar                                                                               (1:1-0)

Prerequisite: Fourth Year

The student should write and present a seminar on a selected scientific topic that is related to one of the mathematics aspects.

104101 General Physics (1)                                                            (3:3-0)

Prerequisite: None

Vectors. Kinematics of Point Particles. Dynamics of Point Particles (Newton’s Laws). Statics; Torque. Circular Motion Work, Energy and Power. Linear Momentum. Elastic Properties of Matter. Stress and Strain. Vibrational Motion; Simple Harmonic Motion.

104102 General Physics (2)                                                            (3:3-0)

Prerequisite: 104101

Electrostatics. Direct Current. Theories in Electricity and Magnetism. Description of Wave Motion. Sound.

104103 General Physics for Medical Sciences                                (3:3-0)

Prerequisite: None

Vectors. One and Two Dimensional Kinematics of Point Particles. Dynamics of point particles (Newton’s Laws). Circular Motion. Work, Energy and Power. Linear Momentum. Elastic Properties of Matter; Stress and Strain. Vibrational Motion; Simple Harmonic Motion. Fluid Mechanics and Viscosity. Static Electricity; Electric Field, Potential and Potential Energy. Direct Current. Magnetism. Wave Motion and Sound Waves. Optics. Wave and Particle Properties of Light. X-Ray.

104106 General Physics Laboratory                                              (1:0-1)

Prerequisite: 104102 (or concurrently)

This Lab. includes experiments on measurements and uncertainties. Simple Harmonic Motion and Hook's Law. Specific Heat Capacity. Ohm’s Law. The Potentiometer and Wheatstone Bridge. Electric Field Mapping, measurement of Capacitance. Specific Charge of Copper Ions. Joule’s Law. Magnetic field of a current and electromagnetic induction.

104107 General Physics for Information Technology                    (3:3-0)

Prerequisite: None

Vectors, Kinematics of Point Particles, Dynamics of Point Particles (Newton’s Laws), Statics; Torque, Work, Energy and Power, Vibrational Motion, Simple Harmonic Motion. Electrostatics, Electric Field, Electric Flux, Electric Potential, Capacitors, Electric Current and Resistance, Electric Energy, Direct Current Circuits, Electromotive Force, Resistors Combinations, Kirchhoff's rules, RC Circuits, Magnetic Field and Magnetic Force.

104108 Electronic Physics                                                               (3:3-0)

Prerequisite: 104107

Direct Current Circuits. Alternating Current Circuits. Digital Signals. Semi-Conductors. Diodes. Rectifiers. Diode as a Logic Gate. Bipolar Junction Transistor (BJT). Bias Circuits of BJT. Transistor as Logic Gate. Families of Logic Circuits. Binary Systems. Boolean Algebra and Logic Gates.

104111 General Physics Laboratory (1)                                         (1:0-1)

Prerequisite: 104101 (or concurrently)

Experiments on measurements and uncertainties. Vectors and Forces. Kinematics of Rectilinear Motion. Force and Motion (Newton’s laws). Linear Momentum and Kinetic Energy. Simple Harmonic Motion; Simple Pendulum and Spiral Spring. Boyle’s Law for Ideal Fluids. Viscosity of a Liquid. Specific Heat Capacity.

104112 General Physics Laboratory (2)                                         (1:0-1)

Prerequisite: 104102 (or concurrently)​

​Experiments on Ohm’s Law, Wheatstone Bridge, Electric Field Mapping, the Potentiometer, measurement of Capacitance, Specific Charge of Copper Ions, Joule’s Law, Kirchhoff’s Laws, measurement of the Earth’s Magnetic field, and Electromagnetic Induction.

104113 General Physics for Medical Sciences Laboratory             (1:0-1)

Prerequisite: 104103 (or concurrently)

Experiments on Measurements and uncertainties. Vectors and Forces. Kinematics of Rectilinear Motion. Force and Motion (Newton’s laws). Linear Momentum and Kinetic Energy. Simple Harmonic Motion (Simple Pendulum). Viscosity of a liquid. Ohm’s Law. Electric Field Mapping. Kirchhoff’s Laws. Joule’s Law. and Magnetism.

104118​ Electronic Physics Laboratory                                            (1:0-1)

Prerequisite: 104108 (or concurrently)

Experiments on Electronic components. Ohm's Law. Kirchhoff’s Laws. Oscilloscope and Function Generator Operations. Diode Characteristics. Half-wave Rectifications. Full-wave Rectifications. Diode as a Logic Gate. BJT Characteristics. Fixed and Voltage Divider Bias of a BJT. Common-Emitter Transistor Amplifiers. Transistor as a Logic Gate. JFET Characteristics. Linear OP-AMP Circuits.

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