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Course Description for Department of Basic Science and Mathematics

The Basics of Scientific Knowledge (0210122)

The concept of knowledge, science, the scientific method, a study of some scientists their achievements through the ages, history of science and ancient civilizations and its impact on science and knowledge and its transition between nations, science in general, the problems facing humanity: global warming and bird flu and swine flu, AIDS and cancer .... etc., the evolution of ideas, science and technology: biotechnology and genetic engineering and stem cells, visions of the future.

Prerequisite: None

Applied Physics (211104)

This module is a first year physics course which will introduce the students to the basic language and ideas of physics that occur in all branches of science and technology. In addition it provides them with a clear and logical presentation of the basic concepts and principles of physics, and to strengthen their understanding through a broad range of interesting applications to the real world. Topics include: space and time; vectors; straight-line kinematics; circular motion; experimental basis of Newton's laws and some application; work and energy; electric charge and force; electric filed; Gauss’s law; electric potential and electrostatic energy; capacitance and dielectrics; current and resistance; elements of circuit analysis and Kirchhoff’s laws; magnetostatics; and sources of magnetic field.

General Physics (211105)

This module is a first year physics course offered to students in the faculty of pharmacy, faculty of nursing and faculty of science (students of Genetic Engineering Department). The module will introduce the student to the basic language and ideas of physics that occur in all branches of science and technology. The course will also provide the students with a clear and logical presentation of the basic concepts and principles of physics, and to strengthen their understanding through a broad range of interesting applications to the real world. Topics include: space and time; vectors; straight-line kinematics; circular motion; experimental basis of Newton's laws and some application; work, energy and power; elastic properties of materials; heat; temperature and the behavior of gases; thermodynamics; electric forces; fields and potentials.

General Chemistry 1 (212101)

This course introduces the fundamental theories of chemistry and covers atomic nature of matter, stoichiometry, periodic table, aqueous solution and concentrations, oxidation – reduction reaction, atomic structure, chemical bonding, law of gases , acids and bases.

General Chemistry 2 (212103)

This course the second course of chemistry intended for students in Sciences and genetics. The courses introduce the fundamentals theories of chemistry, type of forces in compounds, thermodynamic, equilibrium, kinetics and solution properties.

Prerequisite: 212101

Calculus I (250101)

The course deals with the following main topics: differentiation of algebraic and transcendental functions, an introduction to analytic geometry, applications of differentiation, and a brief introduction to integration.

Calculus II (250102)

This course introduces advanced principles of calculus to form the foundation needed for student’s advancement. The module deals with the following main topics: Techniques of Integration, Sequences and Series, and Conic Sections and Polar Coordinates.

Prerequisite: 250101 

Discrete Mathematics (250104)

Sets, relations, and functions. Mathematical induction. Recursion. Propositional logic. Counting techniques. Elements of combinatorics. Introduction to graphs and trees.

Business Mathematics(250105)

Linear Equations, Supply and Demand Analysis, Non-linear Equations, Quadratic Functions, Revenue, Cost and Profit, Differentiation, Marginal Functions, Optimization of Economic Functions, The Derivative of the Exponential and Natural Logarithm Functions, Partial Differentiation, Integration, Application on Economics, Matrices, Cramer’s Rule, Linear Programming.

Prerequisite: None.

Intermediate Analysis (250201)

This course introduces advanced principles of calculus to form the foundation needed for students advancement. The module deals with the following main topics: Multidimensional analytic geometry, functions of several variables, vector-valued functions, partial derivatives, Gradiant, maxima-minima problems and applications, double and triple integrals; potential fields; flux; Green's divergence and Stokes' theorems.

Prerequisite: 250102  

Ordinary Differential Equations (250203)

This course introduces methods, theories, and applications of differential equations. The module covers the following main topics: First and higher order differential equations, Solutions by series near ordinary points, Solving initial value problems using Laplace transform, and finally, Linear systems of differential equations.

Prerequisite: 250201  

Elementary Probability and Statistics (250231)

This is an introductory course in statistics. The course is planned so that students learn the basic concepts needed in probability theory and statistics. It familiarizes students with statistical terms such as population, sample, sample size, random variable, mean, variance, and much more. The course covers materials such as collecting data, graphical methods, descriptive statistics, regression and correlation and probability basics.

Prerequisite: None.

Probability Theory (250232)

This course provides a practical introduction to probability theory. The materials covered in this course represent the corner stone of much of what will be needed in statistical inference in the future. All concepts introduced in the course are illustrated with examples that demonstrate principles. The course covers materials such as Counting Techniques, Probability Axioms, Discrete and Continuous Random Variables, The Moment Generating Function, The Bivariate Distribution, Joint, Marginal, and Conditional Distributions, Independence, Correlation and Covriance.

Prerequisite: 250231

Linear Algebra I(250241)

System of Linear Equations, Gaussian Elimination, Methods to Find A-1, Matrices, Determinants, Euclidean Vector spaces, General Vector spaces, Subspaces, Linear Independence and Dependent Basis, Dimension, Row Space, Column Space, Null Space, Theory and Applications.Vector spaces, matrices, determinants, Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications.

Prerequisite: 250101  

Set Theory ( Foundation of Mathematics (0250251)

This course is an introduction to the foundation of mathematics which emphases in teaching the students how to write a sound proof. Topics include a discussion of what is mathematics? Propositional logic and quantification, simple methods of proof, proof by induction, Well – ordering Principle, set operations and identities, relations, functions, cardinal numbers and countable sets ( if time permitting ).

Prerequisite: 250102  

Modern Euclidean Geometry (0250261)

This course presents, from a modern point of view, Books I, II, III, and V, as well as

parts of Books XI, XII, and XIII of Euclid's Elements. These include thorough treatments of the geometry of the triangle and the geometry of the circle, and the theory of Platonic figures.

Prerequisite: 250251

Partial Differential Equations (250305)

First order linear partial differential equations. Second order PDEs, Classification of PDEs, Characteristics, Fourier Series, Solutions of hyperbolic, parabolic and elliptic equations, Dirichlet and Neumann problems, Fourier Transform methods for PDEs, Laplace transform, Heat and wave equations.

Prerequisite: 250203  

Design of Experiments (Elective) (250331)

This course is designed to introduce the student to the basic ideas of experimental design and accompanying analysis. It also enriches student's knowledge and understanding of the statistical methods as it pertains to the design and analysis of experiments. Emphasis will be on conceptual understanding and application to practical problems. Students completing the course are expected to be knowledgeable in the basic experimental designs. Materials covered in the course include Introduction to Statistics and Data Analysis, Inferential Data Analysis for Simple Experiments, One Factor Designs, One Factor Blocking Designs, Latin Square Designs, Two- and General Factor Factorial Experimental Designs, 2K Factorial Designs.

Prerequisite: 250231 

Real Analysis I (250311)

Real numbers: order relation, absolute value, bounded sets, completeness property, Archimedean property; supremum and infimum; sequences: limit, Cauchy sequence, recurrence sequences, monotone sequences, bounded sequences, subsequences and Bolzano-Weierstrass theorem ; functions: limit, right limit, left limit; continuity: continuity at a point, continuity on an interval; uniform continuity, relations between continuity and uniform continuity.

Complex Analysis (250312)

This course is intended to familiarize the students with the basic concepts, principles, and methods of complex analysis and its applications. The course covers the following subjects: the complex numbers system, polar representation and complex root analytic functions, power series, Mobius transformation, conformal mapping, complex integration, power series representation of analytic functions, residues, Cauchy's theorem, application to integration simple closed curves, Cauchy's integral formula, Morera's theorem, singularities, classification and remainder.

Prerequisite: 250311 

Number Theory (250313)

Studies of the integers: divisibility, prime numbers, the Fundamental Theorem of Arithmetic, the theory of congruences and applications, primitive roots and applications, quadratic reciprocity, and selected cryptographical applications. Prerequisite: 250102 

Mathematical Statistics (250332)

This is an introductory course in mathematical statistics. Topics will include Functions of Random Variables, Basic Concepts and Examples, The Expected Value and Moments, Random Vectors, Joint and Marginal Distributions, Independence, Transforms and Sums, Probability Generating Function, Moment Generating Function, Linear Combination of Normal Random variables, and Point Estimation, Unbiased Estimators, Method of The Maximum Likelihood.

Prerequisite: 250232 

Linear Algebra II (250341)

This module is the second part of the linear algebra two-semester series, covering basic matrix transformations in  and , properties of matrix transformations, eigenvalues and eigenvectors, diagonalization, inner products, inner product spaces, angle and orthogonality in inner product spaces, gram–schmidt process; QR-decomposition, general linear transformations, matrices for general linear transformations, some applications of linear algebra.

Prerequisite: 250241 

Abstract Algebra I (250342)

This module is the first part of the Abstract Algebra two-semester series, covering standard topics in group theory: the modular integers, cyclic groups, normal subgroups, isomorphisms, permutation groups, finite abelian groups, and if time permits, some Sylow theorems.

Prerequisite: 250251 

Graph Theory (Elective) (250351)

Studies in graph theory, Eulerian circuits, trees, shortest path problem, matchings, graph coloring, planar graph, Hamiltonian cycles, metrical representations, digraphs, various applications and algorithms.

Prerequisite: 250251 

Numerical Analysis (250371)

Techniques of numerical solutions to various mathematical problems, solutions of equations, Newton's method, zeros of polynomials, interpolations, numerical differentiations and integrations, numerical differential equations, initial value problems, systems of linear equations, matrix inverse, determinants, and eigenvalues and eigenvectors.

Prerequisite: 250241, 250203 

Computer Aided Mathematics (250372)

Symbolic computational packages and scientific visualization through examples from calculus and geometry. Prerequisite: department agreement 

Linear Programming (250373)

This course will be an introduction to mathematical programming, with an emphasis on techniques for the solution and analysis of deterministic linear models. The primary types of models to be addressed will be linear programming: applications and advances. However, the course will touch on more complex models. The main emphasis will be on solution techniques and on analysis of the underlying mathematical structure of these models. As a supporting theme, the course will also emphasize the use of mathematical solvers such as LINGO.

Prerequisite: 250241

Problem Solving (250381)

Concepts in problem solving; practice in solving a wide variety of mathematical and logical problems; techniques for attacking problems; building mathematical models. Prerequisite: Upon completion of 60 credit hours .

Real Analysis II (250411)

This module is the second part of the Real Analysis two-semester series, covering standard and advanced topics in analysis: differentiation, the Riemann integral, sequences of functions, infinite series, and possibly some generalized Riemann integral.

Prerequisite: 0250311 

Abstract Algebra II (250442)

Studies in rings and fields, ideals, integral domains, rings of polynomials, vector spaces, extension fields, Galois theory, finite fields and selected applications. Prerequisite: 250342 

Topology (250461)

Topological spaces: open sets, closed sets,  interior, exterior, boundary, isolated and cluster points; topologies induced by functions; subspace topology; bases and subbases; finite products of topological spaces; continuous functions; open and closed functions; homeomorphisms; separation axioms; countability axioms; metric spaces, connectedness and compactness.

Mathematical Modeling (250471)

Construction, development, and study of mathematical models for real situations; basic examples, model construction, Markov chain models, models for linear optimization, selected case studies. Prerequisite: 250102 and 250241 

Advanced Applied Mathematics (Elective) (250473)

Covers integral theorems of vector analysis, complex variables, series solutions to differential equations, Laplace and Fourier transforms, and use of mathematical software languages such as Maple and Mathematica. Prerequisite: 250311 

Game Theory (250476)

Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible. Prerequisite: 250241 

Instructional Strategies for Teaching Mathematics (250481)

The student will study and participate in instructional activities and strategies for mathematics that depart from the lecture style; e.g., cooperative learning or open-ended problem exploration. Students will design and conduct a mathematics lesson using such a strategy. Prerequisite: Upon completion of 90 credit hours. 

Special Topics (250492)

This course consists of a collection of 5 to 8 well known problems that are of general interest and that are expected to appeal to a wide spectrum of students. Their solutions would involve a variety of ideas related to courses that the student is supposed to have taken. These courses include calculus, algebra, geometry, number theory, dierential equations, and others. Topis will be taken from well-known books such as those of Martin Gardner, Ross Honsberger, William Dunham, Claudi Alsina and Roger B. Nelsen, and others.