The course aims to provide students with fundamental mathematical concepts, including sets and operations on them in general, inequalities (their properties and solutions), as well as relations and functions of various types and the algebraic operations applied to them, limits, and continuity. It also covers derivatives (definition and rules of differentiation), some theorems related to derivatives, and the study of their applications.

The course covers the concept of the plane, Cartesian and polar coordinates, vectors, vector algebra and its applications. It also studies the different forms of the equation of a straight line, including the directional and parametric forms, and the derivation of other forms. In addition, it addresses translation and rotation of axes, conic sections of all types, and the general second-degree equation in two variables.

The course aims to study vectors in space, coordinate systems, and the locus of a point. It also includes the study of the plane in space and methods of determining its equation in various forms, along with related concepts. The course further introduces the straight line in space and its different equation forms, related concepts, space curves, and some second-degree surfaces (definition, properties, and methods of determining their equations).

This course includes exponential and logarithmic functions, inverse trigonometric functions, hyperbolic functions and their derivatives, L’Hôpital’s rule for limits, and improper integrals (basic concepts and properties). It also focuses on rules of integration, integration of functions of all types, methods of integration, definite integrals (definition and properties), some theorems of integration, and applications of integration (areas, volumes, arc length, and surface area).

The course deals with basic concepts such as constants, variables, forms, and propositions; logical operations/connectives; truth tables; propositional algebra; open sentences; and quantifiers. It also includes methods of mathematical proof (direct and indirect), proof by mathematical induction, properties of integers, divisibility, congruence, and applications of mathematical proof to sets.

The course aims to introduce matrices (their properties and types), operations on matrices, elementary row operations, matrix inverse, and matrix rank. It also studies determinants, cofactors and inverse matrices, and systems of linear equations, including methods for solving linear systems using the inverse matrix, Cramer’s rule, Gaussian elimination, and the augmented matrix.

The course aims to introduce the basic concepts of sets and their types, groups, set algebra, integers, and the fundamental theorem of division. It also includes a comprehensive study of relations and functions, equivalence of sets (types and properties), finite and infinite sets, countable sets, Cartesian products of sets, as well as basic concepts of the axiom of choice, ordered sets, elements, and bounds.

This course covers vector spaces (definitions and basic concepts), subspaces, linear independence and dependence, basis and dimension. It also introduces inner product spaces, orthogonal vectors, orthonormal bases, and the Gram–Schmidt process. In addition, it studies linear transformations, nullity and rank, operations on linear transformations, matrix representation of linear transformations, the space of linear transformations, eigenvalues and eigenvectors.

The course addresses the concept of vectors, motion in one dimension, motion in a straight line with constant acceleration, free fall, motion in two dimensions, position, velocity, and acceleration vectors. It also studies projectile motion, circular motion, Newton’s laws of motion and their applications, force and mass, types of forces, basic concepts of work and energy, conservative and non-conservative forces, oscillatory motion, simple harmonic motion, and its applications.

The course deals with functions of several variables, domain and range, neighborhoods, limits and continuity, partial derivatives and their applications, the geometric meaning of partial derivatives, gradient, directional derivatives, maxima and minima, and critical points. It also aims to study double integrals (definition and properties), computation and applications of double integrals, triple integrals and their applications, and coordinate transformations in triple integrals.

This course aims to introduce the position vector and linear momentum, collisions and their types, relative speed of approach and separation, motion of a system of particles, conservation of linear momentum, kinetic energy and conservation of energy. It also covers rotational motion, moment of inertia, parallel and perpendicular axis theorems, torque, work and power in rotational motion, angular momentum and impulse, Newton’s laws in rotational motion, and rigid body motion.

The course aims to introduce the origin of differential equations, types of solutions, and types of differential equations. It covers methods for solving first-order, first-degree differential equations, and studies the general forms of homogeneous and non-homogeneous linear differential equations of second and higher order, linear independence, existence and uniqueness theorem, solutions of linear differential equations with constant coefficients, and some solutions of linear differential equations with variable coefficients.

The course addresses the basic concepts of vectors, vector operations, scalar and vector products, triple products, vector-valued functions, limits and continuity, differentiation, gradient, divergence, and curl. It also includes applications of differential geometry, directional theorems, line integrals, surface integrals, and some of their theorems.

This course includes the real number line and its properties, limits, n-dimensional Euclidean space, addition, multiplication, and norms, inner products, open, closed, and dense sets. It also covers compact sets, connected sets, sequences and series with convergence, and some basic concepts of continuous functions.

The course aims to study sequences (definition and types), convergence of sequences, algebraic operations on sequences, series and their convergence, convergence tests, infinite series, absolute and conditional convergence, power series, interval and radius of convergence, functions and power series, differentiation and integration of power series, improper integrals, and convergence tests for improper integrals.

The course deals with the system of complex numbers, algebraic operations on complex numbers, polar representation, powers and roots, the complex plane and its topological properties. It also includes the study of complex functions, limits and continuity, differentiation of complex functions, analytic functions, Cauchy–Riemann equations, harmonic functions, and some elementary functions.

This course includes binary operations, groups and their basic properties, types of groups, permutation groups, cosets, Lagrange’s theorem and its applications. It also covers normal subgroups, simple groups, quotient groups, group homomorphisms, the effect of homomorphisms on groups, kernels of homomorphisms and their properties, and the first isomorphism theorem.

The course includes the definition of derivatives of real functions, some theorems of real functions, continuity of derivatives, higher-order derivatives, maxima and minima, integrals, integrable functions, the fundamental theorem of calculus, convergence theorems, sequences and series of functions, uniform convergence, and the relationship between uniform convergence and continuity, differentiability, and integrability.

The course covers Laplace transforms and solving differential equations using them, solving homogeneous differential equations using power series, and the study of systems of first-order linear differential equations. It also includes methods for solving systems with constant coefficients, matrix methods, solutions using eigenvalues and eigenvectors, and methods for solving non-homogeneous systems in matrix form.

This course includes accelerated coordinate systems, translational motion, rotational motion, combined translational and rotational motion, Newton’s second law, motion under the effect of Earth’s rotation, motion of bodies near the Earth’s surface, Lagrange’s equations of motion and their applications, Hamilton’s equations, theory of small oscillations, and general motion of rigid bodies.

The course covers basic concepts of complex integration, line integrals, Cauchy–Goursat theorem, Cauchy integral theorem and its consequences, the fundamental theorem of algebra and some applications. It also studies sequences and series of complex functions, convergence tests, power series of complex functions, residues and poles, conformal mappings, and some special transformations and formulas.

This course includes basic concepts of partial differential equations, solutions of first-order PDEs (linear, quasi-linear, and nonlinear) in two variables, methods for solving second-order linear PDEs with constant coefficients, variable coefficient equations, classification of second-order PDEs, reduction to canonical forms, and nonlinear second-order PDEs.

The course covers basic concepts and properties of rings, special types of rings, integral domains and their properties, fields, ideals and their properties, principal ideals, quotient rings, ring homomorphisms and their properties, the effect of homomorphisms on subrings and ideals, the first isomorphism theorem for rings, maximal ideals in commutative rings, and polynomial rings.

The course aims to study solutions of partial differential equations with initial and boundary conditions, equations of mathematical physics, Fourier series and their convergence, Fourier integrals and transforms, and solving initial and boundary value problems in two or more dimensions using Fourier series and transforms, as well as using Laplace transforms.

The course includes the study of topological spaces, sets in topological spaces, bases and sub-bases, continuous, open, and closed functions, homeomorphisms, separation and countability axioms, regular and completely regular spaces, compactness, local compactness, connected and path-connected spaces, and finite product topology.

The course addresses the basic concepts of fluid mechanics, properties of fluids, fluid statics and dynamics, integral relations of fluid motion, methods of describing and analyzing fluid flow, energy equations, differential relations of fluid motion, fundamentals of ideal flow, and applications of continuity and Bernoulli’s equations.

The course includes Fredholm and Volterra integral equations of the first and second kind, solving integral equations using iterative kernels, Neumann series, resolvent kernels, degenerate kernels, Fredholm theorems, orthogonal systems of functions, solutions of Volterra equations, nonlinear integral equations, singular equations, and Abel’s integral equation.

The course includes the study of linear normed spaces and their properties, sets in normed spaces, convergence, complete normed spaces, Banach spaces, equivalent norms, compact normed spaces, linear and continuous operators, open mapping theorem, types of convergence and continuity, Hilbert spaces, linear functionals, and some types of operators.

The course covers special functions such as Gamma and Beta functions and their properties, evaluation of integrals using special functions, Bessel functions of the first and second kind, Bessel identities and expansions, Legendre equation, Legendre polynomials and functions, Hermite and Laguerre polynomials, Green’s functions, and their applications.

The course includes the division algorithm, linear combinations, congruences and mathematical induction, prime and perfect numbers, arithmetic functions, congruence classes, Euler and Fermat theorems, higher-order congruences, number theory of real numbers, and Diophantine equations.

‏This course provides students with a general overview of the fundamentals of the Arabic language, focusing on spelling, grammar, and morphology. It aims to equip students with the skills necessary for academic and professional writing, while introducing selected examples of Arabic poetry from the pre-Islamic, Islamic, Umayyad, Abbasid, and modern periods, including free verse poetry.

‏This course aims to develop students’ proficiency in Standard Arabic and equip them with the skills necessary for academic and professional writing. It covers advanced grammar topics, including subject and predicate, object of cause, object with, adverbs, interrogative structures, and demonstrative pronouns. The course also introduces students to Andalusian and modern Arabic poetry, while exploring rhetorical devices such as metaphor, simile, and metonymy.

‏This course provides students with the essential fundamentals of the English language, focusing on developing pronunciation and speaking skills to support academic and professional writing. Topics include demonstrative, quantifying, and interrogative determiners, nouns and their types, pronouns, adjectives and their order, subject-verb agreement, transitive and intransitive verbs, adverbs, prepositions, conjunctions, as well as reading comprehension and writing skills.

‏This course aims to enhance students’ English skills following English Language 1. It focuses on developing reading and writing skills, expanding vocabulary, understanding dictionary entries, and covering grammar aspects such as tenses, articles, ability, permission, and necessity. Students will also practice making requests, suggestions, offers, and invitations in English.

The course includes an introduction to operating systems, file and folder management, Microsoft Word, PowerPoint, Excel, basics of the Internet and email, Internet services, search engines, creating email accounts, and sending and receiving messages.

The course covers basic programming concepts, problem-solving steps using computers, algorithms, flowcharts, symbols used in flowchart design, fundamentals and structure of the C++ programming language, writing simple programs, control statements, arrays and their types, and operations on arrays.

The course includes laboratory training on one of the available mathematical programming languages (C++, MATLAB, Maple), building algorithms using software, selecting topics covering various mathematical fields such as calculus, linear algebra, and statistics, and writing programs to solve specific problems.

The course includes laboratory training on one of the available mathematical programming languages (C++, MATLAB, Maple), building algorithms, selecting topics covering differential equations and Laplace transforms, using software packages for matrix operations, and solving systems of linear and nonlinear algebraic equations.

The course includes basic concepts of frequency distributions, relative and cumulative frequency tables, graphical representation, measures of central tendency, measures of dispersion, skewness and kurtosis, correlation and regression, simple linear regression and correlation, basic probability concepts, Bayes’ theorem, conditional probability, and independence.

The course covers random variables and their types, expectation and variance and their properties, central and non-central moments, discrete distributions (binomial, Poisson), continuous distributions (uniform, normal, exponential, t-distribution, chi-square, beta, gamma), marginal and conditional distributions, joint expectation, covariance, and correlation coefficient.

The course aims to introduce the fundamentals of scientific research, academic writing skills, characteristics of good research, how to design a research plan and collect data, literature review skills, writing the theoretical part of the graduation project, writing abstracts and references, and final formatting of research.

Differential Geometry: The course covers the geometry of curves in the plane (arc length, tangent and normal vectors), curves in space (arc length, curvature, torsion, Frenet–Serret formulas), reconstruction of curves, surfaces in space, areas and curvatures, classical surfaces, Gauss’s Theorema Egregium, and the first variation of arc length. History of Mathematics: The course studies mathematics in Babylonian and ancient Egyptian civilizations, contributions of Indians and Chinese, Greek mathematics, development of mathematics in Arab and Islamic civilizations, transmission of mathematics to Europe, invention of analytic geometry and calculus, non-Euclidean geometry, and characteristics of twentieth-century mathematics. Fuzzy Mathematics: The course covers basic concepts of fuzzy mathematics, fuzzy logic, fuzzy sets and their types, properties of fuzzy sets, fuzzy set algebra, fuzzy relations, domain and range of fuzzy relations, fuzzy truth tables, fuzzy vector spaces, fuzzy linear independence and dependence, basis and dimension.

Differential Geometry: The course covers the geometry of curves in the plane (arc length, tangent and normal vectors), curves in space (arc length, curvature, torsion, Frenet–Serret formulas), reconstruction of curves, surfaces in space, areas and curvatures, classical surfaces, Gauss’s Theorema Egregium, and the first variation of arc length. History of Mathematics: The course studies mathematics in Babylonian and ancient Egyptian civilizations, contributions of Indians and Chinese, Greek mathematics, development of mathematics in Arab and Islamic civilizations, transmission of mathematics to Europe, invention of analytic geometry and calculus, non-Euclidean geometry, and characteristics of twentieth-century mathematics. Fuzzy Mathematics: The course covers basic concepts of fuzzy mathematics, fuzzy logic, fuzzy sets and their types, properties of fuzzy sets, fuzzy set algebra, fuzzy relations, domain and range of fuzzy relations, fuzzy truth tables, fuzzy vector spaces, fuzzy linear independence and dependence, basis and dimension.

The course includes the study of Taylor expansions, errors and their sources, types of errors and how to compute them, roots of equations, numerical methods for finding roots of linear and nonlinear equations, interpolation, numerical differentiation, and numerical integration. The practical part includes computer applications (prescribed software) to solve selected problems.

The course includes an introduction to linear programming, linear models and their types, problem formulation, classical solution methods, special cases in linear programming, duality theory, sensitivity analysis, and transportation problems.

The course covers numerical solutions of initial value problems, derivation of Euler and Taylor methods, error analysis and convergence orders, consistency and stability, predictor-corrector methods, boundary value problems, finite difference methods for linear and nonlinear problems, and numerical solutions of partial differential equations.

The course aims to apply mathematical concepts to study a specific problem, use scientific research tools, select a research problem, design a research plan and sources, write main chapters, analyze results, finalize the scientific research, and use techniques for presenting scientific research.