This course is a university requirement and provides students with various topics related to Islamic culture, which contribute to reinforcing the principles of Islam, fostering belief in its values, and understanding its systems. It also enables students to contribute to scientific and technological advancement. Through this course, students learn the correct and balanced approach for a Muslim's interaction with the contemporary world, including its developments and challenges. Additionally, it strengthens the connection to the past and other cultures and examines how Islam has addressed different aspects related to the individual and society

This course covers the essential skills and key concepts related to information and communication technology, computers, hardware, and software. It serves as an introduction to the fundamental concepts and skills related to using devices, creating and managing files, networks, and data security.

This course is a university requirement that provides students with various topics related to Islamic culture, which contribute to reinforcing the principles of Islam, fostering belief in its values, and understanding its systems. It also helps students participate in scientific and technological advancements. Through this course, students gain insight into the correct and balanced approach for a Muslim to engage with contemporary developments and challenges. Additionally, it strengthens the connection to the past and to other cultures, while also exploring how Islam has addressed various aspects related to the individual or society in areas of belief, worship, transactions, and personal status.

The course introduces students to reading and expression skills, the art of dialogue and summarization, and text analysis. It also helps them master writing skills, recognize common spelling errors, and properly use punctuation marks, understanding their impact on meaning. Additionally, students learn to apply rhetorical techniques according to basic grammar principles.

The course introduces the nature of Arabic writing, covering topics such as the concept of Arabic script, the recognition of Arabic letters, the distinction between hamzat al-wasl and hamzat al-qat', as well as other aspects related to Arabic writing. Additionally, students are introduced to various forms of functional writing, the art of essay writing, and its benefits.

This course covers the essential skills and key concepts related to using spreadsheets, including the application of standard formulas and mathematical functions. It also introduces the fundamental concepts and skills necessary for working with presentation software to create and use presentations.

This course covers the basic grammar rules of the English language and their usage, including essential tenses, the formation of interrogative and negative sentences, and affirmative statements. It also introduces the use of language in everyday conversations and teaches students how to write grammatically and orthographically correct sentences in English.

Developing the student's ability to communicate effectively in written English, while equipping them with language skills (reading and writing) that enable them to use the language correctly.

The course contributes to strengthening Libyan identity and shaping students' national cultural awareness by highlighting Libya's significance, location, and its role both historically and in modern times. It also aims to instill a sense of patriotism and pride in belonging to the nation.

This course studies the concept of Arabic writing, focusing on the recognition of Arabic letters, hamzat al-wasl, hamzat al-qat', the letter alif, and other aspects related to Arabic script. It also introduces students to various forms of functional writing, the art of essay writing, and its benefits.

This course studies the concept of Arabic writing, focusing on the recognition of Arabic letters, hamzat al-wasl, hamzat al-qat', the letter alif, and other aspects related to Arabic script. It also introduces students to various forms of functional writing, the art of essay writing, and its benefits.

This course aims to equip student teachers with knowledge, skills, values, and attitudes by introducing the principles of general psychology, the concept of psychology, its historical development, importance, and objectives. It covers the main theoretical and applied branches of psychology, its basic methods, and both traditional and contemporary schools. The course also addresses the key determinants of human behavior, the various classifications of motives, and the relationship between motivation and individual achievement. Furthermore, it explores the essential cognitive variables that shape human behavior, such as sensation, attention, perception, memory, learning, and intelligence.

This course provides student teachers with knowledge, skills, and instills values and attitudes that contribute to their preparation and qualification for the teaching profession. It explores the concepts of education, its types, characteristics, and functions, while reviewing the educational ideas and theories proposed by scholars throughout history. The course highlights the role of Islamic education and its educational philosophy by presenting examples from prominent Islamic thinkers. It also examines educational philosophies and their impact on the educational system, defines the cultural and social foundations of education, their elements, and their influence on societies. Finally, it addresses various issues related to education and its practical applications.

"Equipping the student teacher with the knowledge, skills, values, and positive attitudes required for the teaching profession, helping them understand the nature of the educational process and the relationship between different teaching situations, and providing them with essential modern teaching strategies that make the learner the center of the educational process."

Equipping the student teacher with knowledge, skills, and attitudes regarding the curriculum in terms of its origins, development, significance, and meaning (conceptual definitions), the components of the educational curriculum, the foundations of its construction, the characteristics of the modern curriculum, its organizations and models, leading to curriculum development.

This course covers the study of educational psychology and its importance in the educational process, with a focus on educational objectives, their levels, and their formulation. It also addresses the definition of psychological development and its role in the educational process, as well as cognitive development according to Piaget and emotional and social development according to Erikson.

Equipping the student teacher with knowledge, skills, values, and attitudes through understanding the nature of knowledge, its types, and objectives, distinguishing between scientific research and scientific activity, and its fundamentals, as well as how to approach the steps of scientific research procedurally, starting from defining the problem, through design, methodology, tools, and measurement, up to writing and presenting it according to scientific standards.

Measurement and evaluation are fundamental skills that a teacher must master and incorporate into their professional behaviors. Therefore, they are essential requirements in teacher preparation programs, aiming to clarify and distinguish between basic concepts such as assessment and evaluation. It is important to explain to students that evaluation is a tool, not an end in itself, and is used for learning. This highlights the difference between summative evaluation and continuous evaluation. This course also addresses the importance of evaluating all aspects of a student's personality, including cognitive, emotional, and skill-related domains, identifying strengths and weaknesses using various achievement tests, and addressing them. Evaluation should not be limited to the teacher alone; other methods of evaluation, such as self-assessment, peer assessment, and portfolio assessment, should also be considered.

The content of this course is divided into five main areas: communication skills, instructional materials, educational technologies, systems approach, and e-learning. These are fundamental and essential skills for any teacher in the 21st century.

Providing the student teacher with essential knowledge, skills, values, and attitudes in the field of modern school management, including its technical and human requirements and responsibilities towards its staff, as well as the means to carry out its tasks. This is achieved through studying school and classroom management, reviewing key management styles, understanding the administrative and technical tasks and skills of the school principal, and the processes involved in school and classroom management. The goal is to create a safe and engaging learning environment. Additionally, students will be provided with the concept of technical supervision, its role in the educational process, and its key methods.

Equipping the student teacher with knowledge, skills, values, and attitudes through understanding the concept of mental health and its manifestations, and psychological adjustment from the perspective of different psychological schools. The course also examines normal and abnormal behavior, the characteristics of a healthy personality, the influencing factors, and the effectiveness of those enjoying good mental health compared to others. It reviews the relationship between social institutions such as the family and civil associations and the achievement of mental health, including the role each plays and the types of services provided by each institution. Additionally, it addresses concepts such as frustration, psychological conflict, and stress, and presents models of psychological problems and disorders.

The aim of the course is to equip the student teacher with the essential skills needed for the teaching process, which can be implemented and practiced within the classroom. These skills include (planning, formulating behavioral objectives, execution, evaluation, educational technology, etc.), leading to the application of teaching models through cooperative, individual, and interactive groups that contribute to achieving the desired goals

Practical education is a training program where students apply their theoretical knowledge directly in educational institutions to acquire the competencies needed to qualify them for the teaching profession. It is a fundamental requirement for preparing teachers for various educational levels (preschool, elementary, and secondary)

This course covers: a general study of sets, intervals, and inequalities; relations and functions; types of real algebraic functions; even and odd functions; domain and range; graphing functions; inverse functions; non-algebraic functions; trigonometric and inverse trigonometric functions; logarithmic functions; exponential functions; hyperbolic and inverse hyperbolic functions.

Exponents and roots: exponents, roots, standard exponents, equations involving roots. Polynomials and partial fractions: polynomials, the fundamental division theorem, synthetic division, the fundamental theorem of algebra, real zeros, standard zeros, partial fractions. Permutations, combinations, mathematical induction, and the binomial theorem.

Vectors: addition, subtraction, scalar multiplication, dot product, and cross product. Coordinates in the plane: Cartesian and polar coordinates, distance between two points, coordinate transformation through translation and rotation. Curves and parametric representation of curves. Lines in the plane: slope of a line, various forms of the line equation, line plotting. Applications and exercises.

Some general statistical concepts, tabular and graphical presentation of statistical data, measures of central tendency, measures of dispersion, correlation and regression, time series, index numbers, population and vital statistics.

This course covers limits, continuity, some theorems of continuity, differentiation, applications (increasing and decreasing functions, Rolle's theorem, the mean value theorem, maximum and minimum values, concavity and convexity, inflection points, curve sketching).

Circle: Definition and derivation of the equation, translating the axes, its parametric equation, and plotting. Ellipse: Derivation of its standard equation, ellipse with foci on the vertical axis and once on the horizontal axis. Parabola: Derivation of the equation and plotting. Conic Sections: Polar equation of conic sections. Applications and Exercises

this course covers matrices (their concepts, types, and the operations defined on them), row operations, the reduced matrix, finding the inverse of a matrix, determinants (definitions and concepts, properties, finding the inverse of a matrix using determinants), systems of linear equations, and methods for solving them using matrices and determinants.

A critical analytical study of the topics covered in the prescribed mathematics textbooks for grades 7 to 9, along with solutions to the exercises in the curriculum books.

Probabilities, random variables and their probability distributions, binomial distribution, Poisson distribution, normal distribution, standard normal distribution, approximation of the binomial distribution by the normal distribution, chi-square distribution, t-distribution, f-distribution.

This course covers: definite integrals, indefinite integrals, methods of integration, L'Hopital's rule in limits, and applications of integration.

The coordinate system in three dimensions: Cartesian, cylindrical, and spherical; equations of surfaces and curves in space; the plane equation and conditions for parallelism and perpendicularity of two planes; various forms of the plane equation; the line in space and its different equation forms; the sphere and its equation; intersection and tangency of a plane with a sphere; the cylinder and its equation; the cone and solid shapes; applications and exercises.

"Directional spaces (definitions and basic concepts), linear transformations, inner product space (definitions, examples, and basic properties), eigenvalues and eigenvectors of a matrix."

A critical analytical study of the topics covered in the prescribed mathematics textbooks for grades 10 to 12, along with solutions to the exercises in the curriculum books.

"Logical issues and logical connective tools, truth tables and logical equivalence, propositional algebra, logical arguments and rules of inference, predicate logic, methods of proof, sets, relations, functions, countable sets, and ordered sets."

Functions of several variables Domain and range Neighborhood Continuity and limits Partial derivatives (definition, properties, how to find them) First-order and higher-order partial derivatives Implicit differentiation Applications of partial differentiation Geometric meaning of partial derivatives Gradient Directional derivative Tangent plane and normal line equations Maximum and minimum values Saddle points Lagrange multipliers

:This course covers first-order differential equations Linear and nonlinear Formation of differential equations Methods for solving first-order differential equations (separation of variables, exact and inexact equations, integrating factors) Bernoulli equation Second-order linear differential equations With constant coefficients, homogeneous and non-homogeneous Methods of solving (method of undetermined coefficients, variation of parameters, complementary function) Higher-order linear differential equations Laplace transforms

"This course serves as a foundation for the Teaching Applications and Practical Education course. It covers the concept of the mathematics curriculum, including the study of curriculum elements: objectives, mathematical content, some strategies for teaching mathematics, assessment and measurement, some educational theories in teaching mathematics, and difficulties in teaching and learning mathematics."

"Numbers throughout history, from ancient Egyptians to Arabs and Muslims, the history of the development of the components of mathematics, and famous mathematicians."

"Partitioning, moments, moment-generating function, important discrete and continuous probability distributions, probability distribution function for a discrete and continuous random variable, marginal probability distribution function, joint cumulative probability distribution function, conditional probability distribution function, independent random variables, mathematical expectation, covariance, correlation, probability distribution functions of multivariate random variables (discrete and continuous) and their properties."

This course covers: Double Integrals: Definition, geometric meaning, properties, methods of evaluation. Double Integrals in Polar Coordinates: Applications of double integrals. Triple Integrals: Definition, properties, methods of evaluation. Line Integrals: Surface integrals. Series and Sequences

This course covers: Systems of Linear Ordinary Differential Equations: Existence and uniqueness of solutions, fundamental matrix of solutions. Solving Systems of Linear Differential Equations with Constant Coefficients: Homogeneous and non-homogeneous cases (method of elimination, eigenvalue and eigenvector method, finding particular solutions using the method of undetermined coefficients and the method of variation of parameters). Solving Second-Order Linear Equations in Power Series Form: (Solution around an ordinary point and solution around a regular singular point)."

This course covers: The Real Number Line: Mathematical induction, sequences of real numbers—definition and convergence, bounded sequences, Cauchy sequences, least upper bound and greatest lower bound, Archimedean property. Euclidean Space: Organization and properties of R𝑛 , topology on space, open and closed sets, interior and boundary points, set relations, and accumulation points. Finite, Countable, and Uncountable Sets: Compact sets and connected sets. Sequences and Series in : Limits and continuity—bounded functions, limits of functions, uniform continuity.

Binary Operations and Their Properties: Groups and their fundamental properties, associated groups, Lagrange's theorem and its applications, normal subgroups and their basic properties, simple groups, quotient groups, isomorphisms in groups (examples and fundamental properties), and abelian groups and their basic properties.

Sampling Distributions: Distribution of the sample mean, distribution of the difference between means of two samples, distribution of the sample proportion, distribution of the difference between proportions of two samples. Statistical Estimation: Estimation methods. Hypothesis Testing: Hypothesis tests."

Gradient Operator (or the gradient): The divergence operator (or divergence), the curl operator (or curl). Applications through Potential Theorems: Exercises.

Complex Numbers: The triangle inequality and its generalization to 𝑛 numbers and equality conditions Topology of the Complex Plane: Functions of a complex variable, elementary functions, and transformations.

: This course covers Taylor Series: Maclaurin series, convergence properties. Linear Interpolation: Numerical solution of single equations, numerical solution of systems of linear equations. Differentiation: Forward differences, central differences. Integration: Trapezoidal rule, composite trapezoidal rule, Simpson's rule, composite Simpson's rule. Error Analysis.

Rings (Definitions, basic concepts, and fundamental properties), subrings and their properties, fields (basic definitions and concepts), the relationship between integral domains and fields, the characteristic of a ring and a field, ideals and their properties, principal ideals, the division ring and its properties, ring homomorphisms and their properties, studying the effect of homomorphisms on subrings and ideals, the kernel of a homomorphism and its properties, the first isomorphism theorem for rings and its applications, constructing a field from an integral domain, primary ideals and their properties in commutative rings, maximal ideals and their properties in commutative rings, the study of some important rings.

The benefits of the sampling method and some basic concepts, simple random sampling, stratified random sampling, systematic random sampling, cluster random sampling, selecting a probability sample proportional to size, some specific estimators, estimating sample size with predetermined accuracy, double sampling.

This course covers: Partial Differential Equations: definition, order, linear and nonlinear types, formulation of partial differential equations—first-order partial differential equations (solving some simple equations through direct integration)—solutions using Lagrange's method, nonlinear partial differential equations (solution methods, general method Lagrange, Charpit)—Paff differential equations in three variables (solvability and solution methods), second-order linear partial differential equations with constant coefficients (solutions to homogeneous and nonhomogeneous equations)—separation of variables method for solving second-order partial differential equations: initial and boundary value problems.

The objective of the Teaching Applications course is to practically prepare students for the student teaching phase by providing opportunities to practice teaching in various methods (teaching methods) within the college. This is aimed at acquiring the necessary teaching skills to prepare for both student teaching and regular teaching. The course includes general and specific teaching methods, including training on delivering lessons, lesson planning, interacting with students, evaluation and assessment, classroom management, using technology in teaching, and all other skills and tasks performed by teachers from psychological, behavioral, and scientific perspectives.

The course covers the following topics: training students on certain software used in the field of mathematics and its teaching, such as MATLAB, Geometer's Sketchpad, GeoGebra, etc. Additionally, it includes training students on (Word, Excel, PowerPoint).

Laplace Transform and Its Applications, Fourier Transform and Its Applications, Introduction to Integral Equations, Types of Integral Equations, Volterra Equation, Eigenvalue Problems, Convolution Integral Equations, Louisville and Neumann Series, Iterative Solution Method, Numerical Solutions and Fredholm Formulas, Applications and Exercises.

This course covers: Function Derivatives: Directional derivatives of functions, partial derivatives, differentiability, gradient of a function, matrix representation of the derivative. Integration: Riemann integration and its properties, integrability of Riemann integrals, improper integrals and their properties and convergence tests. Sequences and Series of Functions: Function sequences, uniform convergence of function sequences, uniform convergence and integration, uniform convergence and differentiation. Series of functions: uniform convergence of series, uniform convergence and differentiation, uniform convergence and integration.

Complex Integration: Cauchy's Theorem and Cauchy’s Integral Formula. Sequences and Series of Complex Numbers: Sequences and series of complex numbers. Sequences and Series of Complex Functions: Uniform convergence of sequences and series of complex functions. Power Series: Taylor and Laurent Series. Residue Calculus: Residue Theorem and integration calculations using residues.

Hölder and Minkowski Inequalities Various Metric Spaces Normed Spaces Different Banach Spaces Riesz's Theorem Fischer’s Theorem Hanna’s Theorem Banach and Completion Theorem Hilbert Spaces and Orthogonal Systems Introduction to Linear and Bounded Operators on Various Spaces Applications

the following topics: Tabular and graphical presentation of data Measures of central tendency Dispersion, skewness, and kurtosis Correlation and regression Index numbers Time series Population statistics Probability Some special distributions Statistical estimation Hypothesis testing

Introduction to the concept of Operations Research and its main methods Linear Programming and its Problems Simplex Method Decomposition Problem Duality in Linear Programming and its Properties Transportation Problem Simulation Game Theory

Introduction to Demography: General Population Census Vital Statistics Population Distribution by Gender and Age Groups Graphical Representation of Population Data Study of Birth, Death, Fertility, and Migration Rates (both internal and external) Study of Life Tables: Components and Methods of Construction Study of Population Growth and Methods of Calculation Study of Mathematical Models Related to Population

General Mathematics I aims to introduce students to: Sets and intervals Distance formula Absolute values and relations Graphing linear equations with two variables