# 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 MathStudents |
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 EnvironmentalManagement |
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; 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
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, 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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