Course Descreption 2013

Requirements to obtain a B.Sc. degree in mathematics

All candidates for the B.Sc degree in mathematics should complete successfully 123 credit hours as follow:

1-      University Compulsory Requirements (18 credit hours).

2-      Department Compulsory Requirements (84) credit hours )

3-      Departmental Elective Requirements (21 credit hours).

    The description and names of the departmental courses required are as follow:

A. Departmental Compulsory Courses (54 credit hours)

* 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.

* Offered by the College of Education Sciences (Choose one course from 72138 & 72254).

(3) Course Descriptions

10211103 - 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.

10211104 - 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.

10211105 - 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.

10211201 - 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.

10211203 - 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.

10211211 - Principles of Mathematics

Topics covered in this course include: logic and proofs; set theory, relations and functions; cardinality and examples on mathematical structures.

10211212 - Modern Analysis (1)

Topics covered in this course include: properties of real numbers; open and closed sets; sequences; limits and continuity; differentiation; Riemann integral.

10211220 - 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.

10211231 - 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.

10211232 - 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.

10211241 - 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; Eigen values and eigenvectors.

10211242 - Modern Algebra (1)

Topics covered in this course include: binary operations; groups, subgroups, finite groups, cyclic groups, symmetric groups, factor groups, normal subgroups; group homomorphism; Sylow theorems.

    10211262 - Principles of Geometry

Geometry: Hilbert's postulates, congruence, equivalence, similarities, circles, geometric transformations; space geometry: relations between lines, between lines and planes, between planes, theory of orthogonal projections; solid geometry: prisms, pyramids, cylinders, cones, sphere and related theorems.    10211301 - 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 hyper geometric functions.

10211302 - 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.

10211303 - 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.

10211311 - Modern Analysis (2)

Topics covered in this course include: metric spaces; Riemann-Stetitges integral; functions of bounded variations; sequences and series of functions.

10211312 - 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.

10211314 - 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; extreme; multiple integrals and related theorems.

  10211320 - Software Packages for Mathematics

Topics covered in this course include: mathematical modeling; using some software packages in mathematics and statistics; NETLIB, NAG, Derive, Mathematical, MATLAB, BLAS, Maple, MathCAD, SPSS, Minitab.

10211321 - 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.

10211322 - 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. 

10211323 - Operations Research (1)

Topics covered in this course include: introduction to operation research; inventory models, queuing models; game theory; Markov chains; case studies.

10211331 - 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.

10211332 - 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, and multiple comparisons.

10211334 - 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. 

10211335 - 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.

10211336 - 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.

10211337 - 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.

10211341 - 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; Eigen values and eigenvectors; Hermite matrices; positive definite matrices.

10211342 - Modern Algebra (2)

Topics covered in this course include: rings, sub-rings, ideals, division rings, factor rings; ring homo-morphisms; maximal ideals, principal ideal rings, principal ideal domains; polynomial rings, extension of fields.

  10211343 - 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 non-congruent solutions; arithmetic functions; special numbers: perfect, deficient abundant and Mersenne numbers.

  10211351 - 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, quad rating 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.

10211361 - Principles of General Topology

This course covers topological spaces, basis and sub-basis; functions and homomorphism; separation and countability axioms; connectedness and compactness; Hausdorff space, metric spaces and product spaces.

10211362 - 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 non-metric geometric transformations.

10211373 - Applied Mathematics

This course covers orthogonal functions; Fourier series and Fourier transform; discrete Fourier series and transform, Z-transform, minimization and least square method.

    10211399 - Scientific Research

This course involves discussion of characteristics of scientific thinking and its relationship with scientific research; it requires students to conduct a research on a specific topic in mathematics, and to deliver it and represent this research in a seminar for evaluation.    

10211403 - 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.

10211414 - Functional Analysis

This course covers linear topological spaces, function spaces; weak topology; extension and separation theorems; open mappings; uniform bounded-ness; Banach and Hilbert spaces.

10211421 - Numerical Analysis (2)

This course covers numerical methods for ordinary differential equations and systems; numerical methods for finding Eigen values and eigenvectors; numerical methods for solving nonlinear systems; and introduction to numerical methods for solving partial differential equations.

10211431 - 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.

10211435 - Applied Regression Analysis

This course covers simple linear regression, multiple regressions, estimation, and goodness if fit tests, residual analysis, using matrices a regression, and factor rotation and applications.

  10211462 - 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.

10211474 - 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 non-planar graphs; graph matrices and coloring.

10211481 - Special Topics (1)

This course covers some selected topics in pure and applied mathematics determined by the department and the course lecturer.

10211482 - Special Topics (2)

This course covers some selected topics in pure and applied mathematics determined by the department and the course lecturer.