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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
213732 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 R2 and R3 & surfaces; vector-valued functions; partial differentiation with
applications; multiple integrals.

21203 - Principles of Differential Equations

Topics covered in this course include: classifications and solutions of first-order
ordinary differential equations with applications; higher-order 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 non-parametric 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; Riemann-Stetitges 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 Cauchy-Riemann 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,
two-factors design, multi-factors 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 Rao-Blackwell
theorem and Rao-Cramir 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 1st and
2nd schools, Hindu and Arab mathematics; European mathematics before and after
the 17th century; analytic geometry and related concepts; development before
calculus and transition to the 20th 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, Z-transform, 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,
Jenkins-Box 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, cut-vertices, 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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