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Mathematics Courses
(1) Specialization Requirements
After successful completion of his/her first year at university, the student
specifies his/her
specialization major with the assistance of his/her academic supervisor. Then,
the student fills
and completes an application form submitted to the Faculty of Science.
The following requirements should be met for specialization:
1. Successful completion of two mathematics courses ( 21101 & 21102 ) with a
minimum overall average of 70%.
2. Successful completion of two physics courses (22101 & 22102).
3. Successful completion of at least 30 credit hours of which at least 18 credit
hours are within the Faculty of Science
requirements.
If the number of students applying to the mathematics major is more than the
required number set by the Faculty Council, then the students will be selected
according to their highest average in the 21101 and 21102 courses.
(2) Degree Requirements
All candidates for the B.S. degree in mathematics should successfully
complete 137 credit
hours as follows:
1 University Compulsory Requirements (20 credit hours)
2 University Elective Requirements (6 credit hours)
3 Faculty Compulsory Requirements (30 credit hours)
4 Departmental Compulsory Requirements (54 credit hours)
5 Departmental Elective Requirements (27 credit hours)
The departmental courses required are as follows:
A. Departmental Compulsory Courses (54 credit hours)
Course Number  Course Title  Credits  Prerequisites 
21201  Calculus (3)  3  21102 
21203  Principles of Differential Equations  3  21101 
21211  Principles of Mathematics  3  21102 & Dept. approval 
21212  Modern Analysis (1)  3  21211 
21220  Programming for Mathematics  3  21102 & Dept. approval 
21231  Methods of Statistics (1)  3   
21241  Linear Algebra (1)  3  21201 
21242  Modern Algebra (1)  3  21211 
21311  Modern Analysis (2)  3  21212 
21312  Complex Analysis (1)  3  21212 
21321  Numerical Analysis (1)  3  21241 & 21220 
21334  Probability Theory (1)  3  21201 
21342  Modern Algebra (2)  3  21242 
21361  Principles of General Topology  3  21212 
21362  Modern Methods in Geometry  3  21211 
21399  Scientific Research  3  Dept. approval 
72292  Methods of Teaching Mathematics  3   
72492  Practical Education for Math Students 
3  72292 
Total  54 
Offered by the College of Education Sciences.
B. Departmental Elective Courses (27 credit hours)
Candidates must meet departmental elective requirements by completing:
1 One 3 credit hours course offered by the College of Education Sciences.
2 24 credit hours selected from courses offered by the Department of
Mathematics.
Course Number  Course Title  Credits  Prerequisites 
21232  Methods of Statistics (2)  3  21231 
21301  Special Functions  3  21203 
21302  Partial Differential Equations (1)  3  21203 
21303  Vector Analysis  3  21201 
21314  Advanced Calculus  3  21201 
21320  Software Packages for Mathematics  3  21220 & 21241 
21322  Linear Programming  3  21220 & 21241 
21323  Operations Research (1)  3  21322 
21331  Sampling Methodology  3  21231 
21332  Experimental Design and Variance Analysis  3  21231 
21335  Probability Theory (2)  3  21334 
21336  Mathematical Statistics (1)  3  21334 
21337  Mathematical Statistics (2)  3  21336 
21341  Linear Algebra (2)  3  21241 
21343  Number Theory  3  21211 
21351  History of Mathematics  3  Dept. Approval 
21373^{2}  Applied Mathematics  3  21203 & 21241 
21403  Ordinary Differential Equations  3  21203 
21414  Functional Analysis  3  21361 
21421  Numerical Analysis (2)  3  21321 
21431  Time Series Analysis  3  21336 
21435  Applied Regression Analysis  3  21241+21334+21220 
21462  Differential Geometry  3  21201 & 21241 
21474  Combinatorics & Graph Theory  3  21241 
21481  Special Topics (1)  3  Dept. Approval 
21482  Special Topics (2)  3  Dept. Approval 
72138  Classroom Environmental Management 
3   
72254  Educational Psychology  3   
Offered by the College of Education Sciences (Choose one course from 72138 & 72254).
(3) Course Descriptions
21103  General Mathematics
Topics covered in this course include: the Cartesian plane, equation of a
straight line,
equations and inequalities; linear programming; functions, their types, and the
limits and
continuity of functions; derivatives of polynomials, algebraic, trigonometric,
logarithmic and
exponential functions ; rules of differentiation, applications of derivatives on
extreme values
and graphs; definite and indefinite integrals; applications of definite
integrals; integration by
substitution and by parts ; matrices, determinants and solving systems of linear
equations;
partial differentiation.
21104  Mathematics for Pharmacy
Topics covered in this course include: limits and continuity; the derivative,
applications of the derivative; integrals and applications of the definite
integral;
transcendental functions.
21105  Mathematics for Education
Topics covered in this course include: functions and their graphs  linear,
quadratic, rational ,
natural exponential, natural logarithmic, sine and cosine functions; limits and
the
indeterminate form 0/0, continuity of functions; derivatives using rules of
differentiation ,
applications of derivatives on tangent lines, instantaneous rate of change,
instantaneous
velocity and applications on extreme values and graphs; definite and indefinite
integrals,
integration by substitution and by parts; solving first order ordinary
differential equations;
counting principle, permutations and combinations; the binomial theorem and
Pascal's
triangle, substitution and elimination methods in solving systems of linear
equations in two or
three variables; matrices, determinants and solving systems of linear equations
in two or
three variables using inverses and Cramer's rule.
21201  Calculus (3)
Topics covered in this course include: parametric equations and polar
coordinates;
vectors in R^{2} and R^{3} & surfaces; vectorvalued functions; partial differentiation
with
applications; multiple integrals.
21203  Principles of Differential Equations
Topics covered in this course include: classifications and solutions of
firstorder
ordinary differential equations with applications; higherorder and solutions;
power
series solutions; Laplace transforms; solutions of systems of linear
differential
equations.
21211  Principles of Mathematics
Topics covered in this course include: logic and proofs; set theory,
relations and
functions; cardinality and examples on mathematical structures.
21212  Modern Analysis (1)
Topics covered in this course include: properties of real numbers; open and
closed
sets; sequences; limits and continuity; differentiation; Riemann integral.
21220  Programming for Mathematics
Topics covered in this course include: fundamentals of programming;
algorithms,
types of data and control statements, dimensions, functions and subroutines;
some
mathematical software with applications.
21231  Methods of Statistics (1)
Topics covered in this course include: statistical data classifications;
measure of
central tendency and variability; probability concepts and rules; discrete and
continuous random variables; probability distributions; the binomial and normal
distributions; sampling distributions; point and interval estimations for one
population
mean; tests of hypotheses for one population mean.
21232  Methods of Statistics (2)
Topics covered in this course include: sampling distributions; confidence
intervals;
testing hypotheses for one and two population parameters; regression and
correlation; testing hypotheses for regression line parameters; analysis of
variance;
chi square test and nonparametric tests.
21241  Linear Algebra (1)
Topics covered include: matrices, vectors and elementary row operations;
operations
on matrices; determinants and inverses of matrices; systems of linear equations
and
method of solutions; vector spaces, linear independence and basis; linear
transformations, kernel and range; eigenvalues and eigenvectors.
21242  Modern Algebra (1)
Topics covered in this course include: binary operations; groups, subgroups,
finite
groups, cyclic groups, symmetric groups, factor groups, normal subgroups; group
homomorphisms; Sylow theorems.
21262  Principles of Geometry
21301  Special Functions
Topics covered in this course include: the Frobenious method for solving
differential
equations; special functions like Gamma and Beta functions; Legendre
polynomials;
Bessel functions; Hermite polynomials; Chebyshev, Laguerre and hypergeometric
functions.
21302  Partial Differential Equations (1)
Topics covered in this course include: the formation of a partial
differential equation;
methods of solutions of first order linear and nonlinear partial differential
equations;
methods of solutions of second order linear and nonlinear partial differential
equations; Fourier series and transforms; wave equation, Laplace’s equation,
potential equation, equation of an infinite wire, heat equation.
21303  Vector Analysis
Topics covered in this course include: vector algebra, vector products,
vectors and
scalar fields; the gradient, divergence and curl theorems; line, surface and
volume
integrals, related theorems; curvilinear coordinates.
21311  Modern Analysis (2)
Topics covered in this course include: metric spaces; RiemannStetitges
integral;
functions of bounded variations; sequences and series of functions.
21312  Complex Analysis (1)
Topics covered in this course include: properties of complex numbers; complex
functions, derivatives and CauchyRiemann equations; elementary functions and
elementary transformations; complex integrals, residue theorem and improper
integrals; power series.
21314  Advanced Calculus
Topics covered in this course include: coordinate systems ; functions of
several
variables, parametric representations of curves and surfaces, transformations of
regions; derivatives and directional derivatives; implicit functions, Jacobians
and
related theorems; extrema; multiple integrals and related theorems.
21320  Software Packages for Mathematics
Topics covered in this course include: mathematical modeling; using some
software
packages in mathematics and statistics; NETLIB, NAG, Derive, Mathematica,
MATLAB, BLAS, Maple, MathCad, SPSS, Minitab.
21321  Numerical Analysis (1)
Topics covered in this course include: numbers, Binary, Octal and Hexadecimal
number systems; floating point arithmetic, Errors, sources and types; solving
nonlinear equations, direct and indirect methods in solving systems of linear
equations, solving systems of nonlinear equations; approximation and
interpolations,
numerical integration.
21322  Linear Programming
Topics covered in this course include: problem formulation ; graphic solution;
simplex
method; duality theorem; linear sensitivity analysis and algebraic
representation;
transportation and assignment problems; network (PERT and CPM); game theory.
21323  Operations Research (1)
Topics covered in this course include: introduction to operation research;
inventory
models, queuing models; game theory; Markov chains; case studies.
21331  Sampling Methodology
Topics covered in this course include: simple random samples, estimation of
means
totals and proportions, estimation of the regression parameters, stratified
sampling,
cluster sampling, systematic sampling and other sampling g methods.
21332  Experimental Design and Variance Analysis
Topics covered in this course include: random column design, Latin squares
design,
twofactors design, multifactors comparative experiment , testing model accuracy
in
analysis of variance, insufficient sector model factor analysis, multiple
comparisons
21334  Probability Theory (1)
Topics covered in this course include: basic concepts of probability;
discrete and
continuous random variables; probability distributions; the binomial, geometric,
negative binomial, uniform, gamma and normal probability distributions;
examination
of moment generating functions; probability distributions of functions of random
variables.
21335  Probability Theory (2)
This course includes review of some properties of random variables and
probability
distributions, multinomial distributions, distribution of order statistics, and
moments
and moment generating functions for some probability distributions. Limiting
distributions, types of convergence and characteristic functions are also
examined.
21336  Mathematical Statistics (1)
This course provides an introduction to decision theory, risk and loss
functions,
unbiased estimation, efficient and maximum likelihood estimation, confidence
intervals, testing statistical hypotheses, sufficient statistics, the RaoBlackwell
theorem and RaoCramir inequality.
21337  Mathematical Statistics (2)
This course covers properties of point estimates, the exponential family of
distributions, sufficiency and completeness, Bayesian estimation, most powerful
test,
sequential test, and estimation and testing hypotheses for linear models.
21341  Linear Algebra (2)
Topics covered in this course include: vector spaces; linear independence;
direct
product and direct sum of vector spaces; linear transformations, algebra of
linear
transformations; dual spaces; matrices; linear systems; eigenvalues and
eigenvectors; Hermite matrices; positive definite matrices.
21342  Modern Algebra (2)
Topics covered in this course include: rings, subrings, ideals, division
rings, factor
rings; ring homomorphisms; maximal ideals, principal ideal rings, principal
ideal
domains; polynomial rings, extension of fields.
21343  Number Theory
Topics covered in this course include: divisibility and prime numbers;
Chinese
remainder theorem; congruence; Euler's theorem, Fermat’s theorem, Wilson’s
theorem; linear congruence: congruent and noncongruent solutions; arithmetic
functions; special numbers: perfect, deficient abundant and Mersenne numbers
21351  History of Mathematics
This course covers mathematical development as science; early numeral systems
such as Babylonians, Egyptians and Greek; the three problems of antiquities:
duplicating a cube , quadrating of a circle and trisecting an angle; Alexandria
1^{st} and
2^{nd} schools, Hindu and Arab mathematics; European mathematics before and after
the 17^{th} century; analytic geometry and related concepts; development before
calculus and transition to the 20^{th} century.
21361  Principles of General Topology
This course covers topological spaces, basis and subbasis;
functions and
homomorphisms; separation and countability axioms; connectedness and
compactness; Hausdorff space, metric spaces and product spaces.
21362  Modern Methods in Geometry
Topics covered in this course include: Euclid’s axioms;
incidence geometry; Hilbert’s
postulates; absolute geometry; hyperbolic geometry; Riemann geometry; metric and
nonmetric geometric transformations
21373  Applied Mathematics
This course covers Orthogonal functions; Fourier series
and Fourier transform;
discrete Fourier series and transform, Ztransform, minimization and least
square
method.
21399  Scientific Research
This course involves discussion of characteristics of
scientific thinking and its
relationship with scientific research, conducting a research on a specific topic
in
mathematics, and delivering and represent this research in a seminar for
evaluation.
21403  Ordinary Differential Equations
Topics covered in this course include solving ordinary
differential equations using
series; Laplace transform; existence theorem and applications; solving linear
and
nonlinear systems of ordinary differential equations; dynamical systems.
21414  Functional Analysis
This course covers linear topological spaces, function
spaces; weak topology;
extension and separation theorems; open mappings; uniform boundedness; Banach
and Hilbert spaces.
21421  Numerical Analysis (2)
This course covers numerical methods for ordinary
differential equations and
systems; numerical methods for finding eigenvalues and eigenvectors; numerical
methods for solving nonlinear systems; and introduction to numerical methods for
solving partial differential equations.
21431  Time Series Analysis
This course covers time series description, trends,
periods, moving averages,
filterization, Fourier analysis, models of stable series, self correlation,
predictions,
JenkinsBox methods and spectrum analysis.
21435  Applied Regression Analysis
This course covers simple linear regression, multiple
regression, estimation,
goodness if fit tests, residual analysis, using matrices an regression, and
factor
rotation and applications.
21462  Differential Geometry
Topics covered in this course include: curves in planes
and in space; curvature and
torsion; theory of curves: intrinsic equations, involute curves and evolute
curves;
surfaces, simple surfaces and topological properties; tangent planes; first and
second
forms of a surface; asymptotes; intrinsic geometry, theory of surfaces; tensors
and
families of related curves.
21474  Combinatorics & Graph Theory
This course focuses on graphs: simple graphs, directed
graphs, components,
connected components; blocks, cutvertices, and bridges; Euler graphs; trees,
planar
and nonplanar graphs; graph matrices and coloring.
21481  Special Topics (1)
This course covers some selected topics in pure and
applied mathematics
determined by the department and the course lecturer.
21482  Special Topics (2)
This course covers some selected topics in pure and
applied mathematics
determined by the department and the course lecturer.
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