Modern Algebra I

3

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

Calculus I

3

This course covers the concepts of function, inverse function, models, limits, continuity and derivatives, the differentiation rules and their applications, related rates, linear approximation and hyperbolic functions.
 In addition to the mean value theorem, indeterminate forms and L' Hospital's rule, curve sketching and optimization problems.

Calculus II

3

Definite integral and its properties, limited integration, integration of compensation, the space between two curves, volumes of revolution, ways of integration (integration by parts, integration of partial fractures,
 integration of trigonometric functions and integration with compensation trigonometric functions), integrals ailing, the length of the curve and the area of surfaces of revolution, final sequences and series, tests of convergent series, power series, Taylor series.

Calculus III

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.

Linear Algebra I

3

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.

Principles of Differential Equations

3

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.

Probability and Statistics for Engineers

4

Topics covered in this course include set theory, relative frequency and probability, joint probability and independent events, random variables, distribution functions, density functions, Gaussian random variables, multiple random variables, joint-distribution functions, joint-density functions, conditional distribution functions, central limit theorem,
random processes (stationary and independent), correlation functions, covariance, Gaussian random processes, spectral characteristics of random processes, the power density spectrum, cross-power spectrum, and the relation between correlation functions and power density spectra.

Biostatistics

3

Data description, frequency and cumulative frequency tables, frequency histogram and polygon, measures of central tendency and measures of variability, percentiles, quartiles identifying outliers and constructing a box-plot diagram. Probability: sample space, events, mutually exclusive events, intersection, union and complement of events. Equally likely outcomes, probability axioms, probability rules, conditional probability and independent events. Total probability rule and Bayes’ theorem. Discrete and continuous random variables, p.d.f, p.m.f, binomial and normal distributions.
Sampling distributions of the sample mean and sample proportion, central limit theorem. Point and interval estimations for the mean and the proportion of one and two populations. Hypotheses testing about the mean and the proportion for one and two populations. How to use statistical packages to make inferences about two population parameters. One-way analysis of variance (ANOVA). Chi-square test for independence.

Partial Differential Equations I

3

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.

Discrete Mathematics

3

The Foundations Logic and Proofs: Applications of Propositional Logic, Predicates and Quantifiers, Rules of Inference, Introduction to Proofs.
Number Theory and Cryptography: Divisibility and Modular Arithmetic, Primes and Greatest Common Divisors, Solving Congruences.
Counting: The Basics of Counting, The Pigeonhole Principle, Permutations and Combinations, Binomial Coefficients and Identities.
Graphs: Graph Terminology and Special Types of Graphs, Representing Graphs and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Shortest-Path Problems.

Principles of General Topoloty

3

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.

Methods of Teaching Mathematics

3

This course begins with the identification of the general objectives of teaching mathematics and the objectives of teaching mathematics at key stage level and in secondary branches of the academic (scientific and literary), and vocational (industrial and commercial). This course examines the themes the main stage of higher education (5- 10), where students acquire the methods of teaching algebraic concepts and principles of solving equations, relations and associations, and the types of associations. Additionally, they learn how to teach the principles of probability, statistical representations, Euclidean geometry, how to demonstrate engineering subsidiary and trigonometry. This course also includes a description of recent trends in the teaching of mathematics using the technology of computers and calculators. The course concludes on how to organize modules in the school calendar and how to prepare exams and evaluations.

Math computing 

3

This course is a hybrid course that sits at the intersection of mathematics and programming. This course teaches students the basics of mathematical concepts related to computing and improving the student's programming skills by implementing mathematical problem using different programming languages. The concepts include some basic linear algebra (vector spaces, matrix operations), cryptography (symmetric public key), statistics operations, Linear Equations (Matrix Representation of systems of linear equations, Gaussian elimination, Inverting nXn matrices) and more. The emphasis will be on using the results, not on their proofs.

Mathematical Physics I

3

This course includes the following topics: - Review of series - Complex numbers. - Linear Algebra (matrices, determinates). - Vectors Analysis. - Special functions (Beta, Gamma, etc.). - Series solution of differential equations. - Coordinate Transformations with common special functions (like Legendre, Hermite, Laguerre ?)

Scientific Research Methods

3

This course is a study of research basic concepts, methods and tools used in business management. The course aims at helping students become aware of new methods of research and their applications for academic and professional investigations. By examining the applications, strengths and major criticisms of methodologies drawn from both the qualitative and quantitative traditions, this course permits an understanding of the various decisions and steps involved in crafting (and executing) a research methodology, as well as a critically informed assessment of published research.