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This introductory course on generative artificial intelligence (AI) offers a comprehensive overview of the foundational principles and techniques that enable machines to generate complex outputs, such as text, images, and music. Students will explore the history and evolution of generative AI, including landmark models and milestones that have shaped the field. The course will first review classical approaches such as expert systems, genetic algorithms, Markov models, and constraint satisfaction problems. This will be followed by key algorithms and models in generative AI, including but not limited to neural networks, Autoencoders, generative adversarial networks (GANs), and transformers. Ethical considerations and societal impacts of generative AI will be a critical component of the curriculum, encouraging students to think critically about issues such as bias, fairness, and privacy. Assessment will include project work, where students will demonstrate their ability to develop a generative AI application from concept to implementation. By the end of the course, students will have a solid understanding of generative AI, equipped with the skills to innovate and apply these technologies in diverse and ethically responsible ways.