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MATH 1061 Business Mathematics for Non-Science 1
(2-2-3)
This course is the
first of a sequence of three, given to students from
the College of Commerce and Economics who have an
arts background. It covers the fundamentals of basic
algebra, equations and inequalities, functions and
graphs with emphasis on polynomial and rational
functions, inverses of one-to-one functions and
their graphs.
Prerequisite: English
MATH 1062 Business Mathematics for Non-Science 2
(2-2-3)
This course is the
second of a sequence of three given to all students
from the College of Commerce and Economics who have
an arts background. It covers properties and graphs
of logarithmic and exponential functions, arithmetic
and geometric progressions, matrix algebra,
determinants and inverses of matrices, solutions of
linear systems, marginal analysis, differentiation
techniques and rules.
Prerequisite: MATH 1061
MATH 1063 Business Mathematics for Non-Science 3
(2-2-3)
This course is the
third and final of a sequence given to students from
the College of Commerce and Economics who have an
arts background. It covers optimization techniques
for functions of one and several variables, the
basic techniques of , applications of the definite
integrals to various real life problems from
economics and the social sciences.
Prerequisite: MATH
1062
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MATH 1101 Business Mathematics 1 (2-2-3)
This course is the
first of a sequence of two, given to students from
the College of Commerce and Economics who have a
science background. It covers equations and
inequalities, functions and graphs with emphasis on
polynomial and rational functions, inverses of
one-to-one functions and their graphs, properties
and graphs of logarithmic and exponential functions,
arithmetic and geometric progressions, matrix
algebra, determinants and inverses of matrices,
solutions of linear systems, and marginal analysis.
Prerequisite: English
MATH 1102 Business Mathematics 2 (2-2-3)
This course is the
second of a sequence of two, given to students from
the College of Commerce and Economics who have a
science background. It covers the derivative and the
different rules for differentiation, applications of
the derivative, the optimization techniques for
functions of one and several variables, the basic
techniques of integration, applications of the
definite integrals to various real life problems
from economics and the social sciences.
Prerequisite: MATH 1101
MATH 1106 Precalculus (3-2-4)
Basic algebra: Numbers,
sets, fractions, exponents and basic algebraic
skills. Basic theory of equations and inequalities:
Solving polynomial and rational equations and
inequalities. First and second degree equations and
inequalities. Functions: Definition, domain, range,
composition, inverse. Basic functions. Polynomial
and Rational Functions: Factoring, the rational root
theorem and synthetic division, qualitative behavior
of polynomial and rational functions. Transcendental
Functions: Exponential and logarithmic functions,
properties of logs and exponentials, applications
(growth and decay, finance). Trigonometry: Basic
concepts of trigonometry, the six trig-functions,
trigonometric equations and complex numbers. Law of
sines and cosines.
Prerequisite: English
MATH 1192 Mathematics For Agriculture 1 (3-2-4)
This course will be
given to all agriculture students. It covers the
fundamentals of basic algebra, equations and
inequalities, functions and graphs with emphasis on
polynomial and rational functions, properties and
graphs of logarithmic and exponential functions,
arithmetic and geometric progressions. An appendix
covering basic trigonometry such as graphs of
trigonometric functions, algebraic manipulations of
trigonometric functions will be given to students.
Prerequisite: English
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MATH 2107 Calculus 1 (3-2-4)
Limits and Continuity:
The concepts of limits and all the different
techniques of finding limits of functions.
Continuity and removable discontinuities.
Differentiation and its applications: The meaning of
the derivative, the tangent line problem, definition
of the derivative, techniques of differentiation,
applications of differentiation in the physical
world. Integration and some of its applications: The
meaning and the definition of the integral, the
Riemann sums, techniques of integration, the
integral as the area. Finding the area between
curves. Volumes by slicing and cylindrical shells,
arclength of a curve and area of a surface of
revolution.
Prerequisite: MATH 1106
MATH 2108 Calculus II (2-2-3)
This is the second
standard Calculus course from a sequence of three.
It deals with the various techniques of integration,
transcendental functions graphs and applications,
hyperbolic and inverse trigonometric functions,
sequences and series, Taylor polynomials
approximations; polar coordinate and parametric
curves.
Prerequisite: MATH 2107
MATH 2193 Mathematics For Agriculture 2 (2-2-3)
This course will be
given to all agriculture students. It covers the
standard Calculus topics needed for students
majoring in agriculture, namely: Limits,
Differentiation, Applications of Differentiation,
Introduction to Integration.
Prerequisite: MATH 1192
MATH 2202 Linear Algebra I (2-2-3)
Vector Geometry:
Vectors, Dot product; Projections, Cross product,
Parametric Equations of lines, Planes in 3-space.
Systems of Linear Equations: Row Reduction and
Echelon Forms. Vector and Matrix Equations: Solution
Sets of Linear Systems, Linear Independence. Matrix
Algebra: The Inverse of a Matrix. Determinants.
Eigenvalues and Eigenvectors: The Characteristic
Equation.
Prerequisite: MATH 1106
MATH 3109 Calculus III (2-2-3)
Quadric Surfaces,
cylindrical and polar coordinates. Introduction to
vector-valued-functions, calculus of vector-valued
functions, change of parameter, Arc-length.
Functions of two or more variables, Partial
Derivatives, Differentiability and chain rules for
functions of two and three variables, tangent
planes, total differentials for functions of two
variables, Directional Derivatives and gradients for
functions of two and three variables, Maxima and
minima of functions of two variables. Lagrange
Multipliers. Double Integrals, Double Integrals over
non-rectangular regions and in polar coordinates,
Surface Area, Triple Integrals, Triple Integrals in
cylindrical and spherical coordinates, change of
variables in Multiple Integrals, Jacobians. Vector
fields, Line Integrals, Independence of path;
conservative vector fields, Green's Theorem, Surface
Integrals, Flux, The Divergence Theorem and Stoke's
Theorem.
Prerequisite: MATH 2108
MATH 3171 Linear Algebra & Multivariate Calculus for
Engineers (2-2-3)
This course is given to
all students from the engineering college. It has
two major parts, linear algebra and vector calculus.
The course will concentrate on the application of
the mathematical concepts to engineering. Proofs of
theorems will be omitted if time does not permit.
Linear algebra: Vector algebra (inner product, cross
product, and others). Calculations with matrices,
solutions of systems of linear equations using
different methods such as the Gauss elimination, row
reduction and Cramer's methods, eigenvalue problems,
special matrices (Hermitian, skew-Hermitian and
unitary), diagonalization. Vector Calculus: Vector
functions for representing and investigating curves,
and their applications to mechanics of moving
bodies. Physically and geometrically important
concepts in connection with scalar and vector fields
such as the gradient, divergence and curl.
Integration of vector functions (double, triple and
line integrals) and their applications to area,
surface and vof bodies. Gauss, Green and Stokefor
vector functions.
Prerequisite: MATH 2108
MATH 3207 Mathematics for Teachers I (Algebra)
(2-2-3)
Transformations:
translations, enlargements, reflections and
rotations; transformations represented by matrix
operations. Algebra: Revision of Remainder theorem
and factorization of polynomials of degree greater
than two; Permutation and Combination, Binomial
Theorem. Mathematical Induction, Finite Series,
Arithmetic and Geometric Progressions. The
convergence of an infinite G.P. Arithmetic and
Geometric means; Theory of equations, symmetrical
and unsymmetrical relations between roots and
coefficient, transformations of e, solutions of
cubic equations by Tartaglia's method and quartic
equation by Ferrari's method; Mathematical system
and field of real numbers: Binary operations, one
binary operation (group), two binary operations
(rings, fields). Multibase arithmetic: Different
bases of arithmetic, notation, conversion,
operations, binary number system.
Prerequisite: MATH 2107
MATH 3209 Problem Solving (0-4-3)
To show students how to
solve problems which do not come from any particular
subject area, or for which familiar methods of
calculus / algebra / geometry maybe inappropriate.
The course typicallybegins by testing special cases
and using these to frame conjectures. These can be
tested and found to be correct, partially correct or
false. This in turn leads to new conjectures and
possibly a complete solution.
Prerequisite: MATH2107
/ MATH 2203, MATH 2202 / MATH 2206
MATH 3210 Mathematics for Teachers II (Geometry)
(2-2-3)
Some theorems in plane
geometry (triangles and circles) with emphasis on
concept of proof, geometrical , further geometrical
theorems: Ptolemy, Ceva, Menalaus, Appolonius, etc;
space geometry: axioms, definitions, some theorems,
on parallels. Normals, orthogonal pand dihedral
angles, some geometrical properties of the sphere;
Analytical Geometry of a circle: the locus of a
point and examples, the general equation of a
circle, equations of circles satisfying certain
conditions (alternative methods), tangents, to a
circle, conditions that two circles should intersect
(touch), orthogonal circles; Conic sec: parabola,
ellipse and hyperbola, definitions, governing
equations, equations of chords, tangents and some of
the geometrical properties of the conic sections.
Prerequisite: Math 3207
MATH 3211 Mathematics For Teachers: Algebra &
Geometry (2-2-3)
This course is designed
to introduce advanced algebraic and geometrical
concepts to Education students. Topics include
theory of equations, groups, rings and fields,
classical plane geometry, and space geometry.
Prerequisite: MATH
2108
MATH 3302 Ordinary Differential Equations (2-2-3)
This is an intermediate
course aimed to cover ordinary differential
equations of first and higher orders including
applications in various fields. The emphasis will be
on solution methods. The contents are: Basic
concepts, first order ordinary differential
equations, linear ordinary differential equations of
second order with or without variable coefficients,
including power series.
Prerequisite: MATH
2108/2203
MATH 3303 Linear Algebra II (3-0-3)
Vector Spaces: The
Dimension of a Vector Space, Rank. Eigenvalues and
Eigenvectors: Eigenvectors and Linear
Transformations. Orthogonality and Least Squares:
The Gram-Schmidt Process, Inner Product spaces.
Symmetric Matrices and Quadratic Forms.
Prerequisite: MATH
2202
Math 3350 Foundations of Mathematics (2-2-3)
This
course will be offered for students of 2003 cohort onwards.
The topics are: Introduction to logic, methods of proof,
elementary number theory, induction, set theory, relations
and functions.
MATH 3357 Discrete Mathematics (2-2-3)
Introduction to logic:
Statements, logical connectives, truth tables,
logical equivalence, quantifiers, methods of proof.
Set theory: Sets and subsets, set operations,
infinite unions and intersections. Number theory and
induction: Division algorithm, Euclidean algorithm,
prime factorization, well-ordering principle, the
principle of mathematical induction. Relations:
Binary relations, equivalence relations. Functions:
One-to-one, onto and inverse functions, permutation,
composite function, big 0-notation, bisection,
countability, recursively defined functions.
Combinatorial mathematics: Basic counting
techniques, permutations and combinations, the
binomial theorem, principle of inclusion-exclusion,
recurrence relations, recursive algorithms.
Prerequisite: MATH 1106
/ MATH 1104
MATH 3744 Introduction to Mathematical Modeling (2-2-4)
The course introduces students to the essentials of
present-day mathematical modeling. The course comprises two
elements: providing an overview of the current state of the
art, and, hands-on practice in mathematical modeling.
Students will work under supervision on assignments,
producing a written report describing a mathematical
solution of a problem couched in real-world terms. The
assignments will embrace different areas of application and
types of mathematical model. Use will be made of Maple,
Mathematica, Matlab, or an equivalent software package.
Prerequisite: Math 3109, Math 3302
MATH 3573 Graph Theory (3-0-3)
Definitions and
examples of graphs. Eulerian and Hamiltonian graphs.
Trees. Plane graphs; graphs on other surfaces; dual
graphs. Colouring of graphs. Directed graphs; Markov
Chains. Hall's marriage theorem.
Prerequisite: MATH
3357
Math
3730 Computer Algebra System I (0-4-2)
The main idea behind this course is to do mathematics using
computer algebra systems such as Scientific Notebook,
Scientific Workplace, Maple or Matlab. This is a hands-on
laboratory course. Students are expected to solve equations,
plot functions, and so on, using the softwares.
Prerequisite:
Math 2202, Math 3109
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MATH 4141
Numerical Analysis(2-2-3)
This course concentrates on the
mathematical analysis and implementation of basic numerical
techniques. The topics to be covered include: Background on
Interpolation, Iterative methods and techniques for
accelerating their convergence, Zeros of polynomial
equations (Horner¡¦s method), Solving nonlinear equations
(Fixed point methods, Newton¡¦s method, Quasi-Newton methods,
and Steepest descent method), Differentiation, Integration
(Composite rules, Romberg method, and Gauss Quadrature),
Numerical solution of Initial value problems for Ordinary
Differential Equations (Multistep methods,
Predictor-Corrector methods, and Runge-Kutta methods), and
approximation of matrix eigenvalues.
Prerequisite: MATH 2108, MATH 2202
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MATH 4174 Differential Equations and Applications for
Engineers (2-2-3)
This course is designed exclusively to cater for students
from the College of Engineering. It begins with preliminary
concepts of differential equations. The material covered
includes first order and second order differential
equations, Laplace transforms, Fourier series, partial
differential equations and their applications.
Prerequisite: Math 2108
MATH 4172 Differential Equations for Engineers
(3-2-4)
This course is given to
all students from the engineering college. It deals
with differential equations, partial differential
equations and their applications to engineering. The
course will cover the following: Differential
equations of the first order, linear differential
equations, systems of differential equations, power
series solutions of differential equation, Laplace
transformations, Fourier analysis and their
applications to solving differential and partial
differential equations .
Prerequisite: MATH
2108
MATH 4451 Introduction to Analysis I (3-0-3)
Review of sets and
functions. Sup and Inf of sets of real numbers and
axiom of completeness. Convergence of sequences,
Cauchy Sequences, Sub-Sequences, and the Bolzano-Weierstrass
Theorem. Limit of functions, Limit theorems.
Continuous functions and their properties,
Continuous functions on intervals. Derivatives, Mean
Value Theorems, L' Hopital's Rule.
Prerequisite: MATH 2203
/ MATH 2108
MATH 4452 Complex Variable (3-0-3)
Complex numbers,
functions of a complex variable, limits and
continuity, analyticity, Cauchy-Riemann equations,
harmonic functions, elementary functions, complex
integration, Cauchy's theorem, Cauchy's formula and
its consequences, Taylor series, Laurent series,
zeros and singularities, the residue theorem and its
applications.
Prerequisite: MATH 2108
MATH 4454 Abstract Algebra I (3-0-3)
Preliminaries: Set
Theory, Mappings, Relations, and Numbers. Groups:
Definition, Examples, Basic Properties, Normal
Subgroups, Quotient Groups, and Isomorphism
Theorems. Permutation Groups: Cyclic Decomposition,
An . Rings and Ideals: Definitions, Examples, Basic
Properties and Isomorphism Theorems.
Prerequisite: MATH 2202
/ MATH 2206 / MATH 3357
MATH 4455 Abstract Algebra II (3-0-3)
Groups: Review of group
Theory from Math 4454, Structures, Sylow Theorems,
Permutation Groups. Rings and Ideals: Review of Ring
Theory from Math 4454, Domains. Field Theory:
Irreducible Polynomials, algebraic Extensions.
Prerequisite: MATH
4454
MATH 4473 Linear Programming (3-0-3)
This course is an
exposition of linear programming theory and
applications. Topics include the following:
Introduction to Linear Programming: The linear
programming model, assumptions and formulation of
linear programming. The Graphical Solution in Two
Variables: A simple minimization problem, the
objective function, the constraints, extreme points
and the optimal solution, and special cases. The
Simplex Method: The essence , set up , algebra, and
tabular form of the simplex method, the tie breaking
in the simplex method, adapting to other model
forms, post optimality analysis. Sensitivity
Analysis:: Application of sensitivity analysis.
Special Types of Linear Programming Problems: The
transportation and assignment problems. Integer
Programming: Prototype example, other formulation
possibilities with binary variables, solving integer
programming problems, the branch-and-bound technique
and its application to binary and mixed integer .
Prerequisite: MATH 2202
/ MATH 2206
MATH 4474 Introduction to Partial Differential
Equations (3-0-3)
Introduction:
Eigenvalues and eigenfunctions of Ordinary
Differential Equations. Basic concepts and
definitions, linear operators, superposition.
Mathematical Models: The vibrating string and
membrane, waves in an elastic medium, conduction of
heat in solids, The gravitational potential.
Classification Second-order Equation: Second order
equations in two independent variables, canonical
forms, equations with constant coefficients, general
solution. The Cauchy Problem: Cauchy -Kowalewsky
theorem, homogeneous wave equation, initial-boundary
value problems, nonhomogeneous boundary conditions,
finite string with fixed ends, nonhomogeneous wave
equation. Fourier Series: Piecewise continuous
functions and periodic functions, orthogonality,
Fourier series, convergence in the mean, cosine and
sine series, complex Fourier series, change of
interval. Method of Separation of Variables:
Separation of variables, the vibrating string
problem, The heat conduction problem.
Prerequisite: MATH 3302
/ MATH 3304
MATH 4481 Introduction to Optimization (3-0-3)
Survey of practical
methods for solving unconstrained optimization
problems. The topics include the following.
Mathematical background: norms, orthogonal
projections, quadratic function, partial
derivatives, chain rule, Taylor's Theorem.
Conditions for local extrema. Methods for one
dimensional line search. Unconstrained line search
methods: Steepest descent methods, conjugate
gradient methods, Newton's method and quasi-Newton
Methods. Constrained optimization methods:
Elimination methods, penalty methods and projected
gradient method.
Prerequisite: COMP
4471
MATH 4552 Logic and Set Theory (3-0-3)
Infinite sets: Logical
notation, operations on sets. Set of sets,
orderepairs, infinite union, intersection and
product, well-ordered se, ordinal numbers.
Zermelo-Fraxiomatization: Language of set theory,
the cumulative hierarchy of sets. Zermelo-Fraenkel
axioms, classes, transfinite (ordinal recursion).
Ordinal and cardinal numbers. Addition, multand
exponentiation of ordinal numbers. Cardinal numbers:
addition, multiplication and exponentiation.
Prerequisite: MATH
3357
MATH 5451 Introduction to Analysis II (3-0-3)
Uniform Continuity,
Weierstrass Approximation Theorem. The Riemann
Integral. Pointwise and Uniform Convergence of
Sequences of functions. Series of Functions, Power
Series
Prerequisite: MATH
4451
MATH 5470
Integral Transforms (2-2-3)
This course covers Fourier transforms and Laplace transforms
and their applications in solving ordinary and partial
differential equations. The topics include: Definition and
basic properties of Fourier transforms, applications to ODEs
and PDEs, applications of Fourier cosine and sine
transforms to partial differential equations ; definition
and basic properties of Laplace transforms, convolution
theorem and differentiation and integration of Laplace
transforms ; solutions of ODEs and PDEs using Laplace
transforms ; finite Fourier cosine and sine transforms,
finite Laplace transforms and their applications.
Prerequisite: MATH
4474
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MATH 5472 Integral Transforms, Special Functions and
Applications (3-0-3)
Eigenvalue Problems and
Special Functions: Quick revision of Sturm-Liouville
sys, eigenvalues and eigenfunctions, eigenfunction
expansions. Convergence in the mean, completeness
and Parseval's equality, Bessel's equation and
Bessel's function, adjoint forms, singular Sturm-Liouville
systems, Legendre's equation and Legendre's
function, boundary value problems involving ordinary
differential equations. Green's Function: The delta
function, Green's function, Method of Green's
function, Dirichlet problem for the Laplace and
Helmholtz operators, Method of images, Method of
eigenfunctions, Higher dimensional problems, Neumann
problem. Integral Transforms with Applications:
Fourier series and their properties, convolution
theorem and Fourier transform of step and impulse
functions, Fourier sine and cosine transforms,
asymptotic approximation of integrals by the Kelvin
stationary phase method, Laplace transform and their
properties, convolution theorem and Laplace
transform of step and impulse functions.
Prerequisite: MATH
4474
MATH 5500 Projects ( 6)
A student taking a
project is expected to integrate knowledge from
various subjects to study a problem in mathematics,
and come up with a solution and/or suggestions. The
work requires using the library, references and, if
necessary, computer's software packages. The student
is required to produce a well written report on
which he/she is examined orally. The progress during
the year is monitored with regular meetings and
in term reports.
MATH 5551 Fluid Dynamics (3-0-3)
Kinematics of fluids in
motion: Eulerian and Lagrangian views of fluid
motion. Definitions of velocity and acceleration at
a point of fluid. Streamlines, pathlines, vorticity,
irrotational flows. Continuity equation. Mechanics
of fluid motion: Static and dynamic pressure.
Boundary conditions and the equations of motion for
an ideal fluid. Bernoulli's equation. Kelvin's
circulation theorem. Vorticity and energy equations.
Potential flow: Velocity potential, equations of
motions and kinetic energy for irrotational flows.
Minimum energy, mean value. Solution for some
special flows. Simple source or sink, doublets -
definitions, calculation of velocity potential. The
stream functions: Definition, properties.
Two-dimensional incompressible flows. Axisymmetric
flow, Stokes' stream functions. Boundary conditions.
Two-dimensional flows: The complex potential,
evaluation of standard potentials. Image systems.
The circle theorem.
Prerequisite: MATH
4474
MATH 5553 Differential Geometry (3-0-3)
Calculus on Euclidean
Space: Euclidean Space, Tangent vectors, Directional
Derivatives, Curves in E3 , 1-forms, Differential
Forms and Mappings. Frame Fields: Dot Porduct,
Curves, The Frenet Formulas, Arbitrary-Speed Curves,
Covariant Derivatives, Frame Fields and the
Structure Equations. Calculus on a Surface: Surface
in E3, Patch Computations, Differential Functions
and Tangent Vectors, Differential Forms on a Surface
and Mappings of Surfaces. Shape Operators: The Shape
Operator of M 3, Normal Curvature, Gaussian and Mean
Curvatures, Special Curves in a Surface and Surfaces
of Revolution. Geometry of Surfaces in E3: The
Fundamental Equations, Isometries and Local
Isometries, Intrinsic Geometry of Surfaces in E3.
Riemannian Geometry: Geometric Surfaces, Geodesics,
Length-Mimizing Properties of Geodesics and the
Gauss-Bonnet Theorem.
Prerequisite: MATH 3305
/ MATH 3109, MATH 3303 / MATH 3306
MATH 5558 Number Theory (3-0-3)
This is an introductory
course in number theory covering divisibility,
congruences, quadratic reciprocity, and Diophantine
equations.
Prerequisite: MATH 3357
MATH 5559 Introduction to Metric and Topological
Spaces (3-0-3)
Metric spaces, Complete
metric spaces, Contraction mapping theorem.
Topological spaces, Subspaces, Bases,
Homeomorphisms. Product spaces.Compactness and
Connectedness in topological spaces, Separation
Axioms, Uniform convergence.
Prerequisite: MATH
4451
MATH 5564 Introduction to Functional Analysis
(3-0-3)
Normed Linear Spaces:
Definitions and examples of normed spaces and Banach
Spaces. Properties of normed spaces. Finite
dimensional Normed spaces. Subspaces. Linear
Operators: Bounded and continuous linear operators.
Linear Functionals. Normed Spaces of operators. Dual
Space. Hilbert Spaces: Definition and examples of
Inner Product Spaces and Hilbert Spaces. Properties
of Inner Product Spaces. Orthogonality in Hilbert
Spaces. Functionals on Hilbert spaces. Operators on
Hilbert Spaces. Fundamental Theorems for Normed and
Banach Spaces: Hahn-Banach Theorem, Adjoint
Operators, Reflexive Spaces, Strong and Weak
Convergence.
Prerequisite: MATH 3306
/ MATH 3303 & MATH 5559
MATH 5577 Introduction to Relativity (3-0-3)
Special Relativity:
Principle of special relativity, Lorentz
transformation, Length contraction, Time dilation,
Transformation of velocities, Elements of
relativistic mechanics. Tensor Algebra:
Contravariant tensors, covariant and mixed tensors,
tensor fields, Elementary operation with tensors.
Tensor Calculus: Riemann tensor, Geodesics and
metrics, Christoffel symbols. The Energy - Momentum
Tensor:Perfect fluid, Maxwell's equations, Maxwell
Energy - Momentum tensor. General Relativity:
Principles of general relativity, Field equations,
variational principle.
Prerequisite: MATH 3302
/ 3304
MATH 5*** Special Topics in Mathematics 1
This course treats any
topics from pure mathematics not covered in courses
offered by DOMAS.
Prerequisite: MATH
3357
MATH 5*** Special Topics in Mathematics 2
This course treats any
topics from applied mathematics not covered in
courses offered by DOMAS.
Prerequisite: MATH
4474, 3357
Statistics
Course Description
STAT
1000 Understanding Statistics (English)(1-2-2)
Statistics: Brief description of what
statistics is all about. Common areas of use. Types
of job opportunities. Types of data: Nominal,
ordinal, interval and Ratio. Population, Sample, and
Variable. Descriptive Statistics: Summarizing data.
One and two way frequency tables and how to make
them, Bar and pie charts, stem and leaf displays.
Scatter plots. Measures of central tendency, mean,
median, mode. Measures of variability, standard
deviation, range. Simple uses/application of
binomial and normal distributions. No theory. Simple
indices and rates. Scatter plots and Simple linear
regression.
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STAT 1100 Understanding Statistics (Arabic)(1-2-2)
Statistics: Brief description of what
statistics is all about. Common areas of use. Types
of job opportunities. Types of data: Nominal,
ordinal, interval and Ratio. Population, Sample, and
Variable. Descriptive Statistics: Summarizing data.
One and two way frequency tables and how to make
them, Bar and Pie charts, Stem and Leaf displays.
Scatter plots. Measures of central tendency, mean,
median, mode. Measures of variability, standard
deviation, range. Simple uses/application of
binomial and normal distributions. Simple indices
and rates. Scatter plots and Simple linear
regression.
STAT 1001 Introduction to Statistics (3-2-4)
Descriptive Statistics: Graphically
describing data, stem- and -leaf display, measures
of central tendency, measures of variability,
interpreting the standard deviation, box plots.
Probability: Basic concepts of probability,
assigning probability, additive rule, conditional
probability, multiplicative rule, independent
events. Random Variables and their Distributions:
Discrete and continuous random variables, the
binomial, Poisson and normal distributions. Sampling
Distributions: Parameters and statistics, sampling
distribution of the mean, central limit theorem.
Estimation: Point and interval estimation of means,
proportions, difference between two means, and
difference between two proportions, sample
determination. Hypothesis Testing: Concepts of
hypothesis testing, testing hypotheses about means,
proportions, difference between two means, and
difference between two proportions. P-values. Simple
Linear Regression: Least squares method, model
assumptions, assessing the usefulness of the model,
using the model for estimation and prediction,
coefficient of correlation.
Prerequisite: English
STAT 2102 Introduction to Probability (2-2-3)
This course is a first
course in probability theory and its applications.
It will cover probability of events, random
variables, expectations and moments, discrete and
continuous distributions, joint and conditional
distributions, moment generating functions,
distribution of functions of random variables, limit
theorems.
Prerequisite: STAT 1001
STAT
2103 Probability for Engineers (2-2-3)
This is a service course for the students of
Electrical and Computer Engineering. Topics include:
Statistics in Engineering, Set notation, Counting rules,
Conditional probability and Independence, Discrete
probability distributions, Continuous probability
distributions, Multivariate probability distributions,
Expected values of functions of random variables, Sampling
distributions.
Prerequisite: MATH 2107
Co-requisite: MATH 2108
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STAT
2110 Statistics for Tourism (3-2-4)
Some keywords and basic numerical skills. Data
display, including presenting two variables and Time Series
data. Quick review ¡V using hospitality and tourism examples-
of measures of location and spread and rules of probability.
Binomial Poisson, Normal and t distributions. Estimation and
hypothesis testing. Decision trees. Contingency tables and
tests of association. Testing and estimation using
quantitative bivariate data. Secondary and primary data.
Presenting analysis results in report form. Available
software will be used in the Lab sessions.
Prerequisite: STAT 1001
STAT 3334 Introduction to Inference (3-0-3)
Population parameters
and sample statistics: Review of concepts of
populations, population parameters and sample
statistics. Sampling distribution: Distributions of
sample statistics, normal, t, Chi-square and F
distributions. The Central Limit Theorem. Methods of
point estimation: Estimators and estimates. Finding
estimators using methods of moments, maximum
likelihood and least squares estimation. Properties
of Point estimators: unbiasedness, minimum variance
and Rao-Cramer inequality, mean square error,
efficiency, consistency, sufficiency and
completeness. Interval estimation: Interval
estimation for Means, Variances and Proportions.
Sample size. Hypotheses Testing: Basic concepts of
hypothesis testing, types of errors. Size, power,
and power function of a test; best critical regions
and uniformly most powerful tests. Neyman-Pearson
Lemma and Likelihood ratio tests: Some applications
on tests for population means, difference of means,
proportions and difference of proportions, variances
and ratios of variances.
Prerequisites: STAT
2232, STAT 2331 / STAT 2102
STAT 3336 Computational Techniques in Statistics
(2-2-3)
Introduction to
Statistical Software. Use of MINITAB, SAS, SPSS,
etc. Sorting algorithms. Random number generators.
Simulation of discrete and continuous probability
models.
Prerequisites: STAT
2331, STAT 2102, COMP 2216.
STAT 3337 Introduction to
Actuarial Science I
This course is an introductory course in
actuarial science. It will cover the following: Introduction
to Life Insurance Products and Pricing Factors, Life
Insurance, Life Annuities, Fully Continuous, Fully Discrete,
and Semi-Continuous Models of Benefit Premium, Benefit
Reserves, Multiple Life Functions, Life Table and its
applications.
Prerequisite: STAT 2102
STAT 3338 Statistical Methods (3-0-3)
Many studies, both
experimental and surveys, give rise to data
classified by one or more factors. Such data can be
analyzed using the techniques of analysis of
variance or analysis of contingency table depending
on whether the underlying variable is continuous or
discrete. The course introduces the students to both
types of techniques. Knowledge of some of these
techniques, will be needed for later courses. Topics
covered in this course include: 2´2 contingency
tables: Chi-square test, Fisher’s exact test and MCNemar’s test. r´ c contingency tables: Tests of
homogeneity and independence in r´c tables. One way
analysis of variances: The analysis of variance
table, test of hypothesis, point and interval
estimation of parameters, the problem of multiple
comparisons. Two way analysis of variance: The
analysis of variance table, F-tests, Estimation of
parameters. Introduction to simple linear
regressions. Analysis of covariance (optional):
Analysis of covariance in randomized experiments. Prerequisites: STAT 3334
STAT 4432 Regression Analysis (3-0-3)
Relationships between a
response variable of interest and one or several
other variables that may explain the variability in
the response is of interest in almost every field.
Regression analysis is about seeking the best model
that represent the relationship between the response
and explanatory variables, as well as using the
selected model for prediction and other forms of
inference. Topics covered in this course will
include. Simple Linear Regression: Fitting the
model, partitioning total variability, inference on
slope and intercept, regression through the origin,
residuals. Multiple Linear Regression: Fitting the
model, inference in multiple regression model,
repeated observations, multicollinearity in multiple
regression data. Choice of model: Forward, backward
and stepwise selection of variables. Cross
validation for model selection. Analysis of
Residuals: Plotting residuals, diagnostic plots,
detection of outliers, normal residual plots.
Prerequisites: STAT
3334
STAT 4433 Design and Analysis of Experiments I
(3-0-3)
Principles of
statistical design and analysis of experiments.
Single factor experiments. Factorial experiments of
more than one factor. Fractional designs. Nested
experiments. Applications using either SAS, SPSS
GENSTAT or MINITAB.
Prerequisites: STAT
3334 / STAT 3332
STAT 4434 Nonparametric Statistics (3-0-3)
Tests for single
samples: Sign test, Wilcoxon signed rank test,
associated confidence intervals, runs tests. Methods
for paired samples: Sign and Wilcoxon signed rank
tests for paired data, associated confidence
intervals, McNemar's test. Methods for two
independent samples: Median test, Wilcoxon-Mann-Whitney
test, associated confidence intervals, tests for
equality of variance, Smirnov's test for a common
distribution, Cramer-Von Mises test for identical
populations. Three or more samples: Median test,
Kruskal-Wallis test, location comparisons for
related sample, Friedman and related tests, multiple
comparisons. Correlation: Kendall and Spearman rank
correlation coefficients, tests of correlation.
Regression: Theil's regression method, monotonic
regression.
Prerequisites: STAT
3332 / STAT 3334
STAT 4435 Sampling Techniques (3-0-3)
Selection of Random
samples using random sampling, stratified and
systematic sampling techniques. Selection of samples
of equal and unequal clusters. Methods of estimating
means variances and proportions using these sampling
designs. Comparison of the selection techniques.
Ration estimation and its use in various selection
techniques. Regression estimation and the use of
auxiliary data. Estimation of sample size,
stratification and optimum allocation.
Prerequisites: STAT
2232 / STAT 3334
STAT 4436 Survey Design (3-0-3)
Objectives of a survey.
Population of interest and frame(s) available.
Specification of the variables of interest. Methods
of data collection. Questionnaire design. Treatment
of sensitive data. Specification of desired
accuracy. Specification of resources. Sampling
design and selection of the sample. Organization of
the field work. The pretest. Presentation of the
survey results. Reporting experiences gained.
Prerequisites: STAT
4435
STAT 4500 Internship in Health Statistics (3-0-0)
The course provides the
students with practical training in the Ministry of
Health information departments and other health
centers, under the supervision of experienced health
information officers. Each student will spend about
six weeks in the last summer before graduation, in
the Ministry of Health, during which his performance
will be monitored and evaluated by a supervisor
assigned to him. Assessment will be made on the
basis of performance report submitted by the
supervisor in the Ministry and the evaluation of
the student's own report to the coordinator of the
program at the end of the internship.
Prerequisites: STAT
3338 |