This course explores the mathematical foundations and practical applications of optimization in data science and artificial intelligence. Students will learn how to formulate and solve optimization problems, including unconstrained, constrained, convex, and multi-objective cases. The course covers gradient-based optimization methods and metaheuristic algorithms, with applications in machine learning such as hyperparameter tuning, neural network training, and feature selection. Through hands-on laboratories and real-world case studies, students will implement and evaluate optimization algorithms?including gradient descent, genetic algorithms (GA), particle swarm optimization (PSO), and simulated annealing (SA)?and assess their effectiveness in practical problems such as building machine learning models, feature selection, and loss-function tuning.