This course covers fundamental and advanced topics in discrete mathematics, including Cartesian products, relations and functions, the pigeonhole principle, integer partitions, and exponential generating functions. Emphasis is also placed on solving first- and second-order linear recurrence relations, as well as analyzing nonhomogeneous and nonlinear recurrence relations.

This course covers the theory and applications of numerical analysis methods and focuses on the computer-based solution of mathematical problems. The course includes numerical computation, modeling, and programming, as well as the use of artificial intelligence tools in solving numerical problems.

This course introduces the fundamental concepts of error, stability, and convergence in ordinary differential equations (ODEs). Students will learn to implement and analyze numerical methods for both initial and boundary value problems, gaining hands-on experience with computational tools through programming-based assignments, projects, and in-class demonstrations. The course teaches how good programming practices affect the speed and accuracy of numerical solvers.

This course covers key topics in scientific computing with integrated AI support. It includes matrix norms and stability, direct and iterative methods for linear systems, numerical differentiation and integration, and fundamental eigenvalue algorithms. The course emphasizes computational efficiency, error analysis, and convergence, supported by AI-based coding and verification tools.

This course focuses on the theory and applications of orthogonal polynomials and wavelet-based numerical methods for solving ordinary differential equations. The course covers the use of orthogonal polynomials and wavelet-based approximation techniques in solving ordinary differential equations and error and convergence analysis.

This course focuses on the fundamentals of modern and classical numerical techniques for linear and nonlinear partial differential equations, with application to a wide variety of problems in science, engineering and other fields. The course covers the basic theory of scheme consistency, convergence and stability and various numerical methods.

This course provides a detailed and applied introduction to the mathematical foundations of artificial intelligence. Students learn the mathematical structure of linear algebra, probability and statistics, optimization, machine learning, and basic deep learning, and they implement these concepts using Python.

This course provides a comprehensive introduction to constructing, analyzing, and interpreting mathematical and statistical models for real-world phenomena. Students learn to formulate deterministic and stochastic models using differential equations, optimization structures, probability, and statistical tools. Emphasis is placed on selecting appropriate modeling frameworks and translating theoretical structures into computational implementations. The course integrates hands-on practice with proposed software packages to produce and evaluate model-based solutions. By the end of the course, students will be able to design and communicate robust models through scientific reports and presentations.

Linear Programming: Modeling, Solution Methods, Duality in linear programming; Nonlinear programming: First and second order optimality conditions for unconstrained problems, Lagrange multipliers, convexity in mathematical programming, The KuhnTucker theorem; Discrete optimization.

This course contains the results of linear equations and systems, perturbations of linear systems, the existence and uniqueness of nonlinear initial value problems and the stability theory of linear and nonlinear equations. It also includes the boundary value problems.

This course provides essential materials for analyzing advanced mathematical optimization problem forms, models, and applications by introducing the relevant linear algebra concepts.

In this course, machine learning concepts, supervised learning, classification methods, regression methods, unsupervised learning, clustering methods, and survival analysis topics will be examined.

The topics covered in this course include basic notations and definitions of statistics, data reduction, point estimation, methods of evaluating estimators, and hypothesis testing.

The topics covered in this course include the definitions and the classifications of stochastic processes, Poisson process, renewal theory, Markov chains and processes, Martingales and Brownian motion process.

Most of the nonparametric techniques are based on order statistics, runs, and ranks. Therefore the theory of order statistics, runs, and rank statistics is extensively studied.

System reliability models and their properties are the focus of this course.

The axioms of probability theory and historical probability backgrood are discussed. Random events, random variables as well as their basic characteristics are studied. Limit theorems for sums of independent random variables are also considered. Dependent random variables are studied. Bivariate random variables are discussed.