"Binary operations and their properties; groups and their fundamental properties; left and right cosets; Lagrange’s theorem; isomorphism and its applications; normal subgroups and their basic properties; and simple groups."

"Complex numbers; the triangle inequality and its generalization to n numbers with conditions for equality; topology of the complex plane; functions of a complex variable; and elementary functions and transformations."

"This course covers: derivatives of functions, including directional derivatives, partial derivatives, differentiability, the gradient of a function, and the matrix representation of the derivative. Integration: the Riemann integral and its properties, and Riemann integrability. Improper integrals, their properties, and convergence tests. Sequences and series of functions: sequences of functions, uniform convergence of sequences of functions, and the relationship between uniform convergence, integration, and differentiation. Series of functions: uniform convergence of series, and the relationship between uniform convergence, differentiation, and integration."

"This course covers: first-order differential equations, both linear and nonlinear, the formation (modeling) of differential equations, and methods for solving first-order equations (separation of variables, exact and non-exact equations, and integrating factors), as well as Bernoulli’s equation. Second-order linear differential equations with constant coefficients, both homogeneous and nonhomogeneous, and methods of solution (inverse operator method, undetermined coefficients, and variation of parameters). Higher-order linear differential equations and Laplace transform

"This course covers: the real number line and mathematical induction. Sequences of real numbers: their definition and convergence, bounded sequences, Cauchy sequences, supremum and infimum, and the Archimedean property. Finite-dimensional Euclidean spaces: norms and their properties; topology on ℝⁿ (open and closed sets, interior points, boundary points, closure of a set, accumulation points, finite, countable, and uncountable sets); compact and connected sets. Sequences and series in ℝⁿ. Limits and continuity: bounded functions, limits of functions, and uniform continuity."

This course aims to equip students with the fundamental concepts and skills that every teacher must master as part of their professional behavior. It emphasizes the correct understanding of basic concepts such as evaluation and assessment, psychological measurement, educational evaluation, tests, and assessment. Students will also learn about validity and reliability as essential conditions for measurement and evaluation, as well as the different types of achievement tests.

This course covers the main topics and concepts related to Information and Communication Technology (ICT), including the definition and uses of computers, types of computers, the binary digital system, computer hardware components, types of software, computer networks, Internet fundamentals, computer crimes, and data security and protection.

This course provides a scientific critical analysis of the topics covered in the prescribed mathematics textbooks for grades 10–12, along with a collection of exercises from the curriculum textbooks.

This course provides a scientific critical analysis of the topics covered in the prescribed mathematics textbooks for grades 7–9, along with a selection of exercises from the curriculum textbooks.

This course covers the history of numbers, from the ancient Egyptians to the Arabs and Muslims, the historical development of mathematical concepts, and notable mathematicians.

This course covers functions of several variables, including their domain and range, limits, and continuity. It addresses partial derivatives (definition, properties, and methods of computation) for first- and higher-order derivatives, as well as total differentiation and applications of partial derivatives in geometric and engineering contexts. The course also includes directional derivatives, gradients, tangent planes, and normal lines. Additionally, it covers maxima and minima, saddle points, and Lagrange multipliers.

introduces students to the concept of integration and its main types, focusing on indefinite and definite integrals, fundamental integration rules, and applications of integration in calculating areas, volumes, and selected geometric and physical problems, supported by illustrative examples and exercises

This course covers limits, continuity, and some theories of continuity. It addresses differentiability (including partial derivatives), applications of increasing and decreasing functions, Rolle’s theorem, the Mean Value Theorem, absolute and relative extrema, concavity and convexity, inflection points, and the plotting of curves.

This course covers vectors, including vector addition, subtraction, scalar and vector multiplication. It addresses vector calculus in one dimension, Cartesian and polar coordinates, the distance between two points, vector transformations (translation and rotation), parametric representation of curves, straight lines in space, slopes, and various forms of the straight line equation. The course also includes the plotting of lines and practical exercises.

This course covers some general statistical concepts, including tabular and graphical presentation of statistical data, measures of central tendency, measures of dispersion, correlation and regression, time series, and demographic and vital statistics.

This course covers the following topics: Basics and Roots: Basic concepts, square roots, and nth roots; radical expressions; equations involving roots; limits and partial fractions. Rational Expressions: Polynomials with multiple terms; fundamental theory of division; synthetic division; basic algebraic properties. Operations and Equivalence: Operations with radicals and rational expressions; mathematical induction; Euclidean theory of integers.

This course covers conic sections, including their definition and derivation of equations. Topics include: Circle: Definition, derivation of its equation, translation of axes, and parametric representation and graphing. Parabola: Standard equation derivation, vertex at the origin or shifted along axes, and parametric forms. Ellipse: Standard equation derivation, parametric representation, axes orientation, and graphing. Hyperbola: Standard equation derivation, transverse and conjugate axes, parametric forms, and graphing. Solid Sections: Derivation of equations, three-dimensional graphing, and conic sections in space. The course also includes applications and exercises for practice.

This course covers matrices, including their concepts, types, and operations. Topics include: Matrix Operations: Basic operations on matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. Special Matrices: Properties and applications of special types of matrices. Matrix Inversion: Definition and concepts of the inverse matrix, methods for finding the inverse using determinants, systems of linear equations, and solving them using matrices and determinants.

Probability; discrete random variables and their probability distributions; continuous distribution, “Bernoulli distribution”; natural distribution; standard normal distribution; approximation of the Bernoulli distribution by the normal distribution; square distribution, + distribution; 0 distribution

This course covers definite and indefinite integrals, methods of integration, and L’Hospital’s rule for limits. It also includes applications of integration.

This course covers three-dimensional coordinate systems, including Cartesian, cylindrical, and spherical coordinates, as well as equations of surfaces and curves. Topics include: Planes: Equations of planes, conditions for parallelism and perpendicularity between two planes, and different forms of plane equations. Lines in Space: Equations of lines in space and their various forms. Sphere: Equation of a sphere, intersections, and tangent planes. Cylinders and Cones: Equations and properties of cylindrical and conical surfaces. Solids: Equations of solids and related surfaces. The course also includes applications and exercises for practice.

Directional spaces (basic definitions and concepts), linear transformations; inner product space (definitions, examples, and essential properties), self-values and self-trends for a matrix.

‘Understanding regional clauses and tools of regional connection, tables of truth and regional complementarity, compulsory issues and regional logic, and rules of inference in formal logic, methods of proof, as well as groups of international relations and compatible groups for conjunction and related groups.

This course provides a theoretical foundation for the Teaching Applications and Teaching Practice courses. It covers the concept of the mathematics curriculum, including curriculum elements such as objectives and mathematical content, selected strategies for teaching mathematics, assessment and evaluation, educational theories related to mathematics teaching, and difficulties in teaching and learning mathematics.

This course includes partitions, moments, moment generating functions, major discrete and continuous probability distributions, probability distribution functions for discrete and continuous random variables, marginal probability distribution functions, joint cumulative distribution functions, conditional probability distribution functions, independent random variables, mathematical expectation, covariance, correlation, and probability distributions of multivariate random variables.

This course covers sampling distributions, sampling distribution of the sample mean, sampling distribution of the difference between two sample means, sampling distribution of sample proportions, sampling distribution of the difference between two proportions, statistical estimation, and hypothesis testing.

This course includes double integrals: definition, geometric meaning, properties, and methods of evaluation; double integrals in polar coordinates; applications of double integrals; triple integrals: definition, properties, and methods of evaluation; line integrals; surface integrals; sequences and series.

This course covers Taylor and Maclaurin series, convergence properties, linear interpolation, numerical solutions of single equations, numerical solutions of systems of linear equations, numerical differentiation (forward and central differences), numerical integration using the trapezoidal rule, composite trapezoidal rule, Simpson’s rule, composite Simpson’s rule, and error analysis.

This course covers rings, including definitions, basic concepts, and fundamental properties; subrings and their properties; integral domains and their properties; fields and their basic concepts; the relationship between integral domains and fields; characteristic of rings and fields; ideals and their properties; principal ideals; quotient rings and their properties; ring homomorphisms and their properties; the effect of homomorphisms on subrings and ideals; kernels of homomorphisms and their properties; the first isomorphism theorem for rings and its applications; construction of fields from integral domains; prime ideals and their properties in commutative rings; maximal ideals and their properties; and the study of selected important rings.

This course discusses the importance of sampling methods and basic concepts, simple random sampling, stratified random sampling, systematic random sampling, cluster sampling, selecting probability samples proportional to size, special estimators, determining sample size with predetermined accuracy, and double sampling.

This course covers partial differential equations, including their definition, order, linear and nonlinear forms, origins of partial differential equations, first-order partial differential equations and solving simple cases by direct integration, nonlinear equations and solution methods, the general method and Lagrange’s method, Charpit’s method, second-order linear partial differential equations with constant coefficients, homogeneous and non-homogeneous solutions, separation of variables, and initial and boundary value problems.

This course covers systems of linear ordinary differential equations, existence and uniqueness of solutions, fundamental matrix solutions, solving systems with constant coefficients (homogeneous and non-homogeneous) using elimination methods, eigenvalues and eigenvectors, finding particular solutions using the method of undetermined coefficients and variation of parameters, solutions near regular singular points, and solving second-order linear differential equations using power series around ordinary points.

This course explains the basic skills and main concepts related to the use of spreadsheets, mathematical and logical formulas and functions, computer systems and operating systems, application software, windows and their uses, paint tools, internet browsers, and practical use of application programs such as Word, Excel, and PowerPoint. The practical component represents the major part of the course, aiming to develop students’ applied skills and assist them in completing assignments, graduation projects, and future professional tasks.

This course includes Laplace transforms and their applications, Fourier transforms and their applications, an introduction to integral equations and their types, Volterra equations, eigenvalue problems, Fredholm integral equations, Liouville and Neumann series, iterative solution methods, numerical solutions, Fredholm formulas, applications, and exercises.

This course covers complex integration, Cauchy’s theorem and Cauchy’s integral formula, sequences and series of complex numbers, sequences and series of complex-valued functions and uniform convergence, power series, Taylor and Laurent series, residue theory, and the evaluation of integrals.

This course aims to develop students’ mathematical thinking skills and problem-solving methods, and to introduce them to systematic approaches in mathematical analysis and their application in educational and applied fields. The course also focuses on employing modern technologies in the educational process and developing skills in using digital media and educational technologies in teaching and learning.

This course introduces the concept of operations research and the most important methods used in it, including linear programming and its problems, the simplex method, the dual problem in linear programming and its properties, transportation problems, and simulation.

In this course, students study the concept of Islamic creed, including the meaning of religion and people’s need for it, the main characteristics of Islam, the relationship between faith and deeds, increase and decrease of faith, the pillars of faith, belief in angels, belief in the divine books and their introduction, belief in messengers, belief in the Last Day, and belief in divine decree and destiny.

This course aims to develop students’ ability to deal with the basics of the English language used in scientific fields and daily life. It also helps improve the four English language skills (listening, speaking, reading, and writing) through exercises, conversations, examples, and effective activities, which enhance proper communication. The course provides basic and simple English grammar such as verbs and tenses (present simple, present continuous), as well as commonly used vocabulary and expressions.

This course provides student teachers with knowledge, skills, values, and attitudes that contribute to their preparation and qualification for the teaching profession. It introduces concepts of education, its patterns, characteristics, and functions, and reviews educational ideas proposed by scholars throughout history. The course highlights the role of Islamic education and its educational philosophy through models of prominent Islamic thinkers, examines educational philosophies and their impact on educational systems, and identifies cultural and social foundations and their influence on societies. It also addresses selected educational issues and their applications.

This course studies the Prophetic biography and its role in shaping individual culture, Islamic civilization and its impact on the world, the meaning of knowledge and science, customs and behavior, the concept of ethics and profession, and the concept of the Muslim family, its characteristics, status, and role in building society.

This course aims to highlight the beauty of the Arabic language and reveal its elements of authenticity and strength to increase students’ appreciation and interest. Students apply grammatical rules, especially writing principles, including word meaning, word categories, signs of nouns, verbs, and particles, types of nouns and verbs, tied and open “taa”, and distinctions between similar letters. The course also covers initial hamza (hamzat al-qat‘ and hamzat al-wasl) in terms of definition, writing, pronunciation, position, originality, addition, and rules for differentiation. General applications are provided through texts from the Holy Qur’an, the Prophetic Sunnah, and selected Arabic poetry and prose.

This course aims to enhance students’ ability to deal with concepts used in the English language and raise their level of English proficiency in real-life contexts. It helps students acquire language skills in reading and writing and improve the four language skills (listening, speaking, reading, and writing) through exercises, conversations, examples, and effective activities. It also provides basic grammar such as verbs and tenses (present simple and present continuous) and commonly used vocabulary and expressions.

This course contributes to strengthening Libyan identity and shaping students’ national cultural awareness. It explains Libya’s status, geographical location, historical and modern role, natural and geographical characteristics, population throughout different eras, social system, and economic resources. The course also examines the cultural and civilizational heritage and its role in modernizing society, highlighting Libya’s image, the development of the Libyan home, and systems of governance in Libya. It instills national spirit and pride in belonging to the homeland.

This course aims to enhance students’ ability to deal with concepts used in the English language and raise their level of English knowledge in real-life contexts. It also helps students acquire language skills in reading and writing, enabling correct language use. The course further aims to improve students’ English language skills (listening, speaking, reading, and writing) through exercises, conversations, examples, and effective activities. It provides basic and simple English grammar such as verbs and tenses (present simple and present continuous), as well as commonly used vocabulary and expressions.

In this course, students apply grammatical rules, particularly the principles of writing, during lectures. Topics include nominal and verbal sentences, rules of numbers, deletion and addition of letters, applications on hamza rules, punctuation marks, dictionary usage, report writing, and writing formal requests, with special application on proper job application writing. General applications are provided through texts from the Holy Qur’an, the Prophetic Sunnah, poetry, and prose.

In this course, students apply grammatical rules, especially the principles of correct writing, during lectures. The course includes applications on numerical rules, interrogative style, sentence connection and separation, and general letter writing. It also covers applications of previously studied spelling rules, punctuation marks, and comprehensive knowledge of spelling and linguistic rules. Students are trained on preparing well-structured exam questions linguistically and using appropriate punctuation, writing numbers in words, and general applications through texts from the Holy Qur’an, the Prophetic Sunnah, and selected Arabic poetry and prose.

This course aims to provide students with knowledge, skills, values, and positive attitudes required for the teaching profession. It helps them understand the nature of the teaching–learning process and the relationships among different teaching situations, and introduces the most important modern teaching strategies that make the learner the center of the educational process.

This course provides student teachers with knowledge, skills, and attitudes related to curriculum in terms of its origin, development, meaning, and conceptual definitions. It includes comparison between major trends and theories of curriculum, its historical stages, and factors influencing its development and improvement. The course also enables students to understand the integration of curriculum construction processes, acquire skills in curriculum analysis, compare curriculum organization models, and recognize their responsibility as future teachers in curriculum implementation.

This course covers the concept of general psychology, its definition, objectives, importance, and related sciences, as well as branches of psychology. It addresses key psychological concepts and principles, research methods in psychology, general psychological laws of human behavior, schools of psychology, the nervous system and behavior, higher mental processes, learning, stimulus–response theory, intelligence, perception, sensation, memory, forgetting, thinking, and motivation, including biological and physiological motives. The course emphasizes employing psychological and educational knowledge in serving the educational process.

This course provides student teachers with knowledge, skills, values, and attitudes by introducing the nature of knowledge and its types and objectives, distinguishing between scientific research and scientific activity, and explaining research fundamentals. It also addresses the procedural steps of scientific research, starting from identifying the research problem, through design, methodology, tools, and measurement, to writing and presenting research according to scientific standards.

This course focuses on employing modern technologies in the educational process and developing skills in using digital media and educational technologies in teaching and learning.

This course provides students with essential knowledge, skills, values, and attitudes in the field of modern school administration, its technical and human requirements, and its responsibilities toward staff members. It examines school and classroom administration, major administrative patterns and skills, administrative processes, and their role in achieving a safe and attractive learning environment. The course also introduces the concept of educational supervision, its role in the educational process, and its main methods.

This course provides students with the most important knowledge, skills, values, and attitudes related to the concept of mental health and psychological adjustment from the perspectives of different psychological schools. It examines normal and abnormal behavior, characteristics of healthy personality, and the factors affecting it. The course also clarifies the characteristics of individuals with good mental health and the roles of institutions providing psychological services. It addresses concepts of frustration, psychological conflict, psychological stress, and their role in mental health disorders, and presents examples of psychological problems and disorders.

This course provides student teachers with knowledge, skills, and attitudes related to the curriculum in terms of its origin, development, meaning, and conceptual definitions. It includes comparison between major trends and theories of the school curriculum, its historical stages, and the factors contributing to its development and improvement. The course also helps students understand the integration and interrelation of curriculum development processes and recognize the foundations of curriculum construction. In addition, the course equips students with the knowledge and skills necessary to analyze school curricula, compare different curriculum organization models, and realize the major responsibility placed on them as future teachers in curriculum implementation.

The aim of this course is to prepare students practically for the teaching practicum by providing opportunities to practice teaching in various forms within the college. This enables students to acquire teaching skills necessary for practicum preparation and future teaching. Through this course, students practice modern teaching methods covered in general and specialized teaching methods courses, including lesson delivery, lesson planning, dealing with students, assessment and evaluation, classroom management, use of technology in teaching, and all other skills and tasks performed by teachers from psychological, behavioral, and academic aspects.

The student registers for the Teaching Practicum course in the final semester after fulfilling all academic requirements. The student is required to adhere to the following: Educational institutions for the practicum are determined by the specialized supervisor. Educational institutions are officially contacted according to the administrative procedures approved by the college. Practicum students are distributed among the designated educational institutions. The teaching practicum program is implemented over a full academic semester and is taken into consideration in the student’s timetable. Teaching periods are distributed according to the available classes in the educational institution throughout the week, with a minimum of one lesson per week. During the last two weeks of the semester, the student is assigned a full teacher’s schedule. Practicum students are evaluated according to the specified evaluation forms, with grade distribution as follows: Educational Supervisor: 40% Subject Specialist: 40% School Principal: 10% Cooperating Teacher: 10% Total: 100% The specialized educational supervisor is required to attend the student’s teaching sessions according to the assigned timetable, record observations, and discuss them with the student. The number of supervision hours for the practicum program is counted as the teaching load of faculty members supervising the program.

This course provides a general study of sets, intervals, and inequalities, leading to functions and trigonometric functions and their inverses.

This course covers the following topics: training students on some software used in mathematics and its teaching, such as MATLAB, Geometer’s Sketchpad, GeoGebra, and others. It also includes training on Word, Excel, and PowerPoint.

is a branch of mathematics that studies the general properties of geometric shapes that remain unchanged under continuous deformation such as stretching and bending without cutting or gluing. It focuses on fundamental concepts such as topological spaces, open and closed sets, continuity in its general sense, connectedness, compactness, and separation properties. Topology does not deal with lengths or angles, but rather with the relationships between points. Therefore, it is considered one of the important foundations of mathematical analysis and modern mathematics, with wide applications in physics, engineering, and computer science. It is usually taught to mathematics students to help them understand the general structure of mathematical spaces.