0250102

3 Credit Hours

0250205

Linear Algebra and Vector Calculus

This module is oriented for engineering students. The module covers the following main topics: System of linear equation, Gaussian elimination, Vector space, Rank of a matrix.  The inverse of a matrix.  Determinants, Rank in terms of determinants, Cramer’s rule.  Eigenvalues and eigenvectors, diagonalization. Inner product space, Linear transformations. Vector differential calculus, gradient of a scalar vector field, vector integral calculus, integral theorem, divergence theorem, Stokes’s theorem.

0216111

3 Credit Hours

0250102

Calculus (2)

This is a first-year course and oriented to math and engineering students. 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, integration by parts, integration powers of trigonometric functions, partial fraction, trigonometric substitution, and improper integrals. Applications of the definite integral in geometry in science and engineering. Sequences and Infinite Series, Polar Coordinates.

0250202

3 Credit Hours

0250202

Calculus (3)

This course is a second-year course, and it is oriented to math and engineering students. It covers the following main topics: Rectangular Coordinates in 3-Space: Spheres; Cylindrical Surfaces; Vectors; Dot Product; Projections; Cross Product; Parametric Equations of Lines; Planes in 3-Space; Quadratic Surfaces; Cylindrical and Spherical Coordinates. Vector-Valued Functions: Calculus of Vector-Valued Functions; Change of Parameter; Arc Length; Unit Tangent, Normal, and Binormal Vectors; Curvature. Functions of Two or More Variables: Limits and Continuity; Partial Derivatives; Differentiability, Differentials, and Local Linearity; The Chain Rule; Directional Derivatives and Gradients; Tangent Planes and Normal Vectors; Maxima and Minima of Functions of Two Variables; Lagrange Multipliers. Double Integrals: over Nonrectangular Regions; in Polar Coordinates; Triple Integrals; Triple Integrals in Cylindrical and Spherical Coordinates.

0250202

3 Credit Hours

0250203

Ordinary Differential Equations

The module introduces the main concepts of differential equations. The module covers the following main topics: Classification, solutions and initial value problems, direction field, first order ordinary differential equations and solutions. Second and higher order differential equations. Laplace transforms for solving initial value problems. Series Solutions near ordinary points, linear systems of differential equations.

0216121

0250202

3 Credit Hours

0250232

Probability Theory

This course is an introduction to Probability Theory, covering the standards topics such as sample space, events, counting technique, probability axioms, discrete and continuous random variables and distributions of random variables, conditional probability and  independence, discrete and continuous distributions, univariate, bivariate and multivariate distributions; distributions of functions of random variables, distribution function method, expectation and moment generating function method, and some special distributions.

0216111

3 Credit Hours

0250241

Linear Algebra (1)

This the first course of Linear algebra covering elementary topics: matrices and matrix operations, elementary row operations, inverse of a matrix, some special matrices, determinants and properties of determinants, the adjoint matrix, systems of linear equations, Gauss and Gauss- Jordan methods, homogeneous systems of linear equations, Cramer’s rule, eigenvectors and diagonalization, the vector space Rⁿ Subspaces and spanning, linear independences, dimension, rank

0250102

3 Credit Hours

0250251

Set Theory

This course is an introduction to the foundation of mathematics which emphases in teaching the students how to write a soundproof. 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.

0250251

3 Credit Hours

0250261

Modern Euclidean Geometry (1)

This course presents, from a modern point of view, the elements of Euclidean geometry. It treats the geometry of the triangle, Euclid's proof of the Pythagorean Theorem, including all the perquisite theorems needed in that proof. It treats the law of cosines and the law of sines, and their applications. These applications include Heron’s formula, Apollonius’ theorem, Stewart’s theorem, and other theorems. It also covers similarity of triangles. It also treats the basics of the geometry of the circle, including several post-Euclid theorems, such as Brahmagupta’s formula and Ptolemy’s theorems. It discusses constructability and   presents Euclid’s construction of the regular pentagon, as well as Gauss’s theorem on the constructability of the regular n–gon. It also treats the theory of Platonic and Archimedean figures and gives applications of Euler’s VEF formula. The presentation is modern in the following many ways. It pinpoints the inadequacy of Euclid's axioms and some imperfections in his proofs, together with remedies based on Hilbert's axioms of Euclidean geometry. It gives some history of the fifth axiom, and briefly describes the attempts at proving it that culminated in the creation of non-Euclidean geometries. It includes theorems of Euclidean such as hyperbolic geometry. It uses tools from modern branches of mathematics such as trigonometry and algebra and includes theorems of Euclidean geometry that were discovered after Euclid, such as the theorems above.

0250202

3 Credit Hours

0250302

Calculus (4)

This course introduces advanced calculus to form the foundation needed for student's advancement. The module deals with the following main topics: double integral; triple integral, cylindrical and spherical coordinates, vector fields, line integral, conservative vector fields, Green’s theorem, and Stokes’ theorem.

0250203

3 Credit Hours

0250305

Partial Differential Equations

The module aims to familiarize the students with main concepts in partial differential. This course covers the classical partial differential equations such as heat, Laplace, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems. Moreover, the module covers Sturm-Liouville theory and the method of eigenfunction expansions for nonhomogeneous problems. Laplace transform.

0250251

3 Credit Hours

0250311

Real Analysis (1)

The Algebraic properties of R, order property, the absolute value function, triangle inequality, bounded sets, the completeness property of R, Archimedean property in R, supremum and infimum. Sequences: Limit of a sequence. convergent sequences. monotone and bounded sequences. Cauchy sequences. Subsequences and limit points. Bolzano-Weierstrass Theorem. Limits of real valued functions. Definition of limits by neighborhoods. Definition of limits by sequences. Limit theorems. Continuous functions on R: Sequence definition and neighborhood definition of continuity. Boundedness of continuous functions on compact intervals. The extreme value theorem. The intermediate value theorem. Uniform continuity.

0250311

3 Credit Hours

0250312

Complex Analysis

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.

0250251

3 Credit Hours

0250313

Number Theory

Studies of the integers: divisibility, prime numbers, the Fundamental Theorem of Arithmetic, the theory of congruence and applications, primitive roots and applications, quadratic reciprocity, and selected crypto graphical applications.

0250232

3 Credit Hours

0250332

Mathematical Statistics

This is an introductory course in mathematical statistics. The module covers Functions of Random Variables, Basic Concepts and Examples, The Expected Value and Moments, 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.

0250232

3 Credit Hours

0250333

Applied Probability

Markov Chains, Queuing theory and its application, Markovian decisions processes and applications, Simulation and its applications.

0250241

3 Credit Hours

0250341

Linear Algebra (2)

This is a second course in linear algebra covering topics: vector spaces, examples and basic properties, subspaces, independence and dimension, Linear transformations, kernel and image, the dimension theorem, isomorphism’s and matrices, the matrix of linear transformation, Linear operators and similarity, change of basis, diagonalization, invariant subspaces, direct sums, the Cayley -Hamilton theorem, inner products.

0250251

3 Credit Hours

0250342

Abstract Algebra (1)

This module is the first course in Abstract Algebra covering standard topics in group theory: Introduction to groups, finite groups and subgroups, cyclic groups, permutation groups, cosets and Lagrange’s theorem, External Direct products, normal subgroups and factor group, homomorphism’s of groups and the isomorphism theorems.

0250251

3 Credit Hours

0250352

Graph Theory and Combinatorics

This module is an introductory survey in Graph and algorithms: it covers topics in tree-algorithms: minimal spanning trees, breadth-first and depth-first search, labeled binary trees and traversal algorithms: walk- algorithms: the Chinese postman problem, the traveling salesman problem: coloring-algorithms: Hall’s theorem of matching, chromatic numbers, Wells-Powell algorithm, planar graphs and dual graphs.

0250203

3 Credit Hours

0250371

Numerical Analysis

This module is an introductory course in numerical analysis and methods. It introduces the main concepts of numerical analysis. The module covers 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, system of linear equations, matrix inverse, determinants, eigenvalues and eigenvectors, Jacobi and Gauss-Siedel iterative technique.

0250203

3 Credit Hours

0250372

Computer Aided Mathematics

What is Mathematica? The structure of Mathematica, Notebook interfaces, editing Cells and Text, Palettes. Mathematica as a Calculator: Basic Arithmetic, precedence, Built-in Constants: Built-in functions. Numerical Notation: prefix, postfix, infix forms for Built-in functions, Mathematica help. Variables and functions: Rules for Names, immediate Assignment, functions, substitution rule, anonymous functions. Lists: what is a list? Functions producing lists, working with elements of list, listable functions, useful functions. Logic and set theory: being logical, truth tables, element handling sets, Quantifiers. number theoretic functions, numerical functions, Fibonacci sequence, digits in Numbers, selecting from lists. Computer algebra: working with polynomials and powers. Working with rational functions. working with transcendental functions. Solving equations: equations and their solutions, inequalities, single variable calculus: function domain and range, limits, differentiation, implicit differentiation, Maximum and minimum, integration. Sums and products: sequences, the sum command, Taylor polynomials, the product command, vectors and matrices: vectors, Matrices, the conditional function if. Special types of matrices. Basic matrix operations, solving linear systems.

0250241

3 Credit Hours

0250373

Linear Programming

Introduction to Linear Programming: What is a Linear Programming (LP) Problem? Modeling LP problems. The graphical solution of two-variable LP problems. The corner point theorem and its proof. The Simplex method: idea of the Simplex Method. Converting an LP to standard form. Basic feasible solutions. The Simplex Algorithm. Representing the Simplex Tableau. Solving minimization problem. Artificial starting solution and the Big M-Method. Special cases in the Simplex Method: degeneracy, alternative optima, unbounded solutions, nonexistent (or Infeasible) solutions. Sensitivity Analysis and duality: sensitivity analysis. Finding the dual of an LP. The dual theorem and its consequences. Shadow prices. Duality and sensitivity analysis. Complementary slackness. The dual-simplex method. Software: as a supporting theme, the course will also emphasize the use of mathematical solvers such as LINGO, TORA, Mathematica, and EXCEL.

0250311

3 Credit Hours

0250381

Problem Solving

This course aims at presenting to students the various techniques used in solving mathematical problems, and the methods of thinking when attacking a new problem. This is done ideally by selecting several problems from various areas of mathematics, giving first a summary of the material and the basic tools pertaining to each of these problems, then asking the students to try to solve these problems as a homework, and finally discussing the solutions in full detail in later class meetings. The problems are usually taken from the fields of inequalities, number theory, and geometry. The course takes into consideration the needs of students who will eventually become schoolteachers, and students who will pursue higher studies and go into research.

0250311

3 Credit Hours

0250411

Real Analysis (2)

The derivative of functions: properties of differentiable functions. Rolle’s theorem, mean value theorem, generalized Mean value theorem, applications of mean value theorem, L’Hospital’s rule. Riemann integral: the definition, basic properties of Riemann integral, classes of Riemann integrable functions (step functions, continuous functions, monotone functions), mean value theorem for Riemann integral, fundamental theorem of calculus, substitution theorem, integration by parts. Sequences of functions: the definition and examples, pointwise convergence, uniform convergence, uniform convergence and continuity on [a, b], uniform convergence and integrability on [a, b], uniform convergence of sequences of derivatives, uniform convergence and interchange limit theorems, Dini's Theorem.

0250342

3 Credit Hours

0250442

Abstract Algebra (2)

This module is the second course in Abstract Algebra covering standard topics in Ring theory: Introduction to rings, integral domains, Ideals, Prime and maximal ideals, factor rings, ring homomorphisms, Polynomial rings, factorization of polynomials, divisibility in integral domains, finite field (if time permits). Studies in rings and fields, ideals, integral domains, rings of polynomials, vector spaces, extension fields, Galois theory, finite fields and selected applications.

0250241

3 Credit Hours

0250444

Matrix Theory

Kronecker product of matrices; matrix functions; matrix equations, matrix differential equations; eigenvalues and eigenvectors; the characteristic polynomial; the minimal polynomial; Cayley-Hamilton theorem; canonical forms; Gershgorin’s discs; strictly diagonally dominant matrices; Hermitian and unitary matrices; Schur’s triangularization theorem; the spectral theorem for normal matrices; positive semidefinite matrices; quadratic forms; the polar decomposition and the singular value decomposition; the Moore-Penrose generalized inverse; matrix norms; QR factorization.

0250262

0250313

3 Credit Hours

0250453

History of Mathematics

This course consists of a brief overview of the development of mathematics from ancient civilizations till today. It contains a selection of famous mathematicians, famous books, and famous theorems that played great roles in the development of mathematics. The selection is expected to contain Greek mathematicians (such as Euclid, Archimedes, Apollonius, Diophantus, etc.), mathematicians from medieval Islam (such as al-Khwarizmi, Abu Kamil, al-Khayyam, al-Kuhi, Thabit, etc.), and European mathematicians (such as Fermat, Euler, Gauss, etc.). History of mathematics from medieval Islam may be emphasized, and a selection of papers written in that period may be included in the course.

0250311

3 Credit Hours

0250465

Topology

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.

0250262

3 Credit Hours

0250467

Modern Euclidean Geometry (2)

This course is a continuation of Math 250261, and thus Math has 250261 as a prerequisite. It covers some advanced and mod-ern topics from Euclidean geometry. These include the basics of the modern theory of constructability, various types of constructability (such as constructions by rusty compass and by origami), and Gauss's theorem on the constructability of regular n-gons. It also includes tessellations of the plane by regular, semi-regular, and non-regular polygons, tessellations in the Islamic art and in the art of M. C. Escher. It also covers isometries of the plane and includes an extensive study of a selection of triangle centers, as well as a selection of theorems in the modern geometry of the triangle. It may give brief introductions to spherical, hyperbolic, and tetrahedral geometry, and present examples of proofs of geometry theorems using modern branches of mathematics (such as linear algebra and calculus).

0250203

3 Credit Hours

0250471

Mathematical Modeling

Construction, development, and study of mathematical models for real situations; basic examples, model construction, Markov chain models, models for linear optimization, selected case studies. ended problem exploration.

0250311

3 Credit Hours

0250475

Special Functions

The course aims to familiarize the students with some special functions. It covers the following topics: periodic functions, even and odd functions, orthogonal functions, Fourier series, Beta and Gamma function, Error functions, Legendre polynomials, Leibniz rule and Bessel functions.

0250241

3 Credit Hours

0250476

Game Theory

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

0250262

3 Credit Hours

0250481

Teaching Method Mathematics

The module covers the following main topics: The nature of mathematics and the modern view of mathematics and its curriculums. Aims and goals of teaching mathematics and the curriculums development. Teaching plan. The impact of modern learning theory in the curriculum development and the relation between educational psychology with teaching mathematics.  Selected mathematical models based on educational psychology. The four types of mathematical knowledge: concepts, generalization, skills, and problems. Evaluation and test preparing.

0250341

3 Credit Hours

0250492

Special Topics

This course consists of a collection of several topics that are of general interest and that are expected to appeal to a wide spectrum of students. The material selected may be related to, but not included in other courses, and may lightly depend on and involve a variety of ideas related to courses that the student is supposed to have taken. These courses include calculus, algebra, geometry, number theory, differential equations, and others. Topics may be taken from well-known books of popular fame.