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.
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.
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
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.
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; 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
103241 Linear Algebra
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
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.
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
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
103253 Discrete Mathematics
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.
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)
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
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.
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
103332 Probability Theory (3:3-0)
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)
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.
equations. Prime numbers. The Fundamental Theorem of Arithmetic. Congruence,
linear congruence equations. Fermat's and Wilson's Theorems. Arithmetic
functions, Euler's Theorem.
closed sets. Bases and products. Continuous functions. Separation axioms and
Housdorff spaces. connected spaces. Compact spaces.
103373 Numerical Analysis
Taylor's Theorem and its
applications. Errors. Root findings. Solving systems of linear equations
numerically. Interpolation. Numerical differentiation and integration. Discrete
Least Squares Approximation.
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.
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
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.
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
Gamma and Beta functions.
Legendre polynomials and functions. Bessel functions. Other special functions
(incomplete gamma functions, the error functions, Riemann’s zeta function).
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)
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
Differential Equations (3:3-0)
Homogeneous, nonhomogeneous, constant coefficients and autonomous. Stability.
Linear and almost linear systems. Lyapunov’s method. Existence and uniqueness
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.
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.
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
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
103443 Linear Algebra
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.
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.
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
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
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.
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.
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
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
103482 Calculus of
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
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
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)
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
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
Current. Theories in Electricity and Magnetism. Description of Wave Motion.
104103 General Physics
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
Prerequisite: 104102 (or
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
104107 General Physics
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.
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
Prerequisite: 104101 (or
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
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
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
Prerequisite: 104108 (or
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.